An investigation into quasi-free scattering of light neutron-rich nuclei around N=14

Universidade de Santiago de Compostela FACULTAD DE F´ ISICA Departamento de F´ısica de Part´ıculas An investigation into quasi-free scattering of light neutron-rich nuclei around N=14 Memoria presentada por: Paloma D´ıaz Fern´andez como disertaci´on para optar al Grado de Doctora en Ciencias F´ısicas Septiembre de 2013 UNIVERSIDADE DE SANTIAGO DE COMPOSTELA H´ector ´ Alvarez Pol, Profesor Titular del Departamento de F´ısica de Part´ıculas de la Universidad de Santiago de Compostela, CERTIFICA: que la memoria titulada An investigation into quasi-free scattering of light neutron-rich nuclei around N=14 ha sido realizada bajo su direcci´on por Paloma D´ıaz Fern´andez en el Departamento de F´ısica de Part´ıculas de esta Universidad, y constituye el Trabajo de Tesis que presenta para optar al Grado de Doctora en Ciencias F´ısicas. Santiago de Compostela, a 26 de Septiembre de 2013. Fdo. H´ector ´ Alvarez Pol Fdo. Paloma D´ıaz Fern´andez Contents 1 Introduction 1 1.1 Nuclearstructure......................... 1 1.2 Direct reactions for nuclear spectroscopy . . . . . . . . . . . . 5 1.3 Quasi-free scattering . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Thiswork ............................. 9 2 Experimental Setup 11 2.1 GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH . . . 11 2.2 ALADIN-LAND setup . . . . . . . . . . . . . . . . . . . . . . 13 2.2.1 Incoming beam detectors . . . . . . . . . . . . . . . . . 14 2.3 Detectors surrounding the target . . . . . . . . . . . . . . . . 17 2.3.1 Silicon Strip Detectors . . . . . . . . . . . . . . . . . . 18 2.3.2 Crystal Ball (XB) . . . . . . . . . . . . . . . . . . . . . 19 2.4 ALADIN.............................. 20 2.5 Heavy ion branch detectors . . . . . . . . . . . . . . . . . . . 20 2.5.1 GFIs ........................... 21 2.5.2 TFW (Time of Flight Wall) . . . . . . . . . . . . . . . 22 2.6 Proton branch detectors . . . . . . . . . . . . . . . . . . . . . 23 2.6.1 PDCs (Proton Drift chambers) . . . . . . . . . . . . . 23 2.6.2 DTF (Dicke ToFwand) . . . . . . . . . . . . . . . . . . 25 2.7 Neutron branch detector (LAND) . . . . . . . . . . . . . . . . 25 3 Detector calibrations 29 3.1 Calibration levels . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2 Triggers .............................. 30 3.3 Pedestal subtraction . . . . . . . . . . . . . . . . . . . . . . . 32 3.4 Timecalibration ......................... 32 3.5 Incoming charge calibration . . . . . . . . . . . . . . . . . . . 32 3.6 Incoming velocity calibration . . . . . . . . . . . . . . . . . . . 34 3.7 Silicon Strip Detectors, SSDs . . . . . . . . . . . . . . . . . . 35 3.8 Crystal Ball: gamma and proton readout . . . . . . . . . . . . 37 3.8.1 Gamma energy calibration . . . . . . . . . . . . . . . . 37 3.9 GFIs................................ 42 3.10 Time of Flight Wall (TFW) . . . . . . . . . . . . . . . . . . . 46 4 Analysis procedures 51 4.1 Identification of the outgoing fragments . . . . . . . . . . . . . 51 4.2 Identifying the quasi-free scattering channels . . . . . . . . . . 57 4.3 Cross section calculation and background subtraction . . . . . 58 4.4 Angular correlations . . . . . . . . . . . . . . . . . . . . . . . 59 4.5 Transverse and longitudinal momentum distributions . . . . . 60 4.5.1 Angular straggling . . . . . . . . . . . . . . . . . . . . 63 4.6 The addback algorithms for gammas . . . . . . . . . . . . . . 65 4.7 The invariant mass . . . . . . . . . . . . . . . . . . . . . . . . 69 5 Crystal Ball simulations 73 5.1 R3BRoot ............................. 73 5.2 Crystal Ball γresponse...................... 74 5.2.1 Description of the simulation . . . . . . . . . . . . . . 74 5.2.2 Photopeak efficiency for the individual crystals . . . . . 76 5.2.3 Photopeak efficiency for the addback routine . . . . . . 78 5.2.4 Intrinsic efficiency using the “Coincidence method” . . 80 5.3 Pure kinematical simulations for protons . . . . . . . . . . . . 85 5.3.1 Description of the code . . . . . . . . . . . . . . . . . . 86 5.4 Crystal Ball proton and neutron response . . . . . . . . . . . . 87 5.4.1 Geometrical acceptance of the detector . . . . . . . . . 88 5.4.2 Efficiency calculations . . . . . . . . . . . . . . . . . . 88 6 Results 91 6.1 The reaction channel 21N(p,pn)20N ............... 91 6.1.1 Inclusive cross section . . . . . . . . . . . . . . . . . . 92 6.1.2 Angular correlations . . . . . . . . . . . . . . . . . . . 96 6.1.3 Momentum distributions . . . . . . . . . . . . . . . . . 98 6.2 The reaction channel 21N(p,2p)20C ...............102 6.2.1 Inclusive cross sections . . . . . . . . . . . . . . . . . . 104 6.2.2 Angular correlations . . . . . . . . . . . . . . . . . . . 104 6.2.3 Momentum distributions . . . . . . . . . . . . . . . . . 104 6.3 The breakup channel 21N(p,pn)20N∗→19N+n .........105 7 Discussion of the results 113 7.1 Inclusive cross sections . . . . . . . . . . . . . . . . . . . . . . 113 7.2 Momentum distributions . . . . . . . . . . . . . . . . . . . . . 115 7.3 Gammarays............................118 7.4 The breakup channels . . . . . . . . . . . . . . . . . . . . . . 124 8 Conclusions 127 9 Resumen 131 9.1 Conclusiones............................135 A SSDs alignment 141 B Cross sections 145 C Inclusive momentum distributions 147 Chapter 1 Introduction Nuclear physics investigations began in 1911 when Rutherford discovered that each atom contains a positively charged nucleus [1]. Each nucleus is characterized by its number of protons (Z) and its number of neutrons (N). An element can have more than one isotope (same Z but different N). Since the initial discovery of the nucleus, more than 2800 isotopes have been identified and it is predicted that more than 7000 live long enough to be observed [2]. Figure 1.1 shows the experimentally known nuclei representing the number of protons vs. the number of neutrons. In this image the stable isotopes are shown as black cells, while the other square cells represent the radioactive isotopes, the color relating to their half-lives. The first section of this chapter is a brief overview about the models which have tried to describe the nucleus throughout history, predominantly: the “liquid-drop model” and the “shell model”. The first tries to explain the macroscopic properties of the nuclei, while the second focuses on the microscopic ones. Technological advances since the 80’s have allowed the exploration of the nuclei far from β-stability where new phenomena appear and modifications of these models are needed to explain these new observations. Later, some aspects concerning how the structure of the nuclei are studied through nuclear reactions will be outlined, to focus in the next section on the reaction mechanism used in this work; namely quasi-free scattering. The last section of this chapter is dedicated to explain the aim of this work and to summarize the structure of the dissertation. 1.1 Nuclear structure The first model trying to describe the nucleus general properties (binding energies, sizes, shapes, etc.) used the similarity of the nucleus with a drop 8 Introduction Eexc being the excitation energy of the residual nucleus. The recoil momentum of the MA−1fragment is the same as the momentum of the knockedout nucleon (~ k3) when it was bound in the nucleus before the collision. ~ kA−1=~ k0−~ k1−~ k2=−~ k3(1.7) Using quasi-free scattering reactions it is possible to study not only the surface of the nucleus like in knockout reactions but also the inner regions of the nucleus. In recent experiments performed at GSI Helmholtzzentrum f¨ur Schwerionenforschung, in Darmstadt, Germany [11] within the R3B collaboration [33] inclusive and exclusive measurements of (p,2p) using inverse kinematics using the LAND-R3B setup have been carried out. In these experiments with rare beams, the nucleus of interest is the projectile due to the difficulty to have stationary targets made of unstable isotopes. Reactions such 12C(p,2p)11B [29, 30] and 17Ne(p,2p)16F→15O+2p [31] have already been studied. In the first example, a 12C beam at 400 AMeV was guided to the experimental area. The setup used was very similar to the one used in the experiment analyzed in this work, so it will only be outlined. The beam impinges upon a CH2target, which was surrounded by silicon detectors allowing for identification of the two protons from the reaction and the measurement of their angular distributions and energies. The target and the silicon detectors were inside a vacuum chamber surrounded by a 4πcalorimeter which allows the determination of exclusive results by measuring the γrays. The outgoing fragments were deflected by a large acceptance magnet and identified in the three branches located behind it, one for neutrons, one for heavy fragments and one for protons. The energy differential cross section obtained for 11B is shown in figure 1.4. In this plot the different breakup channels studied are included together with the γrays. The results are found to be in very good agreement with previous experiments studying the same reaction in direct kinematics (see references [29, 30] for more information). For the second example, a 17Ne beam at 500 AMeV has been used to study this borromean nucleus. Borromean nuclei are formed by three parts and if one of them is separated from the others, the other two become unbound (15O+p+p). When a proton is removed from the 17Ne, the 16F decays into 15O+p. This nucleus was investigated in inverse kinematics via electromagnetic dissociation, one-proton removal and quasi-free scattering. The information obtained was: excitation energy spectrum for the 16F (15O+p), inclusive two-proton removal cross sections for 17Ne→15O+X and transverse momentum distributions of 16F. From the comparison of the momentum distributions with theoretical calculations the spectroscopic factors were also 1.4 This work 9 Figure 1.4: Excitation energy spectrum for the 11B. The different decay channels are shown in different colors. Figure taken from [29]. obtained, finding good agreement with previous experiments (see [31] for more details). These two experiments have demonstrated that this reaction type is a very good tool to study the nuclear structure of exotic nuclei. The future FAIR facility will open new investigations with exotic beams, where the R3B setup will be located. This also includes important improvements with respect to the actual LAND-R3B setup [35]. 1.4 This work Quasi-free scattering reactions have been used in this work to study the nuclear structure of light neutron-rich nuclei around N = 14 for charges 6, 7 and 8. The same projectiles, which are 23O, 22O and 21N have been investigated through (p,pn) and (p,2p) reactions in complete and inverse kinematics, allowing the investigation at the same time of both valence nucleons and also 10 Introduction deep-hole states. Thus, a complete study of the whole wave function would be in principle possible. The experiment [36] was performed in the LAND/R3B reaction setup in August-September, 2010, at GSI Helmholtzzentrum f¨ur Schwerionenforschung, in Darmstadt, Germany [11]. The physics topics studied are very diverse including the measurement of astrophysical reaction rates relevant for rprocess nucleosynthesis using heavy-ion induced electromagnetic excitation and quasi-free knockout reactions to study the evolution of shell and cluster structures close to and beyond the dripline. Unbound (ground and excited) states could be populated and identified in (p,2p) reactions. The quenching of single-particle strength in neutron-proton asymmetric nuclei will be addressed by knocking out deeply bound protons and neutrons in (p,2p) and (p,pn) reactions for nuclei with varying neutron-proton asymmetry. The analysis of the complete set of data is still in progress, but the first results have already been presented in dissertations [37] and conferences, like for example [38, 39, 40, 41]. The details about the experimental setup will be given in Chapter 2. The following chapter will explain calibration procedures for the different detectors. The fourth chapter will be dedicated to explain and show the results obtained in simulation. Chapter 5 will be devoted to the procedures used to identify and study the different reaction channels. The sixth chapter will show and discuss the results obtained for the studied reactions which are mainly: inclusive momentum distributions of the (p,pn) and (p,2p) channels, inclusive cross sections of the (p,pn) and (p,2p) channels, exclusive cross sections and branching ratios to the different fragment states and excitation energy distributions for the one neutron breakup channel. Chapter 2 Experimental Setup In August 2010, the S393 [36] experiment was performed at the laboratory GSI Helmholtzzentrum f¨ur Schwerionenforschung, in Darmstadt, Germany. The main goal of this experiment is to study light neutron-rich nuclei using inverse and complete kinematic measurements via quasi-free scattering reactions at relativistic energies. In about twenty days, data for six different settings centred at different A/Q ratios, were collected in the LAND-R3B experimental area at Cave C. Within this chapter the main features of the beam production and the experimental setup will be described in detail. 2.1 GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH GSI1is a laboratory located near Darmstadt, in Germany. A schematic view of the facility at 2010, when the experiment was performed, is shown in Fig. 2.1. A primary beam is produced in an ion source and injected in the linear accelerator UNILAC (UNIversal Linear ACcelerator). In our case the primary beam was 40Ar. This 40Ar+11 beam is then inserted in the SchwerIonenSynchrotron (SIS-18) where it is accelerated to the desired energy. In our case the primary beam leaves the SIS with an energy of about 490 AMeV and goes to the FRagment Separator area (FRS), a high resolution forward spectrometer [42]. At its entrance there is a production target of Be, 4.011 g/cm2. When the primary beam impinges upon this target, a range of ions are produced by nuclear fragmentation. The FRS separates the species of interest depending on their mass-charge (A/Q) ratio: when a particle with 1http://gsi.de/portrait/index.html 12 Experimental Setup Figure 2.1: Schematic view of the GSI facility in 2010. The LAND-R3B experimental area is located in the Experimental Hall II. charge Q and mass A travels through a magnetic field of strength B it experiences the Lorentz force. Also, if the initial particle velocity βis perpendicular to the uniform magnetic field into which it is moving, the magnetic force will have the characteristics of a centripetal force, and the particle will move in a circle of radius of ρ, with Bρ =p Q∝A Z·βγ (2.1) where pis the momentum of the particle, Qwas replaced by Zdue to the non existence of charge states and γis the Lorentz factor. The formula shows that only ions with a given A/Z ratio will follow the trajectory determined by the beam line. The selection of the ions of interest is made in two stages. In the first one, where two dipoles and a plastic scintillator (S2) are involved, the magnetic rigidity of the fragments produced in the target is determined. Only fragments with an appropriate combination of mass, charge and velocity are transmitted. At the intermediate focal place a degrader is placed to slow down the beam in order to enable finer selection. In the second stage, formed 2.2 ALADIN-LAND setup 13 Figure 2.2: Schematic drawing of the FRS. The beam coming from the SIS arrives to the target area (TA). The fragment selection is performed in two stages. Every stage contains two dipoles (indicated in green). The last detector of the FRS is the scintillator paddle S8. by other two dipoles and an additional plastic scintillator (S8), the fragments are selected according to their A/Z ratio by their velocities (determined from time-of-flight) and their magnetic rigidities. After the last scintillator (S8) the secondary beam (also called “cocktail beam” because of the presence of different species) is identified in mass, atomic number and velocity. 2.2 ALADIN-LAND setup After the last scintillator of the FRS area, the beam travels ∼55m to Cave C where the LAND - R3B setup is placed. In figure 2.3 a schematic layout of the setup is shown. The velocity of the beam is measured by using the last scintillator of FRS and the first detector of Cave C, which is another scintillator read-out by two photomultipliers. A collimator called ROLU is used to center the beam. After ROLU, for tracking and energy loss measurements, a position sensitive silicon detector, PSP, is placed. The beam then enters a vacuum chamber where the target surrounded by eight silicon detectors is located. The chamber is embeded in the Crystal Ball, a 4πcalorimeter. After the reaction, the products travelling in forward directions are deflected by the ALADIN magnet and, according to their mass and charge, are going to one of three branches: neutrons are not deflected and are detected by LAND; heavy fragments are tracked via two scintillating fibre detectors GFIs, and a time-of-flight wall TFW; protons are bent further and detected via two proton drift chambers PDCs and a time-of-flight wall DTF. 14 Experimental Setup Figure 2.3: Schematic draft of the experimental setup for the S393 experiment in Cave C (not to scale). The beam comes from the left and finds the following detectors: POS: together with a plastic scintillator detector from the FRS measure time-of-flight which allows to determine the velocity of the fragments, it can also be used to determine the position of the particles; ROLU: 4 movable plastic scintillators, define the accepted beam spot size; PSP: provides energy loss information of the incoming beam from which the charge is obtained; SSDs: used to track and identify the fragments and the quasi-free scattering nucleons; Crystal Ball: array of NaI detectors, γ-rays and quasi-free scattering nucleons detection in ∼4π; ALADIN: large acceptance dipole magnet to bend the particles depending on their A/Q; LAND: tracking and determination of the momentum of the neutrons; GFI’s: used to track the heavy fragments; TFW : tracking, energy loss and time-of-flight measurements of the heavy fragments; DCHs: used for the tracking of the protons; DTF: tracking, energy loss and time-of-flight measurements of the protons. 2.2.1 Incoming beam detectors The secondary beam needs to be identified in charge and mass. In order to do that, four incoming detectors were used. The names of these detectors 2.2 ALADIN-LAND setup 15 are S8, POS, ROLU and PSP. •S8 is a scintillator formed by one paddle and used for the time-of-flight (ToF) measurements. The time signals are provided by two photomultipliers located at both ends of the paddle. •POS (see Fig. 2.4) is a scintillator with square shape, 5.5x5.5 cm2, used as start for the time-of-flight measurements. The scintillation light produced in the detector is read-out by four photomultipliers, which deliver time and amplitude signals. Figure 2.4: Squematic view of POS detector with the direction of the beam indicated. The four photomultiplier outputs provide time and amplitude information, used to calculate time-of-flight, position and energy loss. •ROLU (“Rechts”, “Oben”, “Links”, and “Unten”) (see Fig. 2.5) is a detector comprising of four movable plastic scintillators used to define the beam spot size. Each scintillator is read-out by a photomultiplier and can be moved in order to define the size and position of the beam, acting as a veto for all the particles hitting the scintillators. 16 Experimental Setup Figure 2.5: Schematic layout of ROLU, with the beam direction indicated, which is formed by four movable plastic scintillators which define the beam size on the target. •PSP (the figure 2.6) is a Position Sensitive silicon Pin diode with square shape and an active area of 4.5x4.5 cm2. The detector has four anodes that provide position information (x,y) and one cathode providing the energy loss of the ion which is related to its charge zvia the BetheBloch formula −dE dx =4πz2 mec2β2 NaZρ Mue2 4π02ln2mev2 I−ln 1−v2 c2−v2 c2 (2.2) where Eis the energy of the particle, xthe distance travelled by the particle, methe electron rest mass, cthe speed of light, vthe velocity of the particle, Nathe Avogadro’s number, ethe electron charge, 0 the vacuum permitivity, β=v cand I,Z,A,Muand ρare the mean excitation potential, the atomic number, the mass number, the molar mass and the density of the target respectively. The energy resolution of the PSP is around 1%. The position is calibrated using a mask 2.3 Detectors surrounding the target 17 Figure 2.6: Schematic view of PSP detector. The detector has four anodes to reconstruct the position of the ions (Q1, Q2, Q3and Q4), and one cathode (Q) which is used to identify the ions in charge. attached to the detector with 21x21 square pixels made of scintillator material that can be moved by remote control. For this experiment the pixel mask did not work, so the position information could not be used. The flight time of the particle is measured between S8 and POS and this information is used together with the energy loss in the PSP detector for particle identification. 2.3 Detectors surrounding the target Surrounding the target there was a ∼4πspherical calorimerer made of 159 NaI (Tl) crystals (∼20 cm long) used for detection of gamma rays, protons and neutrons (energies, angular distributions and multiplicities) and inside a vacuum reaction chamber eight Silicon Strip Detectors, four of them setting 24 Experimental Setup Figure 2.13: Layout of the two PDC detectors. produces ionization. The resulting electrons induce a current in the sense wire, causing a localized cascade of ionization which is collected on the wire and results in an electric current proportional to the energy of the detected particle. This allows the determination of the proton trajectory. Field wires Sense wires 16 mm Figure 2.14: Detail of the hexagonal drift cells. The black circles represent the sense wires and the red ones the field wires. 2.7 Neutron branch detector (LAND) 25 2.6.2 DTF (Dicke ToFwand) Figure 2.15: DTF detector front view. The DTF is a Time of Flight Wall formed by scintillator paddles used to measure the time-of-flight and the energy of the protons (see Fig. 2.15). It has 6 vertical paddles of 20 cm width, 120 cm length and 1.5 cm thickness and 3 horizontal paddles of 10.4 cm width, 140 cm length and 0.5 cm thickness, which are separated around 44 cm. All the paddles are read-out by two photomultipliers, one at each end. The detection principles are the same as for the other detectors based on scintillator paddles. 2.7 Neutron branch detector (LAND) The Large Area Neutron Detector (LAND) is used for the detection of neutrons produced in reactions at the target. It was designed to measure neutrons with energies from 100-1000 MeV [47]. The detector measures the ToF, the position and the energy loss of the neutrons, allowing the determination of the velocity and the position (in X,Y,Z) of the neutrons. The detector is placed at 0oand approximately 13 m behind the target. It consists of 10 planes, with 20 scintillator paddles each. In total it has 200 paddles (see Fig. 2.16). Each paddle covers an area of 200 x 10 cm and 10 cm depth 26 Experimental Setup Figure 2.16: LAND detector front view. and is formed by 11 iron sheets and 10 scintillator sheets. Two of the iron sheets are covering the outer parts of the detector and have a thickness of 2.5 mm, the inner ones are 5 mm thick. The 10 scintillator sheets are 5 mm thick. The paddles of each layer and the next are perpendicular to each other in order to measure the horizontal and vertical positions of the hits (see Fig. 2.17). When a neutron impinges in LAND interacts with the iron producing charged particles (protons) which induce light in the plastic scintillators. Each LAND paddle is read-out by two photomultipliers, one at each end. Using some specific algorithms it is possible to reconstruct the hits in the paddles, and from them to obtain the time, energy and position. 2.7 Neutron branch detector (LAND) 27 Figure 2.17: Top: Schematic view of the layer structure of a LAND paddle. Bottom: Picture of a LAND real paddle. 28 Experimental Setup Chapter 3 Detector calibrations This chapter describes the procedures followed to calibrate the detectors used in the experiment, as well as some details needed for the study of specific reaction channels. The text will focus on the detector calibrations where the author of this thesis was more involved. The first parts are focused on the incoming beam detectors which provide a good identification in mass-over-charge (A/Z) of the incident cocktail beam. Later on, we examine the detectors in the heavy fragment branch (GFIs, TFW) and finally the gamma energy branch of the Crystal Ball detector and the SSD calibration. The text will also describe very briefly some calibrations performed by other collaborators, e.g. the calibration of the high energy branch and time of the Crystal Ball detector. 3.1 Calibration levels The data of all the detector channels used in the experiment are collected in events and written into LMD-format files (List Mode Files). The information contained in the lmd files is extracted using the software package land02, originally written by H. Johansson [51]. This program converts the lmd files into rootfiles (via a process called unpacking) and also contains some calibration routines. The calibration procedure is performed in different steps unpacking the data into the following levels [51, 52]: •RAW: conversion from the binary format to an analysis friendly format. The information is ordered by detector, module and channel. The values of the different signals coming from the detectors are given in TDC, QDC or ADC channels. 30 Detector calibrations •TCAL: TDC channels are converted to time units and the QDC pedestal is subtracted. The parameters applied to the RAW level data are calculated by routines included in land02, tcal and clock. •SYNC: the detectors are not usually composed by one piece. In the case of the time-of-flight walls (LAND, TFW), these are formed by several paddles. In the previous levels, each paddle was treated individually. To combine the information from all the paddles and treat the detectors as a unit, the channels are synchronized with respect to each other. The calibration routine for this step is detector dependant. A routine called phase1 calculates the parameters for the synchronization. •DHIT: contains energy loss, position and time values in detector specific coordinates describing the interaction of the particle in the material (hit). •HIT: contains data in laboratory coordinates describing hits. The positions are given in cm, the times are given in ns and the energy in MeV. •TRACK: the mass and the atomic number together with the velocity of the ions is calculated. Sometimes the detector information suffers variations along the time. There is a very useful function LT RANGE, which allows to specify different calibration parameters for different ranges of the data set. 3.2 Triggers A trigger is a system that uses simple criteria to allocate the signals from the detectors, when it is only possible to store a maximum set of events. In order to identify the reaction channels of interest, the signals from different detectors are combined to create triggers. In Table. 3.1 the triggers for the S393 experiment are listed. In the first column the trigger bit running from 1 to 16 is listed. Triggers 1 - 8 are the on-spill triggers, used for the analysis of the reaction channels and 9 - 15 the off-spill triggers used for calibration purposes. The second column indicates the trigger pattern (Tpat) which tells us which bits are set to 1. In the third column there is a short description about the physical meaning of each trigger. The final columns, with ones or blanks, indicate the active inputs. The first row per trigger bit represents an anticoincidence and the second one a coincidence. For example requesting the “Minimum bias” trigger, has nothing in the first row (no anticoincidence is 3.2 Triggers 31 Trigger bit n Tpat (2n−1) Description used by trloctrl tracer Late trigger-kill Early pile-up Spill on CB L+R NTF1 pix S81 CB sum delayed CB sum CB OR delayed1 CB OR1 proton wall delayed1 proton wall fragment wall delayed fragment wall land cosm land multt POS1 POS.!ROLU 1 1 Minimum bias (Good beam (GB)) 1 1 2 2 Fragment 1 (GB + fragment at TFW) 1 1 1 3 4 FRS S8 (plastic scintillator hit) 1 1 4 8 CB SUM 1 1 (Crystal Ball energy threshold) 1 1 1 1 5 16 Proton 1 (hit in the DTF) 1 1 1 1 6 32 GB-pileup 1 (identification of pile-up) 1 1 7 64 Pix (hit in the pixel detector) 1 1 1 8 128 Neutron 1 (hit in LAND) 1 1 1 1 9 256 CB muon 1 1 (offspill trigger) 1 10 512 Land Cosm 1 1 (offspill trigger) 1 11 1024 TFW Cosm 1 1 (offspill trigger) 1 12 2048 CB gamma 1 1 (offspill trigger) 1 13 4096 DTF Cosm 1 1 (offspill trigger) 1 14 8192 NTF Cosm 1 1 (offspill trigger) 1 15 16384 CB L+R-muon 1 1 (offspill trigger) 1 Table 3.1: Trigger matrix used in the experiment. The first column indicates the trigger bit for a certain trigger. The second indicates the trigger pattern (2n−1). The third column is a brief description of the trigger and the other columns are the coincidences or anticoincidences between certain detector signals. 32 Detector calibrations requested). While the other row means POS and not ROLU, a signal in POS is required and nothing in ROLU is also required, i.e. an anticoincidence. There are some triggers which fire very often during the experiment, only a fraction of the eventsassociated to them is then saved. The ratio between the real number of events triggered and the ones stored is called downscale factor. One of the frequent triggers for experimental running trigger is the 2, called “Fragment”, meaning that there is an event with “Minimum bias” that also hits the last detector in the heavy fragment branch, the TFW. Another very common trigger is the number 4 “CB SUM” which indicates deposited energy above a certain threshold in the Crystal Ball detector, indicating a high energy event. The last on-spill trigger used is the neutron detection trigger with number 8 and called “Neutron” that selects a possible neutron hit in the LAND detector. 3.3 Pedestal subtraction The QDC reads-out a small quantity of charge called pedestal, even when no input signal is present. Since the pedestal is always there, it has to be subtracted from the data in order to avoid the usage of signals compatible with noise. The pedestal calculation is done by the land02 routine clock and is subtracted on the TCAL calibration level. 3.4 Time calibration The TDC modules have a nominal gain value, which can fluctuate throughout the experiment (e.g. temperature). In order to correct this effect and to achieve a good time resolution, a time calibrator module was used during the whole experiment to monitor the TDC gain. This module generates two pulses with known delay. One is sent to all electronic channels and the other to the DAQ as a trigger allowing the monitoring of the TDC gain for the entire experiment (explanation about the working principles in Ref. [61]). After this step, the time is represented in ns, but the time difference between detectors is not representing the actual time of flight between them, a synchronization between them is needed. 3.5 Incoming charge calibration The charge identification of the ions is performed with the PSP detector. It is obtained directly from the energy loss measured by the cathode. 3.5 Incoming charge calibration 33 Using the Bethe-Bloch formula it is possible to relate the velocity of the ions to the charge (equation 2.2). To perform this calibration, a run with A/Z=2 was used. 8Be is very short-lived so it does not appear in the identification matrix, this helps with the identification of the other nuclei (see Fig. 3.1). Figure 3.1: Identification plot for a run with A/Z=2. The 8Be does not appear in the matrix allowing the identification of the other nuclei. The trigger two (minimum bias + fragment at TFW) was selected in this plot. PSP cathode signal (ch) 0 500 1000 1500 2000 2500 3000 3500 4000 Counts 2 10 3 10 4 10 Figure 3.2: PSP energy loss measured in the cathode which is related to the charge. The mean value of a Gaussian fit over the peaks relates the energy loss with a certain charge. For the selected nuclei, the signal in the cathode is shown in figure 3.2. The charge assigments are possible because of the missing 8Be. The peaks 40 Detector calibrations in more detail in the next chapters). To get an accurate cluster energy, it is very important that every crystal has a good energy calibration throughout the whole experiment, i.e. the crystals must be aligned in energy. In order to correct the drifts (variations of the peaks positions for the same crystal with the time) and to have a good energy alignment (variations in the peak positions for different crystals during the same run), the natural background (in combination with the available sources) has been used to monitor the energy peaks along the experiment. In figure 3.8 the background energy spectra for the crystals 1 and 9 is shown. The 40K peak at 1.46 MeV it is clearly observed, but it is shifted, showing the misalignment between the different crystals in the same run. Figure 3.8: Example of the observed shift in the crystals 1 and 9 for the background peak of the 40K. In Fig. 3.9 the improvement of the peak resolution is clearly visible comparing the same run before and after correcting the drifts gain of the crystals. High energy branch calibration The ideal way to calibrate the proton branch is with proton beams at different energies in the range where the quasi-free protons are expected (10 - 300 MeV) and also covering the expected angular range. Unfortunately for this experiment there were not available beams to calibrate the high energy 3.8 Crystal Ball: gamma and proton readout 41 Figure 3.9: Comparison between the energy deposited in all the crystals for the same run: before the crystals alignment (left) and after the crystal alignment (right). The 40K peak at 1460 keV is observed. branch. Instead, the proton branch was calibrated using cosmic muons. For that purpose the program gamma2, inside the land02 package, and a simulation (Geant3) were used. The procedure can be outlined in the following steps were followed: •the muon energy is plotted for both branches (high-energy branch vs. low-energy branch). The resultant curve can be fitted to a straight line obtaining an offset and slope. This slope multiplied by the gamma energy gain calculated in the previous section, corresponds to the proton gain. •to complete the calibration, only muons that traverse the XB centrally are used (two opposite crystals are hit). The energy loss of the muons is displayed versus the crystal number. The energy loss for each crystal has a Gaussian shape, the mean value corresponds to the energy loss of a muon traversing the crystal and can be calculated from a simulation. The previous gain is multiplied by this new factor. More detailed information can be found in previous works [31, 60]. Time calibration and synchronization The time signals from the Crystal Ball detector are used to clean-up the events from noise. The measured energies are requested to be inside a certain time window. The conversion from channels to time in ns is done in the same way as it was explained before for the POS detector, using the time calibrator. To synchronize the times the gamma2 program was used. The 42 Detector calibrations algorithm uses a run where a source emitts two gammas in coincidence, the two expected gammas deposit their full energies in two different crystals. If this condition is fullfilled, the time difference between those gammas is saved in a histogram. As the gammas are in coincidence, the peak mean value should be centered in zero. For each combination of two crystals it is possibe to define a histogram, which can be fitted to a Gaussian function. The final equation system can be solved to determine the time offsets. 3.9 GFIs The GFIs detectors provide horizontal position measurements of the heavy fragments after the dipole. When an ion hits the GFIs this produces light which is guided through the fibres creating a well-defined light spot on the photocathode of the PSPM. Depending on the position of the light spot in the photocathode, an electrical signal is generated in some anode wires. From the combination of these signals, the position of the light spot is reconstructed making possible the identification of the hit fibre. To extract the X position, the internal coordinates of the detector (u,v) need to be transformed. The first step of the GFIs calibration is the pedestal subtraction, that is performed as for other detectors using the clock routine. From RAW level data to TCAL data, the pedestals are subtracted. The amplitude of the signals is not the same for all the wires. It depends on its position on the photocathode and on its amplification. So, a proper gainmatch of all the anode wires on the photocathode is needed before reconstruct the hit position. It has been observed that the charge distribution of a hit produces energy in about seven neighbouring wires in each (u,v) direction, and their amplitudes are expected in a Gaussian distribution. This fact is used to perform the gain matching of the wires, taking all the signals from neighbouring wires (cluster) into the distribution. The calibration is done in a run called “sweep run” using the phase1 gfi routine. The calibration parameters are then applied in the DHIT level. In this run the whole detector is illuminated by varying the magnetic field of the dipole. In figure. 3.10 an example of the charge distribution before (top) and after the gain matching (bottom) is shown. After gain matching the clusters, their positions become more regular and well defined. The divided clusters also merge and the extension of the clusters is reduced. Also the distortion observed at the edges decreases. The dots in between the clusters are ions that hit in the non scintillating part of the fibre, depositing low energy. In order to finalize the calibration, the positions of the clusters must be determined. This is done by projecting all the hits onto a two dimensional 3.9 GFIs 43 histogram (u,v). For each cluster the mean positions (¯u,¯v) and the standard deviations (σu,σv) are obtained by fitting the clusters to Gaussians. The cluster neighbours are determined by using the lengths and angles of the vectors connecting them. In figure 3.11 positions of all the clusters and the vectors that connect neighbours for one of the fibres are shown. An index pair (k,l) can be assigned to each cluster, where k and l are the indices for the columns and rows of the matrix k xl. Every (k,l) has a corresponding internal mean position (¯u,¯v) on the PSPM, which is also associated to the horizontal position in the detector (x). To convert the internal coordinates (u,v) to the corresponding x positions a transformation has to be applied. If the position of a hit is inside a cluster (within its width), the fibre assignment is straightforward. Instead, if the hit is between two clusters, there is more than one candidate fibre to assign the hit. In this case, a weighted average of the candidate fibres is used [45]. The reconstructed position is given in cm in the HIT level. The horizontal position for two different fibre detectors, which are approximately 150 cm apart is shown in Fig. 3.11 for the “sweep run” used for the calibration. The good correlation shown between the position measured by the two detectors proves that the calibration is good. 44 Detector calibrations u (arb. units) -2 0 2 4 6 8 10 12 14 16 18 v (arb. units) -2 0 2 4 6 8 10 12 14 16 u (arb. units) -2 0 2 4 6 8 10 12 14 16 18 v (arb. units) -2 0 2 4 6 8 10 12 14 16 Figure 3.10: Reconstructed image of the fibre mask before (top) and after (bottom) gain matching. The clusters have a better-defined shape and the large distortion observed at the edges of the photocathode (upper plot) is improved after the gainmatching procedure (bottom plot). 3.9 GFIs 45 GFI 2 x (cm) -30 -20 -10 0 10 20 30 GFI 1 x (cm) -30 -20 -10 0 10 20 30 Figure 3.11: Top: Mean position of the clusters. Neighbours are indicated by arrows. Bottom: Correlation between the reconstructed position between two fibre detectors 150 cm apart. 46 Detector calibrations 3.10 Time of Flight Wall (TFW) L x t2,E2 t1,E1 t0,E0 -L/2 L/2 Figure 3.12: Position of a hit in a scintillator paddle (x). The time (t1,t2) and energy (E1,E2) signals measured by each PMT are used to calculate the postion of the hit (x), its energy (E0) and its time (t0). The TFW is a detector made by plastic scintillator paddles. Each paddle is read-out by two photomultipliers, one at each end, which provide time and energy signals (see Fig. 3.12). The position information [61] can be obtained by time differences or energy ratios between the measured times and energies, repectively. •Calculation of position and time of a hit using the time signals: The measured times are: t1=t0+x+L/2 vscint (3.7) t2=t0+L/2−x vscint (3.8) where t1and t2are the times measured by the two photomultipliers, t0 is the interaction time, vscint is the effective light velocity in the scintillator, Lis the paddle length and xis the position of the hit in the paddle. The position of a hit in a paddle is calculated as a time difference between the two photomultipliers times. t1−t2=t0+x+L/2 vscint −t0−L/2−x vscint (3.9) x=vscint (t1−t2) 2(3.10) The interaction time is calculated by adding up both photomultiplier times. 3.10 Time of Flight Wall (TFW) 47 t1+t2=t0+x+L/2 vscint +t0+L/2−x vscint (3.11) t0=t1+t2 2−L 2vscint (3.12) •Calculation of energy and position of a hit by using the energies provided vy the photomultipliers: The distance from the hit position to the photomultipliers is bigger than the other paddle dimensions. So, the measured energies can be approximated as it follows: E1=E0exp −(x+L/2) λ(3.13) E2=E0exp −(L/2−x) λ(3.14) (3.15) being λthe attenuation length in a paddle. The interaction energy is calculated by multiplying both photomultiplier energies, E1·E2=E2 0·exp −L λ(3.16) E0=pE1·E2exp L 2λ(3.17) The interaction position is the ratio between the photomultipliers energies, E1 E2 =exp −(x+L/2) λexp −(L/2−x) λ(3.18) x=−λ 2lnE1 E2 (3.19) In all these equations the cable lengths, signal losses and proccesing times were not taking into account, but they are included in the calibration procedure. In the first land02 level (RAW), an energy and a time for each paddle and for each PMT is available. In the TCAL level the same variables are 48 Detector calibrations present but the pedestal is subtracted and the time is converted in ns. The calibration parameters are calculated with the routines clock and tcal. In the SYNC level, the data structure is the same as in TCAL level (energy from paddles with two PMT tubes), but the four parameters calculated using phase1 are applied. The first one provides the gain needed to synchronize the paddles to each other, the second one performs gain-matching over the two energy signals, the third one is the relative offset in time between a pair of horizontal and vertical paddles which synchronizes the mean time calculated by the two paddles and the last one makes the differences between the times provided from Y paddles and X paddles to be zero. In the DHIT level the information about the photomultipliers is lost, the paddles and all the observables are described in the internal coordinates of the detector. The final level is the HIT, at this stage of the calibration the information about the whole detector is in cm and the energy in arbitrary units. The last step, is the detector synchronization between runs [62]. When a channel is studied, several runs are joined and a synchronization between their energies and times is needed. For this purpose the energy loss vs. event number will be studied by fitting to Gaussian distributions different groups of events. The ATIMA code [63] was used to calculate the energy loss in the TFW after the beam went through all the previous detectors, and also the time of flight between the target and the TFW. These values were used to match the mean value from the previous fits. In the top plot of figure 3.13 the energy loss vs. the event number is presented, showing that the energy is not well synchronized between event groups. In the bottom plot of the same figure the result after applying the corresponding corrections to synchronize the runs is shown. At the end of the calibration procedure, the energy is in MeV and the ToF in ns. 3.10 Time of Flight Wall (TFW) 49 Figure 3.13: Top: Energy loss in the TFW before synchronization. Bottom: Energy loss in the TFW after synchronization and energy calibration using ATIMA [63]. In both plots the “Fragment” trigger was selected. 56 Analysis procedures Mass (u.m.a) 14 15 16 17 18 19 20 21 22 23 Counts 0 100 200 300 400 500 600 700 800 900 2 CH C empty Mass (u.m.a) 14 15 16 17 18 19 20 21 22 23 Reaction probability 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 -3 10× 2 CH C empty Figure 4.5: Left: Mass spectrum of all the outgoing fragments measured in coincidence with the Crystal Ball trigger for the three different targets and for the charge 7. Same as before, normalized. performed to obtain the mass resolution are shown. In the left plot are shown the fits for the nitrogen isotopes. Their resolution varies between 3.27% and 2.59% for the highest and lowest masses respectively. In the right plot are shown the carbon isotopes; in this case the resolution varies between 3.33% and 2.57% for the highest and lowest masses respectively. Mass (u.m.a) 14 15 16 17 18 19 20 21 22 23 Counts 0 50 100 150 200 Z=7 N Mass (u.m.a) 12 14 16 18 20 Counts 0 50 100 150 200 Z=6 C Figure 4.6: Mass spectrum of the outgoing fragments with charges 7 (left plot) and 6 (right plot). The fit parameters are shown in table 4.1. The left and right neighbours of each peak produce a contribution in the central one. To evaluate the contamination, the number of events in the left and right gaussian neighbours that contribute to the central gaussian is calculated. The 21N produces a contamination in the 20N peak estimated to 4.2 Identifying the quasi-free scattering channels 57 Charge 7 Mean (u.m.a.) 20.98 19.98 18.97 18.00 17.01 16.03 15.06 Sigma (u.m.a.) 0.29 0.26 0.23 0.23 0.20 0.19 0.17 Charge 6 Mean (u.m.a.) 20.20 19.16 18.05 17.02 15.99 15.01 14.03 Sigma (u.m.a.) 0.29 0.29 0.24 0.24 0.19 0.18 0.17 Table 4.1: Mean and sigma values obtained from the combined gaussian fits in the mass spectra of figure 4.6 for charges 6 and 7. 2.74%. The contamination of the 19N over the 20N was also evaluated to be 1.07%. 4.2 Identifying the quasi-free scattering channels The quasi-free scattering channels are selected by measuring the energies and angular distributions of the two outgoing nucleons from the reaction in the Crystal Ball detector. To aid the identification an addback algorithm is used. The addback algorithm searches for the maximum energy deposition in a crystal per event. Following this, any energy above threshold in the nearest neighbours is added to the main crystal energy to form a cluster. The central angle of the crystal with highest energy is used to determine the angle of the nucleon emerging from the reaction. To reproduce a more realistic angular distribution, the angles of the central crystals are randomized within the solid angle of the crystal, taking into account the non-uniform crystal shape by the use of a randomization algorithm2. As commented previously, the SSDs which are surrounding the target did not work properly. Their sides were either half or completely broken; the angular resolution of the emitted nucleons was determined by the Crystal Ball angular resolution. Another consequence of the malfunctioning of the SSDs is the impossibility to distinguish between neutron and proton in the (p,pn) reactions. In the simulations chapter, it will be shown the angular signature of the quasi-free scattering: the opening angle of the two nucleons emerging from 2created by F. Wamers (more detailed information in the reference [31]) 58 Analysis procedures the collision it is expected at around ∼80o. They are travelling back to back in azimuthal angle, being the difference between their azimuthal angles ∼180o. In order to remove contributions due to non-physical signals, the energy deposited in a crystal has to be above a certain energy threshold. Studies for energy thresholds between 10 - 25 MeV were performed. For the lowest thresholds has been observed contributions at opening angles below 60o, which do not correspond with the quasi-free scattering angular signature. In order to have a cleaner data distribution and avoid contributions at lower opening angles, the threshold required within this work will be 20 MeV. To consider an event to arise from quasi-free scattering it is also required that the events have cluster multiplicity two (only two clusters per event). 4.3 Cross section calculation and background subtraction The cross section is a physical observable that reflects the probability that a nuclear reaction will occur. It is defined by the equation 4.2, σ=1 α·Preac (4.2) where αis a factor that depends on the target: α=ρm M(4.3) with ρmthe target’s mass thickness and M the molar mass. The features of the targets used in the experiment are shown in Table. 4.2. ρm(g/cm2) M (g/mol) α(1/barn) CH20.922 14.026 0.0397 C 0.935 12.011 0.0469 Table 4.2: Characteristics of the reaction targets used in the S393 experiment. Preac is the reaction probability defined as follows: Preac =Nr Na (4.4) 4.4 Angular correlations 59 where Nrstands for the number of reactions that happen for a certain target and Nastands for the number of attempts (incoming nuclei). The number of attempts will be approximated by the number of survivals after the reaction target and they will be counted at the end of the fragment arm in the TFW detector. This approximation is valid because the target is thin enough and the speed of the particles is very high, so the probability to react in the target is low (10−2-10−3). The number of reactions and the number of incoming will be counted at the last detector. In this way, the efficiencies of the different detectors, the acceptance and other effects are cancelled out because the same detectors and similar conditions are used to perform the counting. We are interested in the calculation of the cross section with a proton target. The polyethylene (CH2) is formed by carbon and hydrogen atoms. So, we must subtract the carbon contribution using runs with a carbon target. The contribution of other elements in the setup that could cause additional reactions are taken into account by using the so-called empty runs (without target), both of them properly normalized. The cross section with the hydrogen target is defined as follows: σH=1 2σH2(4.5) being σH2 σH2=1 αCH2·(PCH2−Pempty)−1 αC·(PC−Pempty) = =1 αCH2·PCH2−1 αC·PC+1 αC−1 αCH2·Pempty (4.6) where αCH2and αCare the target factors and PCH2,PCand Pempty the reaction probabilities for CH2, C and the empty targets, respectively. 4.4 Angular correlations The quasi-free scattering events have a very strong angular correlation as has also been shown in previous works [24]. The opening angle between the two outgoing nucleons is given by the dot product of the unit vectors which describe the particle direction, ~n1=~n1(θ1, φ1) and ~n2=~n2(θ2, φ1) (spherical coordinates). This unit vectors are expressed as follows: ~n1= (sinθ1cosφ1, sinθ1sinφ1, cosθ1) (4.7) 60 Analysis procedures Figure 4.7: Schematic view of a quasi-free event. The laboratory angles of the two outgoing nucleons emerging from a quasi-free reaction are shown in spherical coordinates. The beam comes from the left and impinges in the target. ~n2= (sinθ2cosφ2, sinθ2sinφ2, cosθ2) (4.8) The opening angle of the nucleons will be Θ = sinθ1sinθ2cos(φ2−φ1) + cosθ1cosθ2(4.9) The difference between the azimuthal angles of the two particles is given by ∆φ=φ2−φ1,φ2−φ1∈(0,180) ∆φ= 360 −(φ2−φ1) , φ2−φ1∈(180,360) (4.10) 4.5 Transverse and longitudinal momentum distributions One of the physical observables obtained in this experiment is the momentum distribution of the fragment produced in a quasi-free scattering reaction. The momentum distributions contain information about the orbital angular momentum of the removed nucleon in the reaction, i.e. its wavefunction. The total momentum distributions of the fragments are obtained from the tracking procedure and can be divided in two components: the longitudinal 4.5 Transverse and longitudinal momentum distributions 61 component, that goes in the same direction as the beam and the transversal component perpendicular to it. ~p =~pk+~p⊥(4.11) The tracker provides the momentum module (from the fragment mass and beta). To determine the momentum module, the tracker approximates the measured mass to an integer and then assign the corresponding nuclear mass. The longitudinal momentum (from now on will be called PZ) will be determined in the laboratory frame and in the rest frame of the projectile. In the rest frame of the projectile it is expressed as follows PZ=γin ·(Pout −βinEout) (4.12) where γin and βin are the Lorentz factor and the velocity for the incoming fragment, respectively. Pout and Eout are the longitudinal momentum in the laboratory frame and the total energy of the outgoing fragment, respectively. The transverse component can be as well calculated along the X and Y axes as follows: PX=P·sin(αX,out −αX,in) (4.13) PY=P·sin(αY,out −αY,in) (4.14) where Pis the momentum module, αX,out (αY,out) and αX,in (αY,in) are the angles relative to the Z axis in the XZ (YZ) plane for the outgoing and incoming fragments, respectively. The angular distributions of the fragments after the reactions are reconstructed from the positions obtained with the four in-beam Silicon Strip Detectors (SSDs). In addition to having a good calibration for these detectors, a fine relative alignment between them is needed. A way of testing if the alignment is good lies in calculating the difference between the outgoing and the incoming angle for an empty run. As there is no target, this difference should be around zero. Figure 4.8 shows the angles reconstructed with the different detectors for an empty run when the nominal positions of the detectors were used in the reconstruction. A clear misalignment is observed between the detectors. In order to obtain a reliable transversal momentum distributions a better relative alignment is required. To find the right positions of the detectors, a linear least squares fit has been performed. The linear least squares fitting technique provides a solution to the problem of finding the best straight line through a set of points. Assuming that the trajectories of our particles are straight lines, the method to find the best-fitting curve to a given set of points consists in minimizing the sum of the squares of the residuals in each detector, defining the residuals as the 62 Analysis procedures Angle X (rad) -0.06 -0.04 -0.02 0 0.02 0.04 0.06 Counts 0 100 200 300 400 500 600 700 800 Angle Y (rad) -0.06 -0.04 -0.02 0 0.02 0.04 0.06 Counts 0 50 100 150 200 250 300 350 Figure 4.8: Reconstructed angles for the measured hits in the SSDs detectors before and after the target for an empty target run, in the X direction (left) and Y direction (right) for the SSDs. The black dashed lines indicate the angles before the target reconstructed using the first and second SSDs, the solid black lines represent the angles after the target measured by the SSD 3 and 4. difference between the position of the hits in the detector and the position given by the straight line in the detector plane. The functional to minimize will be f=X i=x,y;j=1,2,3,4((pij+δij)−(mi×(pzj+δzj) + ni)2(4.15) where pij(i = x, y, z and j = 1, 2, 3, 4) stand for the positions of the particles in the detectors and δijare the offsets, which are varied until the minimization of the functional converges. miand ni, are the slope and the offset of the straight line. The minimization was performed fixing one of the detectors (the third SSD) and obtaining the relative alignment of the others for unreacted beam in a run without target. To perform a complete study of the convergence and correlations between the parameters, two and three dimensional plots for all the variations have been built. The plots for every combination of each two parameters are shown in the appendix A for the X and Y coordinates. The offsets needed in order to align the SSDs are shown in table 4.3. In the Z direction the corrections are negligible. Figure 4.9 shows the difference in angle in the X and Y components for the 21N after the relative alignment. The distributions are fitted to 4.5 Transverse and longitudinal momentum distributions 63 offset X (cm) offset Y (cm) SSD 1 0.0522 0.0018 SSD 2 -0.0357 0.0045 SSD 3 0.0 0.0 SSD 4 0.071 0.044 Table 4.3: Obtained offsets for the X and Y coordinates for the SDDs by the minimization. Gaussians and characterized by its σ,σX= (1.373 ±0.013)mrad and σY= (1.126 ±0.010)mrad. The resolution is slightly better in the Y direction. The obtained values are perfectly compatible with previous results using the same detectors [31]. Constant 5.5± 398.4 Mean 0.01355± -0.02446 Sigma 0.013± 1.373 Outgoing - Incoming angle X (mrad) -20 -10 0 10 20 Counts 0 50 100 150 200 250 300 350 400 450 Constant 5.5± 398.4 Mean 0.01355± -0.02446 Sigma 0.013± 1.373 Constant 6.4± 482.9 Mean 0.01121± -0.06834 Sigma 0.010± 1.126 Outgoing - Incoming angle Y (mrad) -20 -10 0 10 20 Counts 0 100 200 300 400 500 Constant 6.4± 482.9 Mean 0.01121± -0.06834 Sigma 0.010± 1.126 Figure 4.9: Left: distribution of the outgoing angle minus the incoming angle in the X direction. Right: outgoing angle minus incoming angle in the Y direction. The results of a Gaussian fit (thick line) are shown in the inset. 4.5.1 Angular straggling The charged particles do not follow exactly straight lines. When they traverse matter, they suffer small deviations in their trajectories known as angular straggling. The straggling caused in the different targets is calculated by subtracting quadratically the standard deviations from the Gaussian fits 64 Analysis procedures of the angular differences (outgoing angle minus incoming angle) with and without target. σ2 straggling =σ2 target −σ2 empty (4.16) The standard deviation for the unreacted beam in a run without target gives the intrinsic angular resolution of the setup for a given nucleus at a given energy. In figure 4.10 are shown the σstraggling for different targets and C 2 CH (mrad)σ 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2 X CH 2 Y CH 2 atima CH X C Y C atima C C 2 CH (mrad)σ 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2 X CH 2 Y CH 2 atima CH X C Y C atima C C 2 CH (mrad)σ 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2 X CH 2 Y CH 2 atima CH X C Y C atima C C 2 CH (mrad)σ 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2 X CH 2 Y CH 2 atima CH X C Y C atima C Figure 4.10: Top: results for the σfrom a Gaussian fit to the angular differences in X and Y direction and the ATIMA simulation, for the nucleus 21N and for two different kind of fitting. Left: the whole distribution is fitted to a gaussian; right: only the central part is fitted to a gaussian. Bottom: the same information but for the nucleus 18C. different nuclei. In the top plots the calculations for 21N are shown, on the right when the whole distribution is fitted to a gaussian and on the left when only the central part of the distribution is assumed to be be a Gaussian. These two fits are done because the distributions are not perfectly gaussian. Their tails modify the fit parameters. From these plots it is observed that 4.6 The addback algorithms for gammas 65 the σvalues are different in X and Y. If the Gaussian fit is made only the central part, they agree within the error bars and they are also consistent with the calculations performed using the ATIMA [63] code. Big deviations in the results are observed when the whole distribution is fitted to a Gaussian, because of the tails present in the distributions. The biggest deviation is in the sigma of the X component, which is ∼18% larger than the sigma for the Y component. In the bottom figure the same is shown for a different nucleus, in this case 18C, where the same behaviour is observed. 4.6 The addback algorithms for gammas The energy that a gamma deposits in the Crystal Ball detector might not be completely deposited in one crystal, as it was mentioned in chapter 5. To recover the total energy of the gamma emitted by the nucleus, an addback routine is used. In this section different algorithms used to study the gamma ray spectra will be explained and discussed. A difference between gammas emitted by calibration sources and those emitted by reacting nuclei is that, when a particle moves with relativistic energy and emits gammas, these suffer the Doppler effect. In order to calculate the energy of the gamma in the rest frame of the particle, the velocity of the excited fragment and the gamma emission angle must be known. The correction applied to the energy is shown in equation 4.17, where Edis the corrected energy, Elab is the energy of the gamma measured in the laboratory, γis the Lorentz constant, βis the velocity of the projectile and θis the emission angle of the gamma with respect to the outgoing fragment direction (which is going to be taken as the angle of the first interaction crystal). Ed=Elab ·γ·(1 −β·cosθ) (4.17) For all the algorithms used and in order to eliminate noise events, the energy deposited in any crystal has to be above an energy threshold, which has been tested in the range between 100 and 400 keV. Next, a description of the algorithms is presented: •Method 1 (spectroscopic): looks for the crystal with the maximum energy deposited and adds up the neighbour’s energies. This set of crystals is defined as a cluster. The cluster energy corresponds to the sum of the component crystal energies and the angle to the angle of the crystal with the maximum energy. Once a cluster is built, looks for the next maximum energy and adds up the energy of the neighbours 72 Analysis procedures Chapter 5 Crystal Ball simulations To obtain the physical quantities of interest at a final stage of the analysis, the response of the detectors to different particle interactions needs to be known. In this chapter the Crystal Ball detector simulation results obtained using R3BRoot1will be presented. In the first section, the main features of the simulation program will be outlined. The next ones will be dedicated to the Crystal Ball detector response to γ-rays. In these sections the number of particles registered by the detector with their full-energy deposited (photopeak efficiency) will be studied for the individual crystals and for the whole detector. Also the effect of perform an add back will be discussed in terms of total photopeak efficiency. The intrinsic efficiency, which relates the number of counts in a crystal to the number of particles that hit that crystal will also be study within these sections. The last sections will be devoted to the investigation of the detector response to protons and neutrons. 5.1 R3BRoot R3BRoot [73] is an analysis and simulation framework, specifically developed for the future R3B setup at FAIR [34] by H. Alvarez-Pol and D. Bertini (originally), based on a previous simulation code called R3BSim. The program receive most of its features from the FairRoot framework [74], which is based on ROOT [75]. The framework allows the users to implement their detectors or to modify the existent ones, in order to perform simulation and analysis tasks in a simple way. It also contains some general functionality like track visualization, event structure, etc. The analysis is performed in an event-by-event basis, that goes from the unpacking of the data and the 1http://fairroot.gsi.de/ 74 Crystal Ball simulations detector calibrations until the final stage of the analysis, where the different detectors signals are combined in order to obtain the physical quantities of interest. Geant3 and Geant4 transport engines are supported by R3BRoot [78]. The R3B/LAND setup detectors are included in R3BRoot. All the detectors contain a realistic response to particle interaction. Event generators to simulate quasi-free scattering reactions, γrays deexcitation, etc. have already been implemented. The program is being used in the design phase of FAIR to optimize the detectors, like for example CALIFA and NeuLAND detectors. 5.2 Crystal Ball γresponse One of the purposes of the Crystal Ball detector is to measure the energy deposited by the γ-rays detected in coincidence with the outgoing fragment. When the projectile impinges into the target, the outgoing fragments could be produced in an excited state depending on their excitation energy. Information about the structure of the projectile is obtained by studying the populated states. In this section the efficiency for the individual crystals and the whole detector will be calculated in simulation, and compared with experimental data from sources. 5.2.1 Description of the simulation The detector consists of 159 NaI crystals distributed in a 25 cm radius and 20 cm thickness sphere. There are four different types of crystals. Their shapes are regular pentagons (12 crystals) and three kinds of irregular hexagons (divided in 60 + 60 + 30) (see chapter 2). Each crystal is inside an aluminum shell of 600 µm, which was also included in the simulation [79]. The particles were generated according to realistic decay schemes implemented for the 22Na and 60Co sources. The simulated sources used, are considered as point sources because the real radiating substance is a little drop of about 0.5 mm in diameter, enclosed in a small rectangular plastic slab of about 2 x 1 x 0.1 cm. The sources were placed in the center of the detector, in the target position. The 22Na source decays via β+, in 90.326 % of cases emitting a positron. A gamma of 1275 keV is emitted because of the 22Ne de-excitation to the ground state. The positron annhilation with one electron of the media produces two gammas of 511 keV in opposite directions. In 9.615 % of the cases, an electron capture is produced and only a 1275 kev gamma is emitted. This source was implemented by emitting a gamma with 1275 keV and two gammas of 511 keV with opposite directions, 5.2 Crystal Ball γresponse 75 Source γenergies (keV) decay mechanism 22Na 511, 1275 β+(90.326%), EC (9.615%) 60Co 1173, 1332 β−(100%) Table 5.1: Calibration sources used in the S393 experiment. all isotropically emitted and with the corresponding probabilities. A 60Co source was simulated as well. The 60Co decays to the 60Ni via β−, this deexcites through the 1.332 MeV state. Since the lifetime of this state is very short, the gamma of 1.173 MeV is emitted in coincidence. In table 5.1 are summarized the sources used. The crystal resolution has been included assuming a square root dependence with the energy. For each crystal, the fit σ(E) = p1∗√E+p0was performed and the energy resolution was introduced in the simulation. The figure 5.1 represents the σfrom the Gaussian fits to the 22Na peaks vs. the crystal number. It is observed from this plot that the resolution depends on the crystal number and also is worse when the energy is increased. Crystal number 10 20 30 40 50 60 70 80 (MeV)σ 0.02 0.04 0.06 0.511 MeV 1.275 MeV Figure 5.1: Energy resolution from the Gaussian fits to the individual 22Na peaks vs. the crystal number. The figure indicates that the resolution is dependent both on the crystal and energy. 76 Crystal Ball simulations Figure 5.2 shows the energy of the primary γ’s from 22Na impinging upon the crystals (left), and their deposited energy in all the crystals (right). The total amount of primary simulated events was 1·106. Energy primary gammas (MeV) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Counts 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 6 10× Energy (MeV) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Counts 0 20 40 60 80 100 3 10× Figure 5.2: Left: energy of the primary gammas. Right: simulated energy deposition in all the crystals, taking into account the detector response. 5.2.2 Photopeak efficiency for the individual crystals When a gamma hits a scintillator crystal, the energy is deposited via three processes: photoelectric, Compton scattering and pair production. The occurrence of any of these processes depends on the energy of the incident gamma and on the atomic number of the crystal. In figure 5.3 is shown the total absorption coefficient for NaI, together with the contributions of the different processes, as a function of the gamma energy. The figure illustrates the importance of each process over a range of γray energy. The photoelectric process dominates in the region up to a few hundred keV. If the photoelectric effect occurs, practically all the photon energy is absorbed in one step. As the energy of the gammas increases so does the Compton effect probability and if the energy is well above 1.02 MeV pair production rises in significance. At higher γenergies multiple interactions will occur, rendering highly probable that the energy is not deposited only in a single crystal [64]. The photopeak efficiency of the individual crystals is defined as the number of particles can keep in registered by the detector with their full-energy deposited, divided by the number of particles emitted by the source. This observable is calculated by counting the number of events within two σof a 5.2 Crystal Ball γresponse 77 Figure 5.3: Total absorption coefficient of NaI and the contribution of the photoelectric, Compton and pair processes is shown as a function of the γ energy. The figure indicates the importance of each process dependent on the γenergy. gaussian fit around the centroid of the peak and dividing them by the total number of emitted γ’s. The photopeak efficiency depends on the detector geometry and on the probability of interaction of the particle in the detector. Figure 5.4 shows the photopeak efficiency fitting at two σfor the two γenergies of the 22Na respectively. For the 511 keV γ, the crystal photopeak efficiency mean value is and 0.474±0.097 % while for the 1275 keV γ is 0.297±0.005 % . As it is expected, the more energetic γ, the lower the efficiency. The 511 γdeposits its energy via the photoelectric effect. The Compton scattering probability increases for the most energetic γ, which means that more energy can escape from the crystal without being detected (see more details in [64]). The total photopeak efficiency, i.e., the photopeak efficiency of the whole detector, can be calculated as the sum of the efficiencies of the individual crystals. The obtained results are shown in table 5.2. 78 Crystal Ball simulations Figure 5.4: Left: photopeak efficiency for each crystal and for the photopeak of 511 keV, integrating the peak at 2 σ’s. Right: the same but for the 1275 keV peak. The red dashed lines are the mean values of the photopeak efficiency for each plot. Peak (keV) Effiency at 2 σ(%) 511 72.03 1275 45.17 Table 5.2: Total photopeak efficiency for the calorimeter at 2 σ’s for both energies of the γsource. 5.2.3 Photopeak efficiency for the addback routine The γrays will deposit their energy in one or more crystals depending on their initial energy and the interaction process occurred. In order to recover the energy deposited in other crystals in the vicinity of the crystal where the first interaction happened, a routine called addback is applied. The addback procedure is performed in the same way as for the experimental data: the algorithm searches for the crystal with the maximum energy deposition above an energy threshold and add up the energy of the next neighbors fired. The crystals used are marked as non usable for other clusters in the same event. This is done until all the energies above an energy threshold are employed. Figure 5.5 shows the fits performed in order to calculate the photopeak efficiency after the addback procedure. Each peak is fitted with a superposition of a gaussian function and a linear function representing the background. The resultant function is used to calculate the integral of the peaks, needed 5.2 Crystal Ball γresponse 79 Energy (MeV) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Counts 10 2 10 3 10 4 10 5 10 Figure 5.5: Fits performed over the energy deposited in the whole detector after running an addback routine for the total photopeak efficiency calculation. Peak (keV) Effiency at 2 σ(%) 511 73.23 1275 63.64 Table 5.3: Total photopeak efficiency for the addback calculated for 2 σ’s for both energies of the γsource. for the efficiency determination. Table 5.3 shows the efficiency calculated as the number of counts in the photopeak divided by the number of initial γ’s with that energy. The photopeak efficiency at 2σafter addback increases about a 1% for the lowest energetic peak. The increment is bigger for the highest energetic peak where the efficiency increases an 18%. As it was expected, for lower energies the dominant effect is the photoelectric, so the addback routine do not produce a huge improvement. The result of adding the neighbours energies is more notorious for the highest energy γbecause of the compton effect and the pair production. 80 Crystal Ball simulations 5.2.4 Intrinsic efficiency using the “Coincidence method” The intrinsic efficiency relates the number of counts in a crystal to the number of particles that hit that crystal. It is obtained by dividing the total efficiency (number of counts registered by a crystal divided by the number of particles emitted by the source) by its solid angle. In order to compare the results for simulated data with those for real data, the same method must be applied under the same conditions. With this purpose, data with radioactive sources was simulated and taken with the Crystal Ball detector. In this experiment, all the available runs with radioactive sources where measured with the detector separated in two hemispheres. Sources were located at the center of each Crystal Ball hemisphere. The method presented for calculating the intrinsic efficiency is the “coincidence method”, which requires a γsource emitting two γ’s in cascade and consists in [31, 60]: •For each event, search for a γwith full-energy deposited E1(E2) in any crystal. The total number of events with one γ(E1, E2) is counted. If more than one E1or E2are found in the same event, this is discarded in order to avoid random coincidences •If a γE1(or E2) with the full-energy deposited was found in the previous step, the coincident γE2(or E1) of the cascade is searched for. The number of γ’s which deposited their full energy found in coincidence is counted •The number of γ’s found in coincidence is divided by the total initial γ1 (or 2) and is corrected by the geometrical efficiency g=4π/162 4π •In real data, a time condition for the coincidences was also required, the detection time difference between the γ’s being less than 15 ns to be considered a real coincidence It is considered that a γdeposits its full-energy if it is inside the energy window defined by mean ±2σ, with σbeing the width of the peak for the crystal. In the simulations performed the first source tested was the 60Co which has two γ’s in coincidence with energies of 1.173 and 1.333 MeV. The results for the intrinsic efficiency of each crystal are shown in figure 5.6. The two γ’s have a similar efficiency because their energies are very close. The mean value for the efficiency of the 1.173 MeV peak is 52.24 % with a standard deviation of 8.01% and the one for the 1.333 MeV is 44.17% with a standard deviation of 6.25%. 5.2 Crystal Ball γresponse 81 Crystal number 0 20 40 60 80 100 120 140 160 Intrinsic efficiency 1.333 MeV (%) 10 20 30 40 50 60 70 80 90 100 Crystal number 0 20 40 60 80 100 120 140 160 Intrinsic efficiency 1.173 MeV (%) 10 20 30 40 50 60 70 80 90 100 Figure 5.6: Intrinsic efficiency calculation for the γenergies of the 60Co in simulation using the coincidence method. The red dashed lines are the mean values for each plot. Figure 5.7 shows the efficiency for a 60Co source placed in the left hemisphere of the Crystal Ball detector. The mean value of the efficiency for the 1.173 MeV photon the mean value obtained is 39.31 % with a standard deviation of 8.61 %, while for the 1.333 MeV γis 26.86 % with a standard deviation of 6.10 %. The photo peak efficiencies for the two peaks can be compared. In both cases the simulation overestimates the experimental result. As in the S393 experiment all radioactive sources data were taken with the Crystal Ball opened and the source placed in the middle of one of the hemispheres, it would be interesting to have a measurement with the detector closed, together with all the materials inside that are supposed to be there when an experiment is running. After the S393 experiment, and with the 88 Crystal Ball simulations 5.4.1 Geometrical acceptance of the detector An investigation about the angular coverage of our detector due to acceptance and losses due to the matter between the target and the detectors, as well the crystals wrappings has been undertaken. For this purpose, the polar angle distribution of the protons emitted by a source measured in Crystal Ball after a randomization3is studied. In order to obtain a more realistic angular distribution, a randomized angle within the solid angle of the crystal is used, taken into account the different crystal shapes. As it was commented previously the SSDs ”in the box” did not work properly, so the angular resolution of the nucleons is given by the Crystal Ball detector. This detector does not have a high granularity and consequently the angular resolution is poor. The black line on figure 5.12 shows the polar angle θof the crystal hit by the nucleon after randomization, while the red dashed line shows the reconstucted distribution obtained via simulation. Polar angles below 9o are empty because the crystal along the beam axis is missing. At angles above 72o, it is observed that the statistics decreases sustantially; this can be attributed to the fact that some high polar angle protons are not able to reach the detector as they have very low energies. Thus, one can establish that the polar angle acceptance for protons is in a range from 9oto 72o. 5.4.2 Efficiency calculations The main goal of these simulations is to calculate the efficiency of detecting two protons above a certain energy threshold for each crystal in the (p,2p) reactions for different targets, and the neutron and the proton in the same event in the (p,pn) reactions above an energy threshold. The efficiency is defined as the number of events with two detections above the given energy threshold divided by the total number of events. Table 5.4 shows the efficiencies obtained for both reactions using different targets. As it is expected the efficiency for the empty target is larger because there are no losses produced by the materials. As a final number to correct the number of reactions, the mean value of the efficiencies for all the targets is used. These values are very similar to the ones obtained by other students [84]. 3using a randomization algorithm created by F. Wamers (for a more detailed information [44]) 5.4 Crystal Ball proton and neutron response 89 Theta 1 (deg) 0 10 20 30 40 50 60 70 80 90 100 Counts 0 100 200 300 400 500 600 700 Figure 5.12: Black solid line: Polar angle distribution obtained using the “quasi-free event generator”. Red dashed line: polar angle distribution measured by the Crystal Ball in simulation. At lower and higher angles there are acceptance losses, due to the detector geometry and to the energy range of the quasi-free scattered nucleons. CH2C empty efficiency p, 2p (%) 65.90 ±0.81 66.64 ±0.82 69.35 ±0.83 efficiency p, pn (%) 15.48 ±0.39 15.26 ±0.39 15.95 ±0.40 Table 5.4: Efficiency calculated for the different targets. 90 Crystal Ball simulations Chapter 6 Results Based on the reconstruction and analysis methods described in the previous chapter, here we present the results. The complete procedure to extract the physical quantities of interest will be shown in detail only for one of the projectiles, the 21N. In order to reduce innecessary repetitions, the results for other projectiles analyzed using the same methods will be presented in the following chapter with their corresponding plots included in the Appendix. 6.1 The reaction channel 21N(p,pn)20N Figure 6.1 shows a schematic layout of the different reactions that could be observed for the 21N. The sketch includes the corresponding energy thresholds for the proton and neutron removal. Starting with the incoming projectile 21N, first the bound channels from 21N(p,pn)20N and 21N(p,2p)20C will be studied via their inclusive cross sections, angular correlations and momentum distributions. Then, the unbound states of 20N will be investigated via the reaction 21N(p,pn)20N*→19N+n, the inclusive cross sections and excitation energy spectra for this channel will be presented. The lack of statistics for the proton breakup channel channel 21N(p,2p)20C*→19B+p made the analysis for this reaction impossible. The 21N projectile was selected from the incoming cocktail beam in the analysis by applying a gate in the charge vs. mass-over-charge ratio (A/Z) plot. The outgoing fragments produced by the 21N in the CH2, carbon and empty targets, were identified by the tracking after the target. The quasifree scattering channel 21N(p,pn)20N was selected first, by choosing 20N in the outgoing fragments and second, by requiring the events that fullfill the quasi-free scattering condition. This condition requires the detection of a proton in coincidence with a neutron in the Crystal Ball detector with a 92 Results Figure 6.1: Layout of the different decay channels for the incoming projectile 21N, including the proton and neutron separation energies for some of the possible reaction channels. given energy threshold, selected to be 20 MeV. 6.1.1 Inclusive cross section In this section the results for the inclusive cross sections are presented. Inclusive indicates that the final states of the fragments were not distinguished. Inclusive cross sections were calculated for the channel 21N(p,pn)20N using two different methods. As shown in equations 4.5 and 4.6, the cross section depends on the number of incoming particles, the number of reactions and the target characteristics. The first two quantities can be estimated by selecting the entries inside a two-dimensional elliptical cut in the identification plot charge vs. mass, or can be obtained from one dimensional mass identification plots, via a multi-Gaussian fit (calculating the area of Gaussian distributions). In the first method, the two-dimensional cut, the number of attempts (projectiles), which is approximated by the number of unreacted nuclei (see 4.3), is obtained from the number of events inside the geometrical cut in the outgoing identification plot, charge vs. mass (see figure 6.2). This number 6.1 The reaction channel 21N(p,pn)20N 93 is corrected by the corresponding downscale factor for the trigger. The contamination from other nuclei in the unreacted is negligible. The number of reacted nuclei is counted in two steps. First, a two-dimensional elliptical cut selects the 20N, in the same manner as for the incoming. Then the quasi-free scattering events are selected. In order to identify them, the addback algorithm is used and the number of reactions is corrected for the efficiency of detecting a proton, in coincidence with a neutron above the threshold in the Crystal Ball. Mass (u.m.a) 15 16 17 18 19 20 21 22 23 Z 5 5.5 6 6.5 7 7.5 8 8.5 9 0 50 100 150 200 250 Figure 6.2: Selection cut in the outgoing identification plot atomic number vs. mass. Inside the ellipse the selected events representing the unreacted 21N. In the second method, the so-called one-dimensional, the number of attempts is determined as the integral of a Gaussian fit to the unreacted 21N tracked mass distribution, as shown in figure 6.3. A selection of fragments with charge 7 and the good beam trigger, was also taken. The number of attempts was corrected by the corresponding downscale factor. The number of reactions was measured by fitting the whole mass distribution to various Gaussians (multi-Gaussian fit). Then, the area of the Gaussian curve corresponding to the 20N peak in the mass identification plot was calculated (figure 6.4). In order to do this, only the outgoing fragments with charge 7 and which fulfill the quasi-free scattering conditions were included. The reacted events are corrected by the corresponding Crystal Ball detection efficiency. 94 Results Mass (u.m.a) 15 16 17 18 19 20 21 22 23 24 Counts 0 1000 2000 3000 4000 5000 6000 Figure 6.3: Mass identification plot for the non-reacted nuclei with charge 7. The Gaussian fit used o the counting of the number of attempts is also shown. Mass (u.m.a.) 14 15 16 17 18 19 20 21 22 Counts 0 20 40 60 80 100 120 140 Figure 6.4: Mass identification plot for the quasi free scattering outgoing nuclei with charge 7. A Gaussian fit on the isotope of interest is shown. 6.1 The reaction channel 21N(p,pn)20N 95 2-dimensional σ(mb) 1-dimensional σ(mb) CH2141.2±6.0 143.0±2.9 C 48.6±5.8 47.7±5.6 H 46.3±4.2 47.7±5.6 Table 6.1: Inclusive 21N(p,pn)20N channel cross sections for the CH2, C and reconstructed H for the 1and 2-dimensional methods, corrected by the Crystal Ball efficiency for the detection of a proton and a neutron above an energy threshold of 20 MeV in the Crystal Ball detector. The number of attempts and the number of reactions is measured using both methods for the CH2, carbon and empty targets. Table 6.1 shows the results for the inclusive cross sections using the two explained methods, according to equations 4.5 and 4.6. The uncertainties in the table are purely statistical. The uncertainty associated with the Crystal Ball efficiency still needs to be evaluated. Both results are in good agreement within the error bars, proving that the results are robust. In order to have a unique value for the inclusive cross section on the reconstructed H target, a weighted average xwith its corresponding uncertainty δx will be calculated as follows: x±δx = N X i wixi N X i wi ± N X i wi!−1/2 (6.1) where the weights are given by wi= 1/(δxi)2,xiand δxibeing the value and the error calculated via each method [72]. The uncertainty obtained from the weighted average reduces the individual uncertainties of each method, based on the independency of both analysis approaches. But, in this case, the data used for the new two analysis methods is not independent. The procedure has threw light on the evaluation of the systematic uncertainty associated with the methods. Therefore, the statistical uncertainty is incremented by adding an additional evaluation of the dispersion of the results, the variance of the results distribution. The result obtained for the reconstructed proton target using the weighted average is: (46.8 ±5.7) mb. 96 Results 6.1.2 Angular correlations ) 1 θPolar angle ( 0 10 20 30 40 50 60 70 80 90 ) 2 θPolar angle ( 0 10 20 30 40 50 60 70 80 90 0 0.5 1 1.5 2 2.5 3 Opening angle (deg) 0 20 40 60 80 100 120 140 160 180 Counts 0 10 20 30 40 50 60 ) 1 φAzimuthal angle ( 0 50 100 150 200 250 300 350 ) 2 φAzimuthal angle ( 0 50 100 150 200 250 300 350 0 0.5 1 1.5 2 2.5 3 ) 2 φ - 1 φAzimuthal angle ( 0 50 100 150 200 250 300 350 Counts 0 20 40 60 80 100 120 Figure 6.5: Angular correlations of the neutron and the proton emerging from the reaction 21N(p,pn)20N observed in the Crystal Ball detector for a CH2target. Top left: shows the polar angle of one of the nucleons vs. the polar angle of the other. Top right: shows the opening angle for the neutron and the proton, the peak at ∼80ooriginating from the hydrogen present in the CH2. Bottom left: shows the azimuthal angle of one nucleon vs. the azimuthal angle of the other. Bottom right: shows the difference between the azimuthal angles of both nucleons, the anticorrelation in azimuthal angle being clearly apparent. The two outgoing nucleons in a quasi-free reaction, in this case a neutron and a proton, share an opening angle of about ∼80oand they are emitted back to back in azimuthal angle. In figures 6.5, 6.6, 6.7 are shown the angular correlations for the three different targets, CH2, carbon and empty respectively, used to analyze the reaction of interest. A clear correlation is observed for the CH2. The peak at around ∼80oshown for the opening angle distribution in figure 6.5 is 6.1 The reaction channel 21N(p,pn)20N 97 ) 1 θPolar angle ( 0 10 20 30 40 50 60 70 80 90 ) 2 θPolar angle ( 0 10 20 30 40 50 60 70 80 90 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Opening angle (deg) 0 20 40 60 80 100 120 140 160 180 Counts 0 2 4 6 8 10 ) 1 φAzimuthal angle ( 0 50 100 150 200 250 300 350 ) 2 φAzimuthal angle ( 0 50 100 150 200 250 300 350 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ) 2 φ - 1 φAzimuthal angle ( 0 50 100 150 200 250 300 350 Counts 0 2 4 6 8 10 Figure 6.6: Angular correlations of the neutron and the proton emerging from the reaction 21N(p,pn)20N observed in Crystal Ball for a C target. produced by the reactions in the hydrogen present in the CH2target, which corresponds with quasi-free scattering events. The opening angle distribution for the hydrogen target is reconstructed performing the background subtraction (explained in the section 4.3). The results for the opening angle and the difference between the azimuthal angles is shown in figure 6.8. The experimental distributions can be compared with the results from a kinematical simulation (described in the section 5.3). The opening angle distribution in the simulation has a mean value of 82o±4o(the uncertainty corresponds to the RMS), while the experimental mean value for a Gaussian fit performed at the quasi-free scattering peak is 82oand the width 12o. The two values are in good agreement. In the case of the azimuthal difference, the distributions can be characterized by their mean values and their RMS, obtaining 165o18ofor the mean and width in the simulation and a mean value of 149oand a width of 27ofor the experimental data, respectively. The 104 Results 6.2.1 Inclusive cross sections The inclusive cross sections were calculated via the two analysis methods explained for the (p,pn) channel in section 6.1.1 and exemplified for the (p,pn) channel. The results obtained are shown in table 6.2. Both methods agree within the error bars. The total inclusive cross section using the weighted average and considering the different uncertainty contribution is: (1.96±0.46) mb. 2-dimensional σ(mb) 1-dimensional σ(mb) CH25.37±0.52 5.43±0.50 C 1.60±0.47 1.38±0.42 H 1.89±0.35 2.02±0.33 Table 6.2: Inclusive 21N(p,2p)20C channel cross sections for the 1and 2dimensional methods, corrected by the Crystal Ball efficiency. 6.2.2 Angular correlations The opening angle and the difference in the azimuthal for the two protons are presented in figure 6.15 for the reconstructed proton target. The opening angle distribution was fitted to a Gaussian, yielding a mean value 80.32oand a sigma of 14.96o. A simulation was performed in the same way as it was done for the (p,pn) channel, obtaining a mean value of 72.16oand an RMS of 10.07o. Both results are in reasonable agreement. The difference between the azimuthal angles was found to have a mean value of 157.5owith an RMS of 17.72obeing in reasonable agreement to 146.5oand 33.29oobtained for the mean and RMS values in simulation. 6.2.3 Momentum distributions The longitudinal momentum distribution in the laboratory frame was found to be centred at 19300 MeV/c with an RMS of 146.1 MeV/c (see figure 6.16). Figure 6.17 shows the longitudinal momentum in the rest frame of the projectile. The distribution is centred around -122.4 MeV/c and has an RMS value of 103.3 MeV/c. It exist a considerable deviation from zero, which is caused by the reaction. The transversal momentum distribution is shown in figure 6.18, and is centred at -13.83 MeV/c with an RMS of 108 MeV/c. 6.3 The breakup channel 21N(p,pn)20N∗→19N+n 105 Opening angle (deg) 0 50 100 150 /d(Opening angle) (barn/deg)σd 0 0.1 0.2 0.3 0.4 0.5 0.6 -3 10× Mean 81.51 Sigma 12.33 (deg) 2 φ - 1 φ 0 50 100 150 200 ) (barn/deg) 2 φ - 1 φ/d(σd 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -3 10× Mean 149.04 RMS 26.76 Figure 6.15: Opening angle (left) and difference between the azimuthal angles (right) for the two protons emerging from the reaction 21N(p,2p)20C observed in Crystal Ball for the reconstructed proton target. (MeV/c) z P 18000 19000 20000 21000 ) (barn/(MeV/c)) z /d(Pσd 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 -3 10× 2 CH Carbon Empty (MeV/c) z P 18000 19000 20000 21000 ) (barn/(MeV/c)) z /d(Pσd 0.2 0.4 0.6 0.8 1 -3 10× Figure 6.16: In the left plot are shown the longitudinal momentum distributions in the laboratory frame for the CH2, carbon and empty targets for the reacted 20C. In the right plot is shown the longitudinal momentum distribution in the laboratory frame for the reconstructed hydrogen. 6.3 The breakup channel 21N(p,pn)20N∗→19N+n After the knockout of a neutron from the 21N nucleus, a hole is created in a given neutron shell and, depending on the excitation energy of this residual hole state in the 20N, a particle could be emitted. In this case, the reactions with enough excitation energy to evaporate a neutron (2.161 keV) will be studied. This channel was investigated by measuring in coincidence the out- 106 Results (MeV/c) z P -800 -600 -400 -200 0 200 400 600 800 ) (barn/(MeV/c)) z /d(Pσd 0.2 0.4 0.6 0.8 1 1.2 -3 10× 2 CH Carbon Empty (MeV/c) z P -800 -600 -400 -200 0 200 400 600 800 ) (barn/(MeV/c)) z /d(Pσd 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -3 10× Figure 6.17: In the left plot are shown the longitudinal momentum distributions in the rest frame of the projectile for the CH2, carbon and empty targets for the reacted 20C. In the right plot is shown the longitudinal momentum distribution in the rest frame of the projectile for the reconstructed hydrogen target. (MeV/c) y P -800 -600 -400 -200 0 200 400 600 800 ) (barn/(MeV/c)) y /d(Pσd 0.5 1 1.5 2 2.5 -3 10× 2 CH Carbon Empty (MeV/c) y P -800 -600 -400 -200 0 200 400 600 800 ) (barn/(MeV/c)) y /d(Pσd 0.2 0.4 0.6 0.8 1 1.2 1.4 -3 10× Figure 6.18: In the left plot are shown the transversal momentum distributions in the laboratory frame for the CH2, carbon and empty targets for the reacted 20C. In the right plot is shown the transversal momentum distribution in the laboratory frame for the reconstructed hydrogen target. going fragment 19N and a neutron in the LAND detector in coincidence. The neutron multiplicity distribution measured with the 19N fragment after selecting an incoming 21N and quasi-free scattering conditions is shown in figure 6.19. In most of the cases only one neutron is observed. The time of flight between the target and LAND was used together with 6.3 The breakup channel 21N(p,pn)20N∗→19N+n 107 Neutron multiplicity 0 1 2 3 4 5 Counts 0 20 40 60 80 100 120 140 160 180 200 Figure 6.19: Neutron multiplicity in LAND for coincidences with (p,pn) reactions in QFS regime in the CH2target. the position information obtained from the neutron detector to calculate the neutron velocity [61]. To calibrate the time of flight, γrays produced in the target are used. These gammas present a narrower distribution than the neutrons and appear at earlier times because gammas travel with the speed of light. The LAND time offset is set by moving this γpeak to zero. The land02 package includes an algorithm which reconstructs the spherical coordinates [61] of the neutron hits in LAND. The information needed from the fragment is obtained via the tracking program and the two SSDs after the target. In the left plot of figure 6.20 is shown the neutron velocity distribution, which has a mean value of (22.02±0.94) cm/ns. The angle between the fragment and the neutron is shown in the right plot of figure 6.20 and has a mean value of 42.37 mrad (∼2.86o) and an RMS of 20.5 mrad. The neutrons arising from an evaporation reaction reach LAND with a velocity very similar to the beam. The background events coming from reactions which occur after the target are slower than the evaporated neutrons and could be identified by plotting the neutron energy vs. the fragment mass. In figure 6.21 is shown an example of the neutron velocity distribution as a function of the fragment mass for a CH2target for the incoming projectile 21N. The events inside the window at (20, 25) cm/ns are neutrons which came from evaporation. The tail for lower velocities observed at mass A = 21 is due to the beam. Only events inside the mentioned window are used for the calculation of the excitation energy and the cross section. The probability of detecting one neutron in LAND for a given channel has a strong dependence on the neutron kinetic energy. The number of detected 108 Results Neutron velocity (cm/ns) 16 18 20 22 24 26 28 30 Counts 0 10 20 30 40 50 60 70 Angle between fragment and neutron (rad) 0 0.05 0.1 0.15 0.2 Counts 0 5 10 15 20 25 30 35 40 Figure 6.20: Neutron velocity distribution in LAND (left) and their angles with the 19N fragments (right) measured in coincidence with the (p,pn) reactions for the CH2target (see text for further explanation). Mass (u.m.a.) 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Neutron velocity (cm/ns) 0 5 10 15 20 25 30 Figure 6.21: Neutron velocity vs. fragment mass for the incoming ion 21N. The LAND trigger was selected. The band between the two black lines shows the neutron events from evaporation. neutrons has to be corrected for the detector efficiency. An efficiency distribution was provided by D.Rossi [69] using the simulation code LEG1. Figure 6.22 shows the efficiency distribution of detecting one neutron in LAND. The 1Land Event Generator 6.3 The breakup channel 21N(p,pn)20N∗→19N+n 109 drop in the reconstructed efficiency above 3.3 MeV is due to the acceptance of LAND. Up to that neutron energy, LAND has almost a 100% acceptance. Beyond that energy, a portion of the neutrons pass through LAND, and that portion increases with the increasing of the neutron energy. Neutron kinetic energy (MeV) 0 2 4 6 8 10 12 14 16 18 20 Efficiency x Acceptance 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Figure 6.22: Detection efficiency as a function of the neutron kinetic energy for the detection of one neutron in LAND calculated via simulation using the LEG code (see text for details). To correct for the efficiency, the neutron kinetic energy must be determined. For that purpose the Lorentz-transformation of momentum-energy is used:   ERF pRF k =  γf−βfγf −βfγfγf   E pk (6.3) where ERF and pRF kare the energy and the longitudinal momentum in the rest frame, βfand γfare the velocity and the Lorentz factor and Eand pkare the energy and longitudinal momentum in the laboratory frame. With the help of equation 6.3 it is possible to relate the energy of a particle in the rest frame with its energy in the lab frame ERF =γfE−βfγfpk(6.4) Using E=γm0=Ekin,n +m0and equation 6.4, the neutron kinetic energy in the rest frame is expressed as 110 Results Ekin,n =γfγnmn−βfγfpk,n −mn(6.5) where γfand γnare the Lorentz factors for the fragment and the neutron respectively, mnis the neutron rest mass, βfis the velocity of the fragment and pk,n is the longitudinal momentum of the neutron in the lab frame which is calculated as follows pk,n =mnβnγncosθ (6.6) with θthe angle between the outgoing fragment produced in the quasi-free scattering reaction and the neutron. In figure 6.23 is shown an example of the excitation energy distribution before and after correcting for the detection efficiency for the reaction 21N(p,pn)20N*-¿19N+n in a CH2target in quasi-free scattering conditions. N (MeV) 20 E* 0 2 4 6 8 10 12 14 16 18 20 Counts 0 5 10 15 20 25 30 before efficiency correction after efficiency correction Figure 6.23: Example of the efficiency correction for the excitation energy of 20N in a CH2target. The black curve is the excitation energy before efficiency correction, the red curve is the result of the correction. As we are interested in the quasi-free scattering reactions which occur with the protons in the target, the contribution from the carbon and empty target need to be subtracted. In figure 6.24 is shown the excitation energy spectrum for the reconstructed hydrogen target. The cross section obtained for the neutron break-up channel is (29.63±3.25) mb. The spectra begins above 2.161 MeV, the neutron separation energy for the 20N. Despite the 6.3 The breakup channel 21N(p,pn)20N∗→19N+n 111 E* (MeV) 0 2 4 6 8 10 12 14 16 18 20 /dE* (barn/400 keV)σd 0 0.5 1 1.5 2 2.5 3 3.5 4 -3 10× Figure 6.24: Excitation energy distribution after efficiency correction of 20N reconstructed for the proton target. The neutron separation energy is 2.161 MeV. high uncertainty due to the lack of the statistics, two peaks are observed. In order to check it, we have performed a set of minimizations including two Breit-Wigner functions and a background function. The Breit-Wigner functions were characterized by their width (Γ) and peak position (Er), as follows f(E;Er,Γ) = Γ (E−Er)2+ Γ2/4(6.7) The background function was chosen as the product of an error and an exponential function, f(E) = a×erf(bE)×e−cE (6.8) The combination of the Breit-Wigner and background functions was convoluted with the experimental response obtained via LEG simulation. Then a minimization was performed, obtained as a result (pink curve) the plot shown in figure 6.25. The grey distribution is the combination of the two Breit-Wigner and the background functions previous to the experimental response filter. The first resonance was found to be at 3.2±0.3 MeV with a width Γ of 0.96+0.5 −0.4MeV. The second resonance is at 6.77+0.4 −0.3MeV. Its width have a very high uncertainty. According to [19], it has been observed a γ 112 Results ray with an energy of 2.1 MeV which corresponds to a decay from an state of 2.943 MeV in the continuum. Our first resonance is in agreement with the reported energy value. Regarding to the second resonance, shell model calculations are needed in order to extract some conclusion. N (MeV) 20 E* 2 4 6 8 10 12 /dE* (barn/400 keV)σd 0 0.001 0.002 0.003 0.004 Figure 6.25: Excitation energy spectrum of the unbound states in 20N. The experimental points are shown as blue points, while the result of the minimization is the pink histogram. The black function corresponds to the original resonances and the background functions, previous to the experimental response filter. Two resonances are observed at 3.2±0.3 and 6.77±0.4 MeV. Chapter 7 Discussion of the results After the description of the analysis methods and their application to a particular case, this chapter will be devoted to the interpretation and evaluation of the results. The first part of this chapter will focus on the discussion of the results for the inclusive cross sections in the (p,pn) and (p,2p) reactions for the projectiles 21N, 23O and 22O. Next, the results for the respective momentum distributions and gamma ray emission will be discussed. The last part will be devoted to the discussion of the one neutron break-up channels: 21N(p,pn)20N∗→19N+n, 23O(p,pn)22O∗→21O+n and 22O(p,pn)21O∗→20O+n. 7.1 Inclusive cross sections This section summarizes the results for the cross sections associated to the (p,pn) and (p,2p) channels of the projectiles 21N, 23O and 22O. The results are shown in table 7.1. It is observed that the cross section for a projectile decaying via (p,pn) is larger than the one for (p,2p). This is a natural consequence due to the fact that all the projectiles are neutron-rich nuclei, so there are more neutrons than protons available for reactions. Figure 7.1 shows the total inclusive cross sections for the (p,pn) (left) and (p,2p) (right) are shown as a function of the neutron and proton number of the projectile, respectively. It is observed for the (p,pn) channels that the cross section is larger for N = 15 than for N = 14. This can be understood in terms of the shell model: N=14 can be interpreted as a closed subshell with the level 0d5/2completely full, holding six neutrons, while the N = 15 has a single neutron in the 1s1/2shell. This behaviour of the N = 14 was already observed in previous works [18, 19, 20]. The valence protons of these projectiles all reside in the same shell. The 120 Discussion of the results response of the calorimeter in efficiency and resolution to a given energy emission. The γrays energies have been taken from the literature where accurate determination of the decay schemes were available. The atomic background is represented as an exponential function, taken particular care of fitting this function in the regions where no γwas expected. Other background determination was tested, in particular studying the gamma ray spectra of 16O, where the situation of the lowest excited state, located at 6.05±0.01 MeV, forbids the emission of low energy gamma. An appropriate scaling of the 16O spectrum, taken into account the number of reactions, leads to a very small background correction, and therefore will not be used herein. In any case, the test served to confirm the simple exponential shape of the background above a given energy threshold. In order to compare the simulation with the experimental data, we have minimized by Pearson χ2method the distance between the experimental and the simulated peaks, scaled by factors which will be used to determine the relative γrays intensities. To ensure that this determination is completely robust, the minimization has been performed for a set of energy thresholds (100, 200, 300 and 400 keV) and number of histogram bins (20-50), characterizing the probability distribution function of gamma intensities resulting from each minimization. From the results of this probability function, estimates and uncertainties of the gamma intensities could be obtained on solid grounds. The first spectrum that will be discussed, obtained in coincidence with the fragments from the reaction 23O(p,pn)22O. Based on the level scheme of the 22O, taken from [18, 86], this isotope has three dominant γrays in cascade, with energies and spin parity assignment of: 1383 keV (3+), 2354 keV (2+) and 3199 keV (4+). 23O can be described as the combination of the wave function of a nucleon in the 0d5/2shell or in the 1s1/2shell coupled to the 22O core. According to references [18, 86], the ground state of 23O has spin and parity 1/2+. The ground state of 22Oisa0+and the excited states are 2+, 3+and (0−,1−). This last state is not observed in the reference [18]. According to the spin and parity, only the coupling of the 22O ground state to a neutron in 1s1/2 or the excited states at 1383 and 3199 keV to a neutron in 0d5/2 could be observed. Following the information from [86], another possibility would be the coupling of the neutron in the 1s1/2with the excited state at 5800 KeV (0−,1−). In order to calculate the relative intensity for each γray, we have tried to minimized the difference between the experimental points and a simulation curve including the two γrays with energies of 1383 and 3199 keV and an exponential function representing the background. The experimental spectrum showed a clear indication that the peak, originally assigned to 3199 7.3 Gamma rays 121 Energy (keV) 0 1000 2000 3000 4000 5000 6000 Counts/60 keV 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 Energy (keV) 0 500 1000 1500 2000 2500 3000 3500 /dE (barn/125 keV)σd 0 0.005 0.01 0.015 0.02 0.025 Figure 7.7: Experimental γ-ray spectra (black markers) and best minimization (red histogram line) for 22O. The individual contributions of each gamma are shown, according to the simulated response of the Crystal Ball detector to each mono energetic gamma emission. keV, appears at lower energy, probably due to energy losses not correctly evaluated in the Crystal Ball detector simulation for gammas of high energy. We have performed two different studies of the spectrum for this nucleus: the first including a contribution at 3199 keV and the second replacing it by the response to a lower energy, 2800 keV, to compensate for the unaccounted losses. The last one produces a much better χ2and the results of this second analysis provide intensities which are in better agreement with the ones from [18]. The experimental γray spectrum (black points) together with the result for the minimization performed (solid red line) for this second analysis are shown in figure 7.7. The relative intensities for each γray are shown in table 7.3. The obtained results are compatible with the literature [18, 86]. In both articles the most energetic γwas found to be the most intense, corresponding to the decay of the first excited state 2+. According to [18] the lowest energetic γtransition has a relative intensity of 43±8%, being in a reasonable agreement with our calculation of 58±11%. The γray spectrum corresponding to 21N was also studied, from the gamma coincidences with the fragments from the reaction 22(p,2p)21N. Ac- 122 Discussion of the results Results from this work Results from [18] Eγ(keV) Iγ(%) (2800) Iγ(%) 1383 59 ±11 43 ±8 2800 100 ±16 100 ±15 Table 7.3: Relative intensities determined for the gamma rays of 22O, using the simulated energies of 2800 and 1383 keV. Energy (keV) 0 1000 2000 3000 4000 5000 6000 Counts/60 keV 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 Energy (keV) 0 500 1000 1500 2000 2500 3000 3500 /dE (barn/102 keV)σd 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 -3 10× Figure 7.8: Experimental γray spectra (black) and best minimization (red) for 21N. cording to reference [19], this nucleus has a γray at 1177 (3/2−) keV, with the strongest intensity. This transition is in coincidence with the energies at 1228 (5/2−), 2142 (5/2−), 2438 (5/2+), 1790 (7/2−) and 884 (7/2−) keV. All the information about the spin and parity of the different states has been taken from [19] As it was done in the previous case, the 22O can be described as a core of 21N coupled to a proton in the 0p1/2or 0p3/2shells. The only possible combinations taking into account the spin and parity of the ground and excited states of 21N, lead to the possibility to observe only the γray corresponding to the first excited state, 1177 keV. Then, we first try to interpret the experimental data from the minimization of this unique contribution, additionally to the exponential background. The result can be 7.3 Gamma rays 123 found in figure 7.8; no additional gamma contribution could be necessary to interpret the experimental decay scheme. The last spectrum presented in detail here is the corresponding to the 21O. The decay scheme has been studied previously [18]. According to this reference there are four branches. Two of them are composed by one gamma with energies of 1218 and 3026 keV each one. The other two, are formed by two gammas, namely 2133 + 881 keV and 3073 + 1854 keV. 22O can be described as a nucleon in the shell 0d5/2or in the shell 1s1/2coupled to 21O core. According to reference [18] excited states of 21O have spin and parity 5/2+, 1/2+, 3/2+, 7/2+and 9/2+. So, the combinations that are possible to describe the 22O in its ground state would be mainly the ground state of 21O which has spin and parity 5/2+and the first excited state 1/2+. There is another state with 5/2+, but according to shell model calculations using the WBT interaction [90] the probability to populate this state is very low. The spectroscopic factor for this state is 0.12, while the spectroscopic factor of the ground state is 4.79. In principle it would be possible to produce other excited states via processes like dynamic excitation of the core. But the dynamic excitation requires an exchange of energy which should be not compatible with the conditions of the quasi-free scattering selected in the analysis. Energy (keV) 0 1000 2000 3000 4000 5000 6000 Counts/60 keV 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 Energy (keV) 0 500 1000 1500 2000 2500 3000 3500 /dE (barn/111 keV)σd 0 0.0005 0.001 0.0015 0.002 0.0025 Figure 7.9: Experimental γray spectra (black) and best minimization result (red) for 21O. Taking into account all this information, the initial attempts were per- 124 Discussion of the results formed with a single gamma emission at an energy of 1218 keV. The result of the minimization is shown in figure 7.9 The 20N has a very complicated spectra to be analysed with the Crystal Ball detector, because it has four γrays (615, 843, 944 and 1052 keV) in an energy range relatively small, making really difficult to distinguish the contributions due to the limited detector’s resolution (around 20% for a γ ray with an energy of 1 MeV). However, a minimization was performed using the relative intensities and energies from the literature [19]. Our result are compatible with these relative intensities set from [19], but different parameters combination produce similar χ2values resulting in very different relative intensities and making impossible to extract accurate information from this spectrum. The lack of statistics for the most exotic available nuclei, 20C and 22N, do not allowed us to perform a detailed study. 7.4 The breakup channels In a similar approach to the analysis of the unbound states for the one neutron breakup channel of the projectile 21N, the excitation energy spectra for the reaction channels 23O(p,pn)22O∗→21O+n and 22O(p,pn)21O∗→20O+n were investigated. The excitation energies for the nuclei 22O and 21O were reconstructed by measuring the coincidence between the breakup reaction fragments 21O and 20O and their respective emitted neutrons in quasi-free scattering conditions. The cross sections for these two channels were determined by subtracting from those obtained for the CH2, the carbon and empty target contributions. The values obtained are (15.99±6.79) mb for the 23O(p,pn)22O∗→21O+n and (15.16±1.35) mb for the other channel 22O(p,pn)21O∗→20O+n. The excitation energy spectra, corrected by the efficiency of detecting one neutron in the LAND detector, are shown in figure 7.10 for the two studied cases. The possibility of emitting a neutron for the 22O begins when the energy is above 6.85 MeV (left), while for the 21O this channel opens for energies above 3.806 MeV (right) (separation energies taken from http://ie.lbl.gov/toi2003/MassSearch.asp). 7.4 The breakup channels 125 O (MeV) 22 E* 0 2 4 6 8 10 12 14 16 18 20 /dE* (barn/MeV)σd 0 1 2 3 4 5 6 -3 10× O (MeV) 21 E* 0 2 4 6 8 10 12 14 16 18 20 /dE* (barn/MeV)σd 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -3 10× Figure 7.10: Excitation energy distribution for the 22O (left) and 21O (right) reconstructed for the neutron decay channel. The one-neutron separation energies are 6.850 and 3.806 MeV for the 22O and 21O, respectively The excitation energy distribution for the 21O can be compared with previous results measured by B. Fern´andez-Dom´ınguez et al. [91]. In this work they investigated the spectroscopy of 21O using transfer reactions in inverse kinematics at the SPIRAL facility in GANIL. They observed two resonances, one at 4.77±0.10 and the other one 6.17±0.11 MeV. Figure 7.11: Excitation energy for the unbound states for 21O obtained by B. Fern´andez-Dom´ınguez et al. [91]. From the observation of the obtained excitation energy for 21O, it seems evident the presence of three structures that could correspond to three separate resonances. In order to check it, we have performed a set of minimizations following the procedures described for the analysis of the excitation energy spectrum of 20N (see section 6.3). The positions of the three resonances according to the minimization are: 4.41±0.07 MeV, 5.52±0.10 MeV and 6.74±0.50 MeV. In the case of the first resonance we provide a width of Γ = 0.280±0.140 MeV. For the other two resonances we are only able to give a superior limit of 0.300 and 0.450 MeV, respectively. The result obtained 126 Discussion of the results for the first resonance confirms the previous value obtained by [91]. O (MeV) 21 E* 4 6 8 10 12 14 /dE* (barn/MeV)σd 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 Figure 7.12: Excitation energy for the unbound states for 21O. The points correspond to the experimental data, the pink curve is the simulated response of the excitation function included in black (see text for details). The excitation energy distribution for the 22O presents very low statistics to perform a detailed analysis of the resonances. But, the fact that the spectra starts directly above the threshold could be an indicative of a resonance at an energy very close to the neutron emission threshold. In [92] the structure of 22O was investigated by measuring the βdecay of 22N in an experiment performed at the National Superconducting Cyclotron Laboratory (NSCL). According to [92] the first state above the neutron emission threshold is at 7.65 MeV. This state seems to be compatible with our observation. Chapter 8 Conclusions Light neutron-rich nuclei around N=14 (23O, 22O and 21N) have been investigated via (p,2p) and (p,pn) reactions with a view to study the proton and neutron shells, respectively. The S393 experiment was performed at GSI [11] in 2010, employing six different settings centred on different A/Q ratios. The setup was placed at the LAND-R3B experimental area at Cave C. An 40Ar primary beam was accelerated in the SchwerIonenSynchrotron (SIS-18) up to an energy of about 490 MeV/u. The beam was then directed to the FRagment Separator area (FRS) where, using a beryllium production target, a secondary beam produced via fragmentation was selected depending on the A/Q ratio of the desired species. Following this selection, the isotopes of interest were guided to Cave C, where the reaction target and the detectors needed for the analysis were located. Two key observables have been studied with the aim of shedding light upon the structure of these nuclei. The inclusive cross sections and transversal momentum distributions for the (p,pn) channels reveal a change in the structure of these nuclei when we move from the N=14 to the N=15, i.e., from the 0d5/2shell to the 1s1/2. For the (p,2p) reactions, the measurement of the same observables allowed the same study for the 0p3/2, 0p1/2proton subshells. The comparison of the experimental data with the theoretical calculations allowed to extract spectroscopic information of the neutron shell in the projectiles 21N and 22O. The results obtained for the cross sections provide information about the neutron and proton shells. The results derived from this analysis are shown in table 8.1. The projectiles are neutron-rich nuclei, and as a consequence, the inclusive cross sections obtained for the (p,pn) channels are higher than the ones obtained for the (p,2p). It was observed for the neutron shells that the 23O has the higher cross section. This could be explained by its lower 128 Conclusions separation energy. Also, the other two nuclei (22O and 21N) have the valence neutrons in a closed shell. For the (p,2p) channels it was observed that the nuclei with Z = 8 have the same cross section because they have the same number of protons in the same shell. They have a higher cross section than the 21N due to the larger number of valence protons to be knocked-out. Reaction σ(mb) 21N(p,pn)20N 46.8±3.4 21N(p,2p)20C 1.96±0.24 23O(p,pn)22O 68.6±8.7 23O(p,2p)22N 5.02±0.72 22O(p,pn)21O 40.8±1.8 22O(p,2p)21N 4.98±0.20 Table 8.1: Inclusive cross sections for the (p,pn) and (p,2p) reactions for the projectiles 21N, 23O and 22O. Regarding the momentum distributions, it was observed for the (p,pn) channels that the FWHM decreases when moving from N = 14 to N = 15; this can be interpreted as neutrons passing from a d-shell with angular momentum l = 2 to an s-shell with angular momentum l = 0, which has a narrower momentum distribution and a wider spatial distribution. The measured FWHM are: 190±33 MeV/c for the 21N(p,pn)20N, 108±25 MeV/c for the 23O(p,pn)22O and 240±16 22O(p,pn)21O. From the comparison with theoretical calculations, it was possible to obtain the weights for the different waves. In the case of the 21N nucleus, a contribution of 0.91±0.18 and 0.09±0.18 for the d and s waves, respectively has been measured. For the 22O, it has been observed that the composition of the ground state requires some strength of the s wave, coupled with the first excited state of 21O. The (p,2p) channels were also investigated, obtaining the next FWHM: 204±41 MeV/c for the 21N(p,2p)20C, 95±51 MeV/c for the 23O(p,2p)22N and 254±12 MeV/c for the 22O(p,2p)21N. From the comparison of the FWHM for the two oxygen isotopes, it is observed that the 23O has a narrower momentum distribution because it has a larger separation energy. The γray spectra for the nuclei 22O, 21N, 21O, 20N, 20C and 22N were studied by measuring the coincidence of these isotopes with the gamma rays measured in the Crystal Ball detector. For 22O, 21N and 21O cases, the 129 gamma rays relative intensities were determined. It was found via the observation of the γrays with energies of 3199 and 1383 keV, that 23O could be described as the combination of an 22O core in its ground state coupled to a neutron in the 0s1/2, an 22O core in its first excited state (3199 keV) 2+ coupled to a neutron in the 0d5/2and an 22O core in its second excited state (1383 keV) 3+coupled to a neutron in the 0d5/2. The calculated relative intensities were found to be in good agreement with previous results from [18, 86]. The study of the 21N revealed that the ground state of the 22O can be described as a combination of the 21N core either in its ground state (spin and parity 1/2−) coupled to a proton in the 0p1/2 or in its first excited state 3/2−, where will emit a γray with an energy of 1177 keV. The study of the excitation energy spectra allowed the determination of three resonances for the unbound states of 21O. The resonances are found to be at 4.4±0.1 MeV, 5.5±0.1 MeV and 6.8±0.1 MeV, being the width of the first resonance 0.280±0.140 MeV. The energy obtained for the first resonance confirms the previous value obtained by [91], which also has a compatible value for the width. The study of the excitation energy spectrum for the 20N revealed the existence of two resonance at 3.2±0.2 MeV and 6.77±0.4 MeV. The first one is compatible with the result found by [19] where they measured a state in the continuum at 2.943 MeV. Despite the lower statistics in the case of the excitation energy spectrum for 22O, the fact that the spectrum rises steeply just above the one neutron separation energy could be an indication of the existence of a resonance around 7.5 MeV. 136 Resumen Figure 9.3: Esquema del dispositivo experimental usado en el experimento S393. El beam viene desde la izquierda y encuentra el centelleador POS que junto que el ´ultimo detector del FRS mide el tiempo de vuelo que nos permite identificar los fragmentos en velocidad. Despu´s est´a colocado ROLU, que est´a compuesto por cuatro pl´asticos centelleadores que pueden moverse para definir el tama˜no y la posici´on del haz en el blanco. El siguiente detector es PSP se usa para medidas de posici´on y p´erdida de energ´ıa (Q). En la zona del target tenemos ocho detectores de silicio, los cuatro de la l´ınea de haz se utilizan para determinar las trayectorias de los fragmento e identificarlos en carga; los cuatro que rodean al blanco se usan para la identificaci´on de los eventos producidos por el mecanismo de reacci´on quasi-free scattering. Rodeando al blanco tenemos el calor´ımetro Crystal Ball para medidas de gammas y fragmentos de quasi-free. ALADIN: dipolo de gran aceptancia que desv´ıa las part´ıculas dependiendo de su A/Q; LAND: determinaci´on de trayectorias y momento de los neutrones; GFI’s: medida de la posici´on horizontal de los fragmentos pesados; TFW : posici´on en X e Y, p´erdida de energ´ıa y tiempo de vuelo de los fragmentos pesados; DCHs: reconstrucci´on de la trayectoria de los protones; DTF: medidas de posici´on, p´erdida de energ´ıa y tiempo de vuelo de los protones. 9.1 Conclusiones 137 Reacci´on σ(mb) 21N(p,pn)20N 46.8±4.3 21N(p,2p)20C 1.96±0.38 23O(p,pn)22O 69±11 23O(p,2p)22N 5.02±1.3 22O(p,pn)21O 40.8±2.3 22O(p,2p)21N 4.98±0.54 Table 9.1: Secciones eficaces inclusivas para las reacciones (p,pn) y (p,2p) de los proyectiles 21N, 23O y 22O, corregidas por la eficiencia de Crystal Ball y en un blanco de hidr´ogeno. imental usado posee mejor resoluci´on para el momento transversal que para el longitudinal, por lo tanto las conclusiones extra´ıdas en este trabajo se han basado en el estudio de esta componente. En la tabla 9.2, se muestran los resultados para la anchura a mitad de altura (FWHM) para todos los canales estudiados. Para obtener la informaci´on de la estructura, se realiz´o un estudio similar al realizado para la secci´on eficaz. Se ha observado que la FWHM decrece con el aumento del n´umero de neutrones. Esto puede ser explicado haciendo uso del modelo de capas, ya que los neutrones de valencia para N = 14 est´an en la capa 0d5/2que tiene momento angular l = 2, sin embargo el neutr´on de valencia para N= 15 est´an en la capa 1s1/2que posee un momento angular l = 1. Por lo tanto la distibuci´on de momento de l = 1 es m´as estrecha. En los canales (p,2p), se observa que la FWHM del 22O es mayor que la del 21N, esto sucede porque el 22O est´a en capa cerrada lo cual hace que el n´ucleo sea m´as compacto espacialmente y por lo tanto su distribuci´on de momento es m´as extensa. Para hacer un estudio m´as detallado de las distribuciones de momento, los datos experimentales han sido comparados con c´alculos te´oricos que nos han permitido obtener informaci´on espectrosc´opica. Los espectros γpara los n´ucleos 22O, 21N, 21O, 20N, 20C y 22N han sido estudiados midiendo en coincidencia los fragments salientes de la reacci´on con los rays γen el detector Crystal Ball. Para los is´otopos 22O, 21N and 21O, las intensidades relativas de los rayos gamma han sido determinadas. Se ha encontrado, a trav´es de la observaci´on de los rayos γcon energ´ıas de 3199 y 1383 keV, que 22O puede describirse como una combinaci´on del core 21O en su estado fundamental acoplado a un neutron el la capa 0s1/2, 138 Resumen Reacci´on FWHM (MeV/c) 21N(p,pn)20N 189.97±33.40 21N(p,2p)20C 203.86±40.61 23O(p,pn)22O 107.56±25.25 23O(p,2p)22N 95.12±50.92 22O(p,pn)21O 240.49±16.22 22O(p,2p)21N 254.54±11.77 Table 9.2: Transversal momentum distribution FWHM for the (p,pn) and (p,2p) reactions for the projectiles 21N, 23O and 22O. un core de 21O en su primer estado excited (3199 keV) 2+acoplado a un neutr´on en la caps 0d5/2y un core de 21O en su segundo estado excitado (1383 keV) 3+acoplado a un neutr´on en la capa 0d5/2. Los c´alculos de las intensidades relativas realizados est´an en buen acuerdo con resultados previos de [18, 86]. El estudio del 21N ha revelado que el 22O puede ser descrito como una combinaci´on del core de 21N os bien en su estado fundamental (esp´ın y paridad 1/2−) acoplado a un prot´on en la capa 0p1/2 o en su primer estado excitado 3/2−, donde emitir´a un γcon una energ´ıa de 1177 keV. Cuando el n´ucleo posee una energ´ıa de excitaci´on que est´a por encima de alg´un umbral de separaci´on de part´ıcula, la emisi´on de gammas compite con la emisi´on de otras part´ıculas. A trav´es de la reconstrucci´on de la energ´ıa de excitaci´on es posible el estudio de los canales no ligados situados en el continuo. En nuestro caso se han estudiado los canales 23O(p,pn)22O∗→21O+n, 22O(p,pn)21O∗→20O+n y 21N(p,pn)20N∗→19N+n por medio de la detecci´on en coincidencia del fragmento producido despu´es de la evaporaci´on y el neutr´on. Estos estudios han servido para comparar en el caso de la energ´ıa de excitaci´on del 21O con resultados previos obtenidos por B. Fern´andezDom´ınguez et al. [91]. Se observa en este trabajo la existencia de dos resonancias, una a 4.77 MeV y otra a 6.17 MeV [91]. El estudio del espectro de energ´ıa de excitaci´on del 20N y del 22O revela existencia de tres resonancias a 4.4±0.1, 5.5±0.1 y 6.8±0.1. La primera es una confirmaci´on del resultado obtenido en [91]. La anchura de esta resonancia es de 0.280±0.140 MeV,compatible con el resultado de [91] y con las predicciones del modelo de capas. La distribuci´on de energ´ıa de excitaci´on analizada para la reacci´on el 22O, a trav´es de la 23O(p,pn)22O∗→21O+n. A pesar de que este caso tiene 9.1 Conclusiones 139 muy poca estad´ıstica, el hecho de que el espectro comience justo por encima de la energ´ıa de separaci´on de 22O podr´ıa ser un indicativo de la existencia de una resonancia. La reconstrucci´on del espectro de energ´ıa de excitaci´on para el 20N permiti´o la determinaci´on de dos resonancias a energ´ıas de 3.2±0.3 MeV y 6.77 MeV. La observaci´on de la primera resonancia podr´ıa confirmar el resultado previo obtenido en [19], donde observaron un estado en el continuo a 2.943 MeV. 140 Resumen Appendix A SSDs alignment In this appendix are shown some results of the SSDs alignment performed using a linear least squares fit. The positions of three of the four in-beam SSDs were varied to determine the configuration with the minimum distance between the real hits in the SSDs detectors and the ones defined by a straight ion trajectory. Two and three dimensional plots for every two offset combination are shown in figure A.1 for the X coordinates and in figure A.2 for the Y coordinates. The plots on the left show one SSD offset versus another. The χ2values are given by the color scale, where violet indicates the smallest. The black dots in the two dimensional plots mark the position of the minimum obtained. It is observed from the plots a strong correlation between the offsets of the first and second SSD, which is not observed with the fourth SSD. This is due to the fact that the third SSD positions are fixed, so when the first is moved in one direction the second moves in the same. This observation was also confirmed by studying the covariance matrix and the global correlation coefficients. 142 SSDs alignment Figure A.1: Functional maps for the X coordinates in two (left) and three (right) dimensional plots for each set of two parameters. The different SSDs offsets mapped are in the X and Y axes. The Z axis is the functional value, shown in the color scale in the left plots and in color and height in the right plots. The minimal areas can be distinguished in the plots, highlighted by a dot. 143 Figure A.2: Functional maps for the Y coordinates in two (left) and three (right) dimensional plots for each set of two parameters. The minimal areas can be distinguished in the plots. 144 SSDs alignment Appendix B Cross sections This appendix contains a table summarizing the total inclusive cross sections for the projectiles 21N, 23O and 22O. The table contains the results for the different targets and using the two analysis methods described in Section 6.1.1. The final inclusive cross sections resulting from this work for the (p,pn) and (p,2p) reactions can be found in Section 8.