Structure of low-lying states in 140Sm studied by Coulomb excitation
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This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Author(s): Title: Year: Version: Please cite the original version: All material supplied via JYX is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Structure of low-lying states in 140Sm studied by Coulomb excitation Klintefjord, M.; Hadyńska-Klȩk, K.; Görgen, A.; Bauer, C.; Garrote, F. L. Bello; Bönig, S.; Bounthong, B.; Damyanova, A.; Delaroche, J.-P.; Fedosseev, V.; Fink, D. A.; Giacoppo, F.; Girod, M.; Hoff, P.; Imai, N.; Korten, W.; Larsen, A.-C.; Libert, J.; Lutter, R.; Marsh, B. A.; Molkanov, P. L.; Naïdja, H.; Napiorkowski, P.; Nowacki, F.; Pakarinen, Janne; Rapisarda, E.; Reiter, P.; Renstrøm, T.; Rothe, S.; Seliverstov, M. D.; Siebeck, B.; Siem, S.; Srebrny, J.; Stora, T.; Thöle, P.; Tornyi, T. G.; Tveten, G. M.; Van Duppen, P.; Vermeulen, M. J.; Voulot, D.; Warr, N.; Wenander, F.; De Witte, H.; Zielińska, M. Klintefjord, M., Hadyńska-Klȩk, K., Görgen, A., Bauer, C., Garrote, F. L. B., Bönig, S., Bounthong, B., Damyanova, A., Delaroche, J.-P., Fedosseev, V., Fink, D. A., Giacoppo, F., Girod, M., Hoff, P., Imai, N., Korten, W., Larsen, A.-C., Libert, J., Lutter, R., . . . Zielińska, M. (2016). Structure of low-lying states in 140Sm studied by Coulomb excitation. Physical Review C, 93(5), Article 054303. https://doi.org/10.1103/PhysRevC.93.054303 2016
PHYSICAL REVIEW C 93, 054303 (2016) Structure of low-lying states in 140Sm studied by Coulomb excitation M. Klintefjord,1K. Hady´ nska-Kle¸k,1,2A. G¨ orgen,1,*C. Bauer,3F. L. Bello Garrote,1S. B¨ onig,3B. Bounthong,4,5 A. Damyanova,6J.-P. Delaroche,7V. Fedosseev,8D. A. Fink,8F. Giacoppo,1,†M. Girod,7P. Hoff,9N. Imai,10 W. Korten,11 A.-C. Larsen,1J. Libert,7R. Lutter,12 B. A. Marsh,8P. L. Molkanov,13 H. Na¨ ıdja,4,5P. Napiorkowski,14 F. Nowacki,4,5 J. Pakarinen,15,16 E. Rapisarda,8,17 P. Reiter,18 T. Renstrøm,1S. Rothe,8,19 M. D. Seliverstov,13 B. Siebeck,18 S. Siem,1 J. Srebrny,14 T. Stora,8P. Th ¨ ole,18 T. G. Tornyi,1G. M. Tveten,1P. Van Duppen,17 M. J. Vermeulen,20 D. Voulot,8N. Warr,18 F. Wenander,8H. De Witte,17 and M. Zieli´ nska11 1Department of Physics, University of Oslo, N-0316 Oslo, Norway 2INFN, Laboratori Nazionali di Legnaro, I-35020 Legnaro, Italy 3Institut f¨ ur Kernphysik, Technische Universit¨ at Darmstadt, Darmstadt D-64289, Germany 4IPHC, Universit´ e de Strasbourg, IPHC, 23 Rue du Loess F-67037 Strasbourg, France 5IPHC, CNRS, UMR7178, F-67037 Strasbourg, France 6University of Geneva, Bd du Pont-d’Arve 40, CH-1211 Gen´ eve, Switzerland 7CEA, DAM, DIF, F-91297 Arpajon, France 8CERN, CH-1211 Geneva 23, Switzerland 9Department of Chemistry, University of Oslo, N-0316 Oslo, Norway 10High Energy Accelerator Research Organization (KEK), Oho 1-1, Tsukuba, Ibaraki 305-0801, Japan 11CEA Saclay, IRFU, SPHN, F-91191 Gif-sur-Yvette, France 12Fakult ¨ at f¨ ur Physik, Ludwig-Maximilians-Universit¨ at M¨ unchen, D-85740 Garching, Germany 13Petersburg Nuclear Physics Institute, NRC Kurchatov Institute, Gatchina 188300, Russia 14Heavy Ion Laboratory, University of Warsaw, 02-093 Warsaw, Poland 15University of Jyv¨ askyl¨ a, Department of Physics, P.O. Box 35, FIN-40014 University of Jyv¨ askyl¨ a, Finland 16Helsinki Institute of Physics, University of Helsinki, P.O. Box 64, FIN-00014 Helsinki, Finland 17Instituut voor Kernen Stralingsfysica, KU Leuven, Leuven B-3001, Belgium 18Institut f¨ ur Kernphysik, Universit¨ at zu K¨ oln, K¨ oln D-50937, Germany 19Institut f¨ ur Physik, Johannes Gutenberg-Universit¨ at Mainz, D-55128 Mainz, Germany 20Department of Physics, University of York, York YO10 5DD, United Kingdom (Received 5 March 2016; revised manuscript received 6 April 2016; published 2 May 2016) The electromagnetic structure of 140Sm was studied in a low-energy Coulomb excitation experiment with a radioactive ion beam from the REX-ISOLDE facility at CERN. The 2+and 4+states of the ground-state band and a second 2+state were populated by multistep excitation. The analysis of the differential Coulomb excitation cross sections yielded reduced transition probabilities between all observed states and the spectroscopic quadrupole moment for the 2+ 1state. The experimental results are compared to large-scale shell model calculations and beyond-mean-field calculations based on the Gogny D1S interaction with a five-dimensional collective Hamiltonian formalism. Simpler geometric and algebraic models are also employed to interpret the experimental data. The results indicate that 140Sm shows considerable γsoftness, but in contrast to earlier speculation no signs of shape coexistence at low excitation energy. This work sheds more light on the onset of deformation and collectivity in this mass region. DOI: 10.1103/PhysRevC.93.054303 I. INTRODUCTION The shape of atomic nuclei is a fundamental property which is governed by the interplay between single-particle and collective degrees of freedom. Nuclei with closed proton *[email protected] †Present address: Helmholtz Institute, D-55099 Mainz, and GSI, D-64291 Darmstadt, Germany. Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. and neutron shells are spherical in their ground state, whereas the occupation of shape-driving orbitals causes nuclei with open shells to be deformed. The majority of deformed nuclei is found to have prolate (elongated) quadrupole shapes. For heavy nuclei with Z,N > 50, oblate ground-state shapes are rare and mostly found in regions with holes in high-spin, low- orbitals near the top of the proton and neutron shells [1]. Mean-field calculations based on Gogny [2]orSkyrme[3] interactions predict oblate ground states, e.g., for platinum and mercury isotopes with N>106 and for N≈78 and N≈120 isotones with Z>60. In certain regions of the nuclear chart, prolate and oblate shapes are found to coexist at low excitation energy. Shape coexistence at low energy can generally be expected when there is a competition between an energy gap and a residual 2469-9985/2016/93(5)/054303(14) 054303-1 Published by the American Physical Society
M. KLINTEFJORD et al. PHYSICAL REVIEW C 93, 054303 (2016) interaction that favors excitations across the gap [4,5]. Prominent examples for shape coexistence based on this mechanism are found in the Z=82 region near neutron midshell, e.g., in 186Pb [6] and the neighboring mercury isotopes [7]. Not surprisingly these nuclei lie in the region where mean-field calculations predict the transition from prolate to oblate ground-state shapes. From these observations one may expect to find shape coexistence also in the N≈78 region near proton midshell, where the role of protons and neutrons is interchanged. However, clear experimental indication for shape coexistence near the ground state is lacking in this region, and it was argued that the Z=64 subshell closure could explain the absence of shape coexistence in this region [4]. There is, however, evidence for shape coexistence at higher excitation energy in the N=78 isotones 140Sm and 142Gd. Two isomeric 10+states based on the configuration (πh11/2)2and (νh11/2)−2are found in both nuclei [8]. Lifetime measurements found the rotational bands built on top of the 10+states with proton-particle and neutron-hole character in 140Sm to be consistent with prolate and oblate shape, respectively [9]. The shape associated with the states in the ground-state band of 140Sm below the 10+isomers is not clear and is the subject of the present investigation. Relativistic mean-field calculations restricted to axial deformations predicted the ground state of 140Sm to have oblate shape, whereas prolate deformation was found to develop rapidly in the lighter samarium isotopes with N⩽76 [10]. More recent relativistic Hartree-Fock-Bogoliubov (HFB) calculations find a smooth transition from spherical 144Sm to well-deformed prolate 134Sm with a γ-soft potential energy surface for the transitional nucleus 140Sm [11]. The observation and tentative assignment of a (2+ 2) state at 990 keV and a (3+ 1) state at 1599 keV in 140Sm following the βdecay of 140Eu was interpreted as evidence for a low-lying γband [12]. The observation was supported by triaxial-rotor calculations based on a Woods-Saxon potential, which reproduced the excitation energies of the presumed γband and also found the potential energy surface for 140Sm to be soft in the triaxial degree of deformation [12]. However, a subsequent β-decay experiment revised the earlier spin values and tentatively assigned spin-parity (0+) and (2+) to the states at 990 and 1599 keV, respectively [13]. The presence of a second 0+ state at such low excitation energy is somewhat surprising when comparing with the systematics of excited states in neighboring nuclei. On the other hand, such a low-lying 0+ 2 state could indicate the presence of shape coexistence near the ground state of 140Sm. The spin assignments for the two states in question were clarified in a recent measurement of γ-γ angular correlations following the βdecay of 140Eu, which firmly showed that the state at 990 keV in 140Sm has spin-parity 2+and the state at 1599 keV 0(+)[14]. The level scheme for the states of the ground-state band and the lowest non-yrast states is shown in Fig. 1. The collectivity of the 2+ 1state in 140Sm was studied in a recent recoil distance lifetime measurement [15]. The resulting B(E2; 2+ 1→0+ 1) value and its comparison to the neighboring samarium isotopes indicates a gradual onset of deformation when removing neutrons from the closedshell nucleus 144Sm 82. The experimental B(E2; 2+ 1→0+ 1) 0 0 2531 41246 62082 2990 01599 531 715 836 609 1068 459 FIG. 1. Partial level scheme showing low-lying states in 140Sm. The spin assignments for the excited states at 990 and 1599 keV are taken from a recent angular correlation measurement [14]. values for the entire chain of neutron-deficient samarium isotopes are well reproduced by microscopic HFB calculations with the Gogny D1S interaction with mapping to the fivedimensional collective Hamiltonian (5DCH) for quadrupole excitations [15]. The theoretical calculations explain the onset of quadrupole collectivity in the samarium isotopes below N= 82 by a gradual shape transition from large prolate deformation with axial symmetry for the lightest isotopes to spherical shape in 144Sm, with the triaxial degree of freedom becoming more important as N=82 is approached. The Gogny 5DCH calculations find average quadrupole parameters of β=0.17 and γ=29◦for the ground state of 140Sm [15]. It appears that the onset of deformation in the samarium isotopes is different above and below the neutron shell closure. For N>82 the samarium nuclei show an abrupt increase in deformation at N=90, whereas the onset of deformation is more gradual for N<82 with apparent triaxiality in the transitional region around 140Sm. The rapid increase in deformation from N=88 to N=90 in the samarium and gadolinium isotopes can be explained by the occupation of proton and neutron spin-orbit partner orbitals which causes the disappearance of the Z=64 subshell closure for N⩾90 [16]. The transitional nucleus 152Sm was identified as one of the best realizations of the so-called X(5) critical point symmetry [17,18], which represents a first-order phase transition from a spherical vibrational to a deformed rotational nucleus. The analysis of excitation spectra for the samarium isotopes with N<82 using the interacting boson approximation (IBA) found model parameters for 138Sm and 140Sm that place these nuclei between the U(5) and the SO(6) limits of the IBA [19], i.e., at the transition between a spherical vibrator and a γ-soft vibrator characterized by the so-called E(5) critical point symmetry [20]. However, without any experimental B(E2) values beyond the 2+ 1state and uncertain spin assignments for the lowest non-yrast states it was not possible to evaluate a possible E(5) character for 140Sm. In this article we present the results of a Coulomb excitation experiment using a radioactive 140Sm beam, which provides several B(E2) values and also the spectroscopic quadrupole moment for the 2+ 1state. Low-energy Coulomb excitation is an ideal method to study the collectivity and deformation in this nucleus, because both yrast and non-yrast states can 054303-2
STRUCTURE OF LOW-LYING STATES IN 140Sm . . . PHYSICAL REVIEW C 93, 054303 (2016) be populated and transition probabilities extracted without interference from the isomeric 10+states. The comparison of the experimental results with theoretical calculations sheds more light on the onset of deformation and collectivity in this mass region. The article is organized as follows: The experimental details and data analysis are described in Sec. II. The extraction of electromagnetic matrix elements from the Coulomb excitation yields is described in Sec. III. The results are discussed and compared to theoretical calculations in Sec. IV, followed by a summary and conclusions in Sec. V. II. EXPERIMENTAL DETAILS The application of the isotope separation on-line (ISOL) technique in combination with selective laser ionization and post-acceleration made it possible to study the electromagnetic properties of 140Sm by Coulomb excitation. Radioactive 140Sm atoms with a half-life of 14.8 min were produced at the CERNISOLDE facility by spallation of a primary tantalum target with 1.4-GeV protons from the PS Booster. Samarium atoms were selectively ionized using the Resonance Ionization Laser Ion Source (RILIS) [21], which was equipped with a GdB6 low-work function cavity [22] to reduce the surface ionization of isobaric impurities. After selection of mass A=140 using the general purpose separator GPS, the ions were bunched, cooled, and trapped in the REXTRAP [23], and then further ionized to charge state 34+using the EBIS charge breeder [24]. Finally the highly charged 140Sm ions were accelerated to an energy of 2.85AMeV in the REX linear accelerator [25]. An average intensity of 2 ×105particles per second was achieved over a beam time of approximately 100 h. The 140Sm projectiles were scattered on a secondary 94Mo target of 2 mg/cm2thickness. Both 140Sm projectiles and 94Mo target nuclei were excited in the low-energy Coulomb excitation reaction. The distance of closest approach of 19.2 fm between the projectiles and target nuclei for the given reaction parameters is larger than the distance of 17.2fm, which is obtained by applying the safe distance separation criterion [26], d>1.25A1/3 p+A1/3 t+5fm,(1) where Apand Atare the mass numbers of the projectile and target, respectively. Under these conditions, it is safe to neglect all influence of the strong nuclear force and assume that the excitation process can be described by a pure electromagnetic interaction. Gamma rays from excited states in the 140Sm projectiles and 94Mo target nuclei were detected in the MINIBALL HPGe detector array [27], which at the time of the experiment consisted of seven triple-cluster modules, each of which comprised three sixfold segmented germanium crystals. An energy and efficiency calibration for the germanium detectors was performed using standard 152Eu and 133Ba sources. An annular double-sided silicon strip detector (DSSSD) of 1000-μm thickness was mounted in the MINIBALL target chamber and used to detect both scattered projectiles and recoiling target nuclei. The DSSSD consisted of four individual quadrants with each 16 concentric annular strips on the front side and 12 azimuthal sector strips on the back side. The annular strips −4000 −3000 −2000 −1000 0 1000 time [channel] 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 counts/channel (104) Random particle-γ Prompt particle-γ FIG. 2. Particle-γcoincidence time spectrum. A normalized fraction of the random gate was used for background subtraction. had a strip pitch of 2 mm and the azimuthal strips covered 3.5◦each. In total, the DSSSD covered 5000 mm2with an active area of 93% [28]. The detector was mounted in forward direction at a distance of 25.2 mm from the target, covering the angular range from 19.7◦to 58.4◦in the laboratory frame. In the center-of-mass frame, the angular coverage corresponded to 49.7◦<θ c.m.<146◦for the detection of 140Sm projectiles and 63.1◦<θ c.m.<140.7◦for the detection of recoiling target nuclei. The data acquisition was triggered and events were built when the MINIBALL and DSSSD detectors gave coincident signals. Prompt particle-γcoincidences were selected by applying a prompt gate in the time spectrum, and background from random coincidences was subtracted as shown in Fig. 2. The energy spectrum for particles as a function of scattering angle measured with one DSSSD quadrant in coincidence with γrays detected in MINIBALL is shown in Fig. 3. The contours illustrate the separation and selection for scattered projectiles and recoiling target nuclei. The innermost annular strips of the DSSSD could not be used in the further analysis because 0 2 4 6 8 10 12 14 16 Ring number 0 100 200 300 400 500 600 Particle energy [MeV] 140Sm 94Mo 0 15 30 45 60 75 90 105 120 FIG. 3. Energy spectra of particles detected in the DSSSD as a function of the laboratory scattering angle. The cuts to select between detected 140Sm projectiles and recoiling 94Mo target nuclei are marked. Ring number 1 corresponds to laboratory angle 19.7◦ and ring 16 to laboratory angle 58.4◦. 054303-3
M. KLINTEFJORD et al. PHYSICAL REVIEW C 93, 054303 (2016) 0 200 400 600 800 1000 E [keV] 100 101 102 103 104 105 counts/keV 94Mo (4+ 1→2+ 1) (2+ 2→2+ 1) (2+ 1→0+ 1) FIG. 4. Background subtracted γ-ray spectrum in coincidence with a particle in the DSSSD, with Doppler correction for 140Sm. The 2+ 1→0+ 1transition at 531 keV, the 4+ 1→2+ 1transition at 715 keV, and the 2+ 2→2+ 1transition at 460 keV are visible. The broad structure originates from the 871 keV 2+ 1→0+ 1transition in 94Mo. The purple arrow marks the 2+ 1→0+ 1transition of the potential beam contaminant 140Nd. of insufficient separation between the projectiles and target nuclei. The inverse kinematics with heavier projectiles and lighter target nuclei leads to an ambiguity where different center-of-mass scattering angles result in the same laboratory detection angle for the 140Sm projectiles, which is further complicated by the low-energy cutoff for projectiles with the largest center-of-mass scattering angles. For this reason, the detection angle of the recoiling target nuclei was used to determine the center-of-mass scattering angle. For those center-of-mass scattering angles where both projectiles and recoiling target nuclei are expected to hit the sensitive region of the DSSSD, it was required that both particles were detected in opposite quadrants of the detector. The reaction kinematics and the hit pattern in the DSSSD were furthermore used to verify that the beam was well centered. The γrays detected in MINIBALL are Doppler shifted depending on the velocity and angle with respect to the emitting particle. Because it is not possible to determine if agivenγray is emitted from a 140Sm or 94Mo nucleus, two spectra are produced with the assumption that all γ rays are emitted by either the projectiles or target nuclei and by applying the appropriate Doppler correction using the information from the DSSSD. This procedure results in two spectra where some transitions were properly Doppler corrected and appear as sharp peaks, whereas others are very broad because of a wrong Doppler correction. As long as the sharp and broad peaks are not overlapping it is possible to determine the intensities of the transitions from the respective spectra. Background subtracted spectra with Doppler correction for 140Sm and 94Mo are shown in Figs. 4and 5, respectively. The 2+ 1→0+ 1transition at 531 keV, the 4+ 1→2+ 1transition at 715 keV, and the 2+ 2→2+ 1transition at 460 keV are visible in the spectrum that is Doppler corrected for the 140Sm velocity. A hint of a transition is visible at 774 keV, marked by a purple arrow in Fig. 4. The energy corresponds to the 0 200 400 600 800 1000 E [keV] 10−1 100 101 102 103 104 counts/keV 95Mo 140 Sm (2+ 1→0+ 1) 160 200 240 500 700 900 1100 95Mo FIG. 5. Background subtracted γ-ray spectrum in coincidence with a particle in the DSSSD, with Doppler correction for the 94Mo recoils. The 2+ 1→0+ 1transition in 94Mo was observed at 871 keV. The inset shows an enlarged part of the same spectrum, where the 3/2+→5/2+ gs transition in the target contaminant 95Mo is seen at 204 keV. 2+ 1→0+ 1transition in 140Nd, which could be present as a contaminant in the beam. From the intensity of the transition this contamination is estimated to have an upper limit of 0.8% of the total beam intensity. The γ-ray energy spectrum with Doppler correction for the projectiles contains no indication of other beam contaminants. The beam composition was monitored by performing regular measurements during which the RILIS lasers were periodically switched on and off. Figure 6shows the spectra acquired during periods in which the lasers were turned on and off, respectively. Even in the spectrum with the lasers turned off only the 2+ 1→0+ 1transition in 140Sm is visible, although with much lower intensity compared to the spectrum taken with laser ionization. The acceleration of 140Sm without laser is from surface ionization. The presence of any beam contaminants should be enhanced in the spectrum taken without lasers. The absence of any other transitions further supports the conclusion that the beam was composed of at 101 102Laser ON Laser OFF 0 200 400 600 800 1000 100 101 E [keV] counts/keV FIG. 6. Gamma-ray spectra obtained with and without RILIS laser ionization in a measurement during which the lasers were periodically switched on and off. The spectra are Doppler corrected for the 140Sm projectiles. 054303-4
STRUCTURE OF LOW-LYING STATES IN 140Sm . . . PHYSICAL REVIEW C 93, 054303 (2016) 500 600 700 E [keV] 10−1 100 101 102 103 104 counts/4keV (125◦<θ<112◦) 500 600 700 E [keV] (112◦<θ<95◦) 500 600 700 E [keV] (95◦<θ<82◦) 500 600 700 E [keV] (82◦<θ<71◦) 500 600 700 E [keV] (71◦<θ<63◦) FIG. 7. Gamma-ray spectra for five separate ranges of center-of-mass scattering angles with Doppler correction for γemission from the 140Sm projectiles. least 99.2% 140Sm during the measurements with the lasers switched on. An additional germanium detector was placed behind the beam dump downstream from MINIBALL to monitor the γ-ray spectra following the βdecay of the beam particles. The spectra taken with this detector show no evidence for any radioactive beam contaminants. The small possible 140Nd contaminant was considered negligible, and all further analysis was performed under the assumption that the 140Sm beam was pure. Figure 5shows the total γ-ray spectrum with Doppler correction for the recoiling 94Mo target nuclei. The 2+ 1→0+ 1 transition in 94Mo at 871 keV is clearly visible, whereas the transitions in 140Sm appear as broad structures. Closer inspection reveals a weak line at 204 keV. This peak is most likely from the 3/2+→5/2+ gs transition in 95Mo, which could be present as a small isotopic contamination in the target. This interpretation is supported by the fact that the same weak transition was also observed in previous experiments using the same target foil [29]. Because the electromagnetic matrix elements are well known for both 94Mo [30] and 95Mo [31], the amount of 95Mo in the target can be determined from the Coulomb excitation analysis, as will be discussed below. III. COULOMB EXCITATION DATA ANALYSIS The analysis of the Coulomb excitation data and extraction of electromagnetic matrix elements utilizes the angular dependence of the differential Coulomb excitation cross sections. For this purpose, the data were subdivided into various ranges of scattering angles as measured with the DSSSD. It was found that a division into five angular bins represents a good compromise between the maximum number of data points for differential cross sections and the minimum level of statistics in the spectra corresponding to each angular bin. The resulting spectra for five angular ranges and with Doppler correction for γ-ray emission from the 140Sm projectiles are shown in Fig. 7. The spectra reveal how the relative strengths of the 4+ 1→2+ 1and 2+ 2→2+ 1transitions, which require two-step excitations, change with scattering angle compared to the 2+ 1→0+ 1transition. The measured intensities for the three observed transitions in 140Sm, the 2+ 1→0+ 1transition in 94Mo, and the 3/2+ 1→5/2+ gs transition in the target contaminant 95Mo are listed in Table Ifor five angular ranges. The coupled channel code GOSIA [32,33] was used to extract the electromagnetic matrix elements. The program combines semiclassical Coulomb excitation calculations with a multidimensional fitting procedure of the matrix elements. In this procedure, the set of matrix elements is found that best reproduces the measured γ-ray intensities observed for the different ranges of scattering angles, taking into account the geometry and efficiency of both particle and γ-ray detectors. Known lifetimes, branching ratios, and mixing ratios can be included in the χ2minimization. The γ-ray yields are obtained by integrating the Coulomb excitation cross section over the range of scattering angles covered by the experiment and integrating over the range of projectile energies resulting from the energy loss in the target. The measured γ-ray intensities were corrected for the relative efficiency values obtained from source calibrations. Finally, the correlated uncertainties were TABLE I. Measured γ-ray intensities for all observed transitions for the five ranges of center-of-mass scattering angles. Values are rounded to two significant figures in the uncertainty. Transition [63◦,71 ◦][71 ◦,82 ◦][82 ◦,95 ◦][95 ◦, 112◦] [112◦, 125◦] 140Sm 2+ 1→0+ 110200 ±140 13840 ±170 14350 ±170 13780 ±170 6860 ±120 140Sm 4+ 1→2+ 1118 ±18 209 ±24 286 ±31 389 ±34 199 ±23 140Sm 2+ 2→2+ 147 ±22 150 ±33 239 ±58 306 ±60 300 ±110 94Mo 2+ 1→0+ 1743 ±39 1073 ±47 1213 ±50 1090 ±47 543 ±34 95Mo 3/2+ 1→5/2+ gs 175 ±40 197 ±45 249 ±43 224 ±53 179 ±62 054303-5
M. KLINTEFJORD et al. PHYSICAL REVIEW C 93, 054303 (2016) calculated for the set of reduced transitional and diagonal matrix elements. To convert the measured γ-ray intensities into absolute cross sections, it is possible to normalize to the elastic Rutherford cross section obtained from particle-singles events. However, this requires precise knowledge of the particle detector efficiency, dead time, and beam intensity. The latter is often difficult to obtain with good precision in experiments with weak radioactive ion beams. In cases where the lifetime of one or more excited states are known, the corresponding reduced matrix element can be used to obtain absolute cross sections in the normalization procedure. Without prior knowledge of matrix elements, a different normalization technique is required. The GOSIA2 code [33,34] was developed to allow for the simultaneous analysis of both projectile and target excitation, using known reduced matrix elements for the scattering partners in the normalization. The ratio of observed transitions from the projectiles Npand the target Ntis independent of the particle detection efficiency part and the time-integrated luminosity L, as seen in Eq. (2): Np Nt=Lpartbpγ(Ep)σp Lpartbtγ(Et)σt ,(2) where bpand btare the γ-ray branching ratios, γ(Ep) and γ(Et)theγ-ray efficiencies, and σpand σtthe integrated cross sections for projectile and target excitation, respectively. Two approaches were used in the data analysis from the current 140Sm Coulomb excitation experiment. Because the low-spin structure of 140Sm was initially unknown, the first approach was based on the normalization to the target excitation. After the measurement of the lifetime of the 2+ 1 state in 140Sm [15] it was also possible to use the resulting B(E2) value for normalization. A detailed description of both analysis approaches is presented below. A. Normalization to the target excitation Several criteria had to be considered for the choice of the target material in the Coulomb excitation experiment. Because the energy of the REX post-accelerator is limited to 3 AMeV, high-Zmaterials are disadvantageous because they would lead to large distances between the scattering partners and consequently to low cross sections. The mass of the target nucleus also has to be sufficiently different from the mass of the projectile to avoid ambiguities in the kinematics and ensure sufficient separation between the projectile and target nuclei in the plot of the particle energy as a function of scattering angle (c.f. Fig. 3). The energies of the γ-ray transitions in the projectile and target nuclei should be well separated to avoid overlapping peaks in the spectra. Finally, the matrix elements for the low-lying states should be well known to use the excitation of the target nucleus as normalization. It was found that 94Mo was a suitable target material fulfilling the above criteria. The relevant electromagnetic matrix elements are known from Coulomb excitation experiments with αand 16Oprojectiles [35,36]. As mentioned above, the observation of a transition at 204 keV in the spectrum that was Doppler corrected for the target recoils suggests the presence of 95Mo in the target foil. The number of 95Mo atoms N95, relative to the number of 94Mo atoms N94, in the target foil can be found as N95 N94 =Y95 Y94 95 94 σ94 σ95 ,(3) where YAand Aare the respective γ-ray yields and efficiencies for the 2+ 1→0+ 1and 3/2+→5/2+transitions in the two isotopes, and the cross sections σAfor the populations of the 2+ 1and 3/2+states that are calculated from the known reduced matrix elements. An admixture of 4.4(11)% 95Mo is found in this way, which is in good agreement with the value of 5(2)% that was found in another Coulomb excitation experiment using the same target foil [29]. An iterative procedure with alternating use of the codes GOSIA and GOSIA2 was employed to determine reduced matrix elements in 140Sm with normalization to the target excitation. The procedure, which is explained in more detail elsewhere [34], is illustrated in Fig. 8and summarized below. 0 2 0 2 4 B E2 BE2 B E2 QsQs 140 Sm 94 Mo a b c 2 0 2 4 Qs BM1 E2 B E2 B E2 BE2 140 Sm 2 0 2 4 Qs BM1 E2 B E2 B E2 0 2 4 B E2 B E2 BE2 Qs 140 Sm 94 Mo Fixed Free Spectroscopic data FIG. 8. Illustration of the iterative procedure to fit the reduced matrix elements using the codes GOSIA and GOSIA2, with parts (a), (b), and (c) corresponding to steps 2, 3, and 4 as described in the text. The level schemes indicate which matrix elements were included in the fit as free parameters, as fixed values, or as free parameters with spectroscopic data to constrain the fit. Iterations between step 3 and step 4 were performed until the solution converged. 054303-6
STRUCTURE OF LOW-LYING STATES IN 140Sm . . . PHYSICAL REVIEW C 93, 054303 (2016) TABLE II. Counts observed for the 2+ 1→0+ 1transitions in the 140Sm projectiles and the 94Mo target nuclei and their uncertainties for 10 different ranges of scattering angles in the center-of-mass frame. These are the values used in the second step of the GOSIA-GOSIA2 iteration where θc.m.<100◦. Values are rounded to two significant figures in the uncertainty. Angular range 140Sm 94Mo [95◦, 100◦] 4770 ±240 397 ±29 [90◦,95 ◦] 3290 ±160 245 ±23 [86◦,90 ◦] 4300 ±220 351 ±27 [82◦,86 ◦] 5040 ±250 450 ±31 [78◦,82 ◦] 5030 ±250 439 ±30 [75◦,78 ◦] 4320 ±230 311 ±26 [71◦,75 ◦] 4010 ±200 323 ±26 [68◦,71 ◦] 4070 ±200 310 ±26 [66◦,68 ◦] 3560 ±180 250 ±23 [63◦,66 ◦] 2610 ±130 206 ±24 (1) In the first step, the standard GOSIA code is used for 94Mo with the intensities of the 2+ 1→0+ 1transition as input data and the known reduced matrix elements included as spectroscopic data. In this way an initial set of normalization factors was obtained. (2) In the second step, the code GOSIA2 was used to simultaneously fit the reduced matrix elements in both 140Sm and 94Mo. The purpose of this step was to obtain a first estimate of the 0+ 1E22+ 1matrix element in 140Sm. Therefore only the matrix elements 0+ 1E22+ 1and 2+ 1E22+ 1and the γ-ray intensities for the 2+ 1→0+ 1transition were included for 140Sm [c.f. Fig. 8(a)]. To minimize the influence of multistep Coulomb excitation, only data for θc.m.<100◦were included in this step. With the high level of statistics for the 2+ 1→0+ 1transition, the data could be divided into 10 angular ranges for this step, resulting in a better sensitivity for the 2+ 1E22+ 1matrix element. The measured intensities for this subdivision of the data are given in Table II. With the normalization from step 1 as starting values, the χ2minimization yielded a new set of normalization factors and the 0+ 1E22+ 1and 2+ 1E22+ 1matrix elements for 140Sm. Their uncertainties were obtained from the contour for χ2 min +1 in a two-dimensional χ2map. (3) In the third step, the standard GOSIA code was used for 140Sm. The 0+ 1E22+ 1matrix element obtained in step 2 and its uncertainty were treated as known spectroscopic data, whereas all other relevant matrix elements, 2+ 1E22+ 1,2+ 1E24+ 1,2+ 1E22+ 2, 2+ 1M12+ 2, and 0+ 1E22+ 2, were treated as free parameters [c.f. Fig. 8(b)]. In this step the γ-ray intensities from the division into five bins covering the entire angular range (c.f. Table I)wereusedto ensure sufficient statistics for the 4+ 1→2+ 1and 2+ 2→ 2+ 1transitions. An upper limit was included for the unobserved 2+ 2→0+ 1transition. This step yielded a first realistic estimate of all relevant reduced matrix elements in 140Sm. 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00 FIG. 9. Result of the χ2minimization for the 0+ 1E22+ 1and 2+ 1E22+ 1matrix elements in 140Sm obtained after the last iteration of step 4 of the fitting procedure using target normalization. Note that the final uncertainties of all matrix elements were obtained after one more iteration of step 3. (4) In the fourth step, the code GOSIA2 was again used for simultaneous χ2minimization of reduced matrix elements in 140Sm and 94Mo. Only the 0+ 1E22+ 1and 2+ 1E22+ 1matrix elements in 140Sm were treated as free parameters; all other matrix elements for 140Sm were fixed to the values from the previous step [c.f. Fig. 8(c)]. The γ-ray intensities from the division into five angular ranges were included for all observed transitions. This step yielded more realistic values for 0+ 1E22+ 1and 2+ 1E22+ 1, because effects from coupling to higher-lying states were taken into account. Uncertainties for the free matrix elements were again taken from the χ2 min +1 contour in the χ2map as shown in Fig. 9. In addition, a new set of normalization factors was obtained. Steps three and four of the GOSIA-GOSIA2 iteration procedure were then repeated until the final solution stabilized. Overall uncertainties of all determined matrix elements were calculated by using the GOSIA code as the last stage of the data analysis. The resulting reduced matrix elements are presented in Table III. Reduced transition probabilities and spectroscopic quadrupole moments can be extracted from the transitional and diagonal matrix elements, respectively, using the following TABLE III. Reduced matrix elements for 140Sm and associated B(E2) values and spectroscopic quadrupole moment with correlated errors obtained with the target normalization approach. IiIfIfE2Ii[eb] B(E2; Ii→If)[e2b2] 2+ 10+ 11.11+0.03 −0.03 0.25+0.02 −0.01 4+ 12+ 11.63+0.05 −0.05 0.30+0.02 −0.02 2+ 22+ 11.33+0.08 −0.09 0.35+0.05 −0.05 II||E2||I[eb] Qs(I)[eb] 2+ 1+0.03+0.54 −0.20 +0.02+0.41 −0.15 054303-7
M. KLINTEFJORD et al. PHYSICAL REVIEW C 93, 054303 (2016) TABLE IV. Reduced matrix elements for 140Sm and associated B(E2) values and spectroscopic quadrupole moment with correlated errors obtained with the lifetime normalization approach. IiIfIf||E2||Ii[eb] B(E2; Ii→If)[e2b2] 2+ 10+ 11.02+0.04 −0.03 0.21+0.02 −0.01 4+ 12+ 11.61+0.05 −0.05 0.29+0.02 −0.02 2+ 22+ 11.32+0.08 −0.09 0.35+0.04 −0.05 IIE2I[eb] Qs(I)[eb] 2+ 1−0.17+0.51 −0.19 −0.13+0.38 −0.14 relations: B(E2; Ii→If)=|If||E2||Ii|2 2Ii+1,(4) Qs(I)=16π 5II20|II √2I+1IE2I,(5) where II20|IIis a Clebsch-Gordan coefficient. The data, and by consequence also the χ2minimization, was very insensitive to the 2+ 2M1|2+ 1matrix element, and no reliable value could be extracted. The 2+ 2E20+ 1matrix element was also included in the analysis together with an upper limit for the intensity of the transition, which yielded an upper limit for the transition strength, B(E2; 2+ 2→0+ 1)<0.001 e2b2. B. Normalization to the lifetime of the 2+ 1state The lifetime of the 2+ 1state in 140Sm was recently measured to be 9.1(6) ps in an experiment using the recoil-distance Doppler shift technique [15]. The resulting matrix element, 0+ 1E22+ 1=1.03(3) eb, can be used to normalize the Coulomb excitation data instead of normalizing to the excitation of the 94Mo target nuclei. In this case, the lifetime is included as an additional data point in the χ2minimization within the standard GOSIA code. The χ2minimization is equivalent to step 3 in the iterative procedure described in Sec. III A and illustrated in Fig. 8. The reduced matrix elements obtained in this way are presented in Table IV. Note that the obtained matrix element 0+ 1E22+ 1differ slightly from the value corresponding to the lifetime used as normalization. This is possible because the matrix element is allowed to vary in the χ2minimization to best fit all available data. The resulting B(E2; 2+ 1→0+ 1) value reproduces the value from the lifetime measurement and is slightly smaller than the value obtained using the target normalization approach. It is interesting to note that the matrix elements connecting the 2+ 1state with the 2+ 2and 4+ 1states are hardly affected and the values obtained with the lifetime normalization are almost identical to the ones obtained with target normalization. The quadrupole moment for the 2+ 1state becomes slightly more negative when normalizing to the lifetime. However, the value is still rather small and the two results agree well within their uncertainty. The small discrepancy between the two normalization approaches for the 2+ 1E20+ 1matrix element could be from unaccounted-for systematic errors. One possible source for such errors could be unknown target impurities. The discrepancy could also be from systematic errors for the lifetime of the 2+ 1state in 140Sm or for the matrix elements in the 94Mo target nucleus. C. State at 990 keV In an earlier β-decay experiment the state at 990-keV excitation energy was tentatively assigned to have spin parity Iπ=(0+)[13], but a more recent experiment revised this result and firmly assigned spin parity Iπ=2+to this state [14]. In the early stages of the analysis of the present Coulomb excitation experiment, the spin assignment for the state at 990 keV was not yet resolved, and the complete analysis, using both target and lifetime normalization approaches as described above, was performed with the assumption that the state at 990 keV had spin parity 0+. The results concerning the 2+ 1and 4+ 1states were almost identical to the ones presented in Tables III and IV. However, the 0+ 2E22+ 1matrix element yielded B(E2; 0+ 2→2+ 1)=1.02(15) e2b2, which corresponds to 236 Weisskopf units. This very large transition probability was difficult to understand, and motivated the new experiment to measure the spin of the state at 990 keV using γ−γangular correlations. This experiment also found that the 2+ 2→2+ 1 transition is of almost pure E2 character with only a very small M1 admixture [14]. IV. DISCUSSION The values using the target normalization approach are in good agreement with those obtained by normalizing to the measured lifetime of the 2+ 1state. Only for the 2+ 1E20+ 1reduced matrix element is a discrepancy of 1.8σfound between the two techniques. Both the target and lifetime normalization techniques rely on data from independent measurements. The former approach relies on reduced matrix elements for the 94Mo target nucleus measured in separate Coulomb excitation experiments [35,36], whereas the latter relies on the lifetime of the 2+ 1state in the 140Sm projectiles from a recoil-distance Doppler shift measurement [15]. Without any obvious weaknesses in either approach or independent measurement, it is difficult to choose which results should be trusted more. We therefore adopt the average values from the two normalization methods for the following discussion. The adopted B(E2) values are shown in Table Vtogether with results from various theoretical calculations. The experimental excitation energies of the states are compared to the theoretical calculations in Fig. 10. A. Geometric models The spectroscopic quadrupole moment for the 2+ 1state is consistent with zero, although the uncertainty is large. The spherical shape is inconsistent with an interpretation of the ground-state band as a rotational excitation with axial symmetry. An average spherical shape could indicate a quadrupole vibrational nature of the 2+ 1state. However, the B(E2; 4+ 1→2+ 1) value is only insignificantly larger than the B(E2; 2+ 1→0+ 1) value, and not twice as large as would be required for a harmonic vibration. The energy 054303-8