In-beam γ-ray spectroscopy of 136Te at relativistic energies

PHYSICAL REVIEW C 99, 034306 (2019) In-beam γ-ray spectroscopy of 136Te at relativistic energies V. Vaquero,1A. Jungclaus,1,*P. Doornenbal,2K. Wimmer,3,2A. M. Moro,4K. Ogata,5T. Furumoto,6S. Chen,2,7E. Nácher,1 E. Sahin,8Y. Shiga,9D. Steppenbeck,2R. Taniuchi,2,3Z. Y. Xu,10 T. Ando,3H. Baba,2F. L. Bello Garrote,8S. Franchoo,11 K. Hadynska-Klek,8A. Kusoglu,12,13 J. Liu,10 T. Lokotko,10 S. Momiyama,3T. Motobayashi,2S. Nagamine,3N. Nakatsuka,14 M. Niikura,3R. Orlandi,15 T. Y. Saito,3H. Sakurai,2,3P. A. Söderström,2G. M. Tveten,8Zs. Vajta,16 and M. Yalcinkaya12 1Instituto de Estructura de la Materia, CSIC, E-28006 Madrid, Spain 2RIKEN Nishina Center, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan 3Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo, Tokyo 113-0033, Japan 4Departamento de FAMN, Universidad de Sevilla, Apartado 1065, E-41080 Sevilla, Spain 5Research Center for Nuclear Physics, Osaka University, Ibaraki 567-0047, Japan 6Graduate School of Education, Yokohama National University, Yokohama 240-8501, Japan 7School of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Bejing 100871, People’s Republic of China 8Department of Physics, University of Oslo, NO-0316 Oslo, Norway 9Department of Physics, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima, Tokyo 172-8501, Japan 10Department of Physics, The University of Hong Kong, Pokfulam, Hong Kong 11Institut de Physique Nucléaire Orsay, IN2P3-CNRS, F-91406 Orsay Cedex, France 12Department of Physics, Faculty of Science, Istanbul University, Vezneciler/Fatih, TR-34134 Istanbul, Turkey 13ELI-NP, Horia Hulubei National Institute of Physics and Nuclear Engineering, RO-077125 Magurele, Romania 14Department of Physics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan 15Advanced Science Research Center, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan 16MTA Atomki, P.O. Box 51, Debrecen H-4001, Hungary (Received 18 September 2018; revised manuscript received 30 November 2018; published 5 March 2019) The reduced transition probability B(E2; 0+ 1→2+ 1) to the first excited 2+state of the neutron-rich nucleus 136Te, with two protons and two neutrons outside the doubly magic 132Sn core, was measured via Coulomb excitation at relativistic energies at the RIKEN Radioactive Isotope Beam Factory. A value of B(E2) = 0.191(26) e2b2was extracted from the measured inelastic scattering cross section on an Au target taking into account the contributions from both Coulomb and nuclear excitations. In addition, an upper limit for the transition strength to a 2+state of mixed-symmetry character in the excitation energy range of 1.5–2.2 MeV was determined and compared to the predictions of various theoretical calculations. Because of the high statistics gathered in the present experiment the error of the deduced B(E2) value is dominated by the systematic uncertainties involved in the analysis of Coulomb excitation experiments at beam energies around 150 MeV/u. Therefore, the latter are for the first time assessed in detail in the present work. DOI: 10.1103/PhysRevC.99.034306 I. INTRODUCTION Since the pioneering study of the neutron-rich Te isotopes by Radford and collaborators [1] using low-energy Coulomb excitation of radioactive beams in inverse kinematics at the Holifield Radioactive Ion Beam Facility (HRIBF) of the Oak Ridge National Laboratory (ORNL) more than 15 years ago, significant theoretical effort was devoted trying to achieve a better understanding of these nuclei close to the doubly magic 132Sn. In particular the low value of the reduced transition probability to the first excited 2+state of 136Te at an excitation energy of Ex=607 keV, B(E2; 0+ 1→2+ 1)=0.103(15) e2b2[in the following abbreviated B(E2)], which implied *[email protected] a significant asymmetry of this quantity with respect to the N=82 shell closure in the chain of Te isotopes [for 132Te a value of B(E2) =0.172(17) e2b2was measured in the same work], was considered as a real surprise at that time. Later this low B(E2) value was confirmed by the preliminary results of a fast timing experiment performed at ISOLDE which yielded B(E2) =0.122(24) e2b2[2]. In 2011 it was reported that the data analysis, which led to the results presented in Ref. [1], was based on an erroneous assumption on the target thickness [3]. Consequently, corrected B(E2) values were quoted for 132,134,136Te which, although slightly larger as compared to Ref. [1][B(E2) =0.216(22) e2b2for 132Te and B(E2) =0.122(18) e2b2for 136Te], still reflected the asymmetry mentioned above. While shell model calculations were not able to reproduce this peculiar behavior of the E2 strength [4], the calculations performed by Terasaki et al. 2469-9985/2019/99(3)/034306(14) 034306-1 ©2019 American Physical Society V. VAQ UERO et al. PHYSICAL REVIEW C 99, 034306 (2019) using the quasiparticle random phase approximation (QRPA) traced it to a reduced neutron pairing above the N=82 gap which causes a neutron dominance in the wave function of the 2+ 1state of 136Te [5]. Very recently a new measurement was reported upon [6], performed again at the HRIBF using Coulomb excitation in inverse kinematics. This time, however, a heavier titanium target was used as compared to the carbon target which had been employed in the first experiment. The new value of B(E2) =0.181(15) e2b2is in clear conflict with the previously reported results. In view of this inconsistent body of experimental information a re-measurement of the B(E2; 0+ 1→2+ 1) value in 136Te using an independent approach seemed highly desirable. We therefore conducted an experiment at the Radioactive Isotope Beam Factory (RIBF), operated by the RIKEN Nishina Center and the Center for Nuclear Study of the University of Tokyo, using the technique of Coulomb excitation at relativistic energies. An additional motivation for this measurement was the search for an excited 2+state of mixed proton-neutron symmetry in 136Te, which several theoretical studies predict to exist in the excitation energy range of 1.5–2.2 MeV [4,7–9]. The study of the decay properties of such a 2+ ms state, the isovector analog of the 2+ 1level, in 136Te, in comparison to those of the recently observed 2+ ms state in 132Te [3], constitutes an alternative approach to probe the proton-neutron balance of the nuclear wave function. Note that at relativistic energies the Coulomb excitation cross section for a 2+state is nearly independent on the excitation energy. Therefore, the population of higher-lying excited 2+states in this experiment is favorable as compared to the studies using low-energy Coulomb excitation, in which the cross section for the excitation of a 2+level decreases with its excitation energy. Finally, the high statistics gathered in the present experiment allowed one for the first time to evaluate in detail the validity of the chosen analysis approach. The latter will be described in detail in this article to serve as a guideline for the evaluation of the different systematic uncertainties involved in the analysis of other experiments using the same technique but accumulating less statistics. II. EXPERIMENT The experiment was carried out at the RIBF at RIKEN. A primary beam of 238U at 345 MeV/u bombarded a 4-mm- thick beryllium target located at the entrance of the BigRIPS fragment separator [10]. The fission products around 136Te were selected and purified by employing the Bρ-E-Bρ method through a combination of magnetic rigidity (Bρ) selection and two wedge-shaped aluminium degraders. The particle identification was performed on an event-by-event basis using the E-Bρ-TOF method, where the energy loss E was measured by an ionization chamber located at the focal plane F7, Bρwas determined from position measurements using parallel plate avalanche counters (PPACs), and the time of flight (TOF) was measured with two plastic scintillators located at the focal points F3 and F7. The atomic number (Z) and the mass-over-charge (A/Q) ratio of each ion were determined with this method [11]. The primary beam intensity 2.56 2.58 2.6 2.62 2.64 2.66 2.68 49 50 51 52 53 54 55 1 10 2 10 3 10 2.56 2.58 2.6 2.62 2.64 2.66 2.68 2.7 2.72 2.74 50.5 51 51.5 52 52.5 53 53.5 1 10 2 10 aoq_z_ZD[8] 2.62 2.6 (a) (b) 136Te 136Te51+ 136Te50+136Te52+ Atomic Number Z Mass to Charge Ratio A/Q FIG. 1. Particle identification plots for (a) BigRIPS and (b) the ZeroDegree spectrometer requiring the identification of 136Te ions in BigRIPS obtained with the Au target. Note that the 136Te ions were observed in different charge states in ZeroDegree. was kept below 2.5 pnA to limit the counting rates in the beam detectors, in particular the ionization chambers, to such a level that a clean particle identification can be achieved. The particle identification plot obtained in this way is shown in Fig. 1(a). After the selection and identification, the secondary beams were transported to the focal point F8 where they impinged in two different runs on reaction targets consisting of 950 mg/cm2Au and 535 mg/cm2C, respectively. In total 2.36 ×108136Te ions interacted with the Au target while 6.72 ×107impinged on the C target. The high-ZAu target (Z=79) was used to induce Coulomb excitation, while the low-ZC target (Z=6) allowed one to extract the nuclear contribution to the inelastic scattering cross section measured with the Au target. At the center of the target, the energies of the 136Te ions were 139 MeV/u (corresponding to β=0.493) and 140 MeV/u(β=0.494) for the Au and C targets, respectively [165 (110) and 165 (112) MeV/u before (after) the target]. The scattering angles of the elastically and inelastically scattered ions were measured with two PPACs installed upstream and one PPAC installed downstream of the reaction target. The reaction products were identified by the ZeroDegree spectrometer [10] using again the previously described E-Bρ-TOF method. Figure 1(b) shows the ZeroDegree particle identification following the interaction of 136Te ions with the Au target. Note that the 136Te ions were 034306-2 IN-BEAM γ-RAY SPECTROSCOPY OF 136Te AT … PHYSICAL REVIEW C 99, 034306 (2019) detected in the ZeroDegree spectrometer in three different charge states, namely 50% fully stripped, 42% hydrogenlike, and 8% heliumlike (the corresponding numbers for the C target are 64%, 33%, and 3%, respectively). To measure γrays emitted following the decay of excited states of the reaction products, the target was surrounded by the DALI2 spectrometer [12], a high-efficiency γ-ray detector array consisting of 186 NaI(Tl) detectors covering angles from 20◦to 150◦. To reduce the low-energy bremsstrahlung background, the beam pipe at the F8 focus was enclosed by 1-mm lead and 1-mm tin shields. A DALI2 energy calibration was performed using 60Co, 88Y, and 137Cs sources. The fullenergy-peak efficiency and energy resolution (FWHM) were obtained to be around 15% and 6%, respectively, at 1.33 MeV (60Co). This efficiency value is in good agreement with simulations performed using the GEANT4 code [13]. To reduce the dead time of the data acquisition system, during the present experiment only the 92 NaI(Tl) crystals placed at forward angles θ<60◦in the laboratory frame (layers 10 and 11 plus the forward wall [12]) were used. In this angular range, because of the Lorentz boost and the background properties, the peak-to-background ratio was largest. Considering only this subarray and assuming prompt emission, the efficiency reduced from 24% to 13% for a γray with an energy of 600 keV emitted by ions moving with a velocity of β=0.5. To increase the detection efficiency for high-energy γrays and to improve the peak-to-total ratio over the full energy range an add-back algorithm was applied for the data taken with the C target. All energy depositions registered in NaI crystals within a range of 15 cm from the center of the crystal with the highest energy signal were summed. Doppler correction was then performed assuming that the largest energy deposition corresponds to the first interaction of the γray in the array and using the midtarget velocity. Add-back was applied to increase the statistics of the γ-ray spectra and in particular for the analysis of γγ coincidences. However, all cross sections reported in the present work were determined from γ-ray spectra without add-back. The reason for that is that the γ-ray efficiency applying the add-back algorithm strongly depends on the background which is not included in the GEANT4 simulations. III. RESULTS A. γ-ray spectra and level scheme The Doppler-shift corrected γ-ray spectrum from inelastic scattering of 136Te on the C target is shown in Fig. 2(a).Five lines at energies around 330, 400, 600, 810, and 960 keV are visible in this spectrum. From spontaneous fission and β-decay studies [14–16], γrays with 353, 423, and 607 keV are known to form the 6+ 1→4+ 1→2+ 1→0+ 1sequence in 136Te and we therefore identify the first three lines in the spectrum of Fig. 2(a) with these transitions. Furthermore, a 962-keV γray was observed in Ref. [15] and assigned as decaying from a (2+ 2) state at 1568 keV to the 2+ 1level at 607 keV. Most probably this transition corresponds to the highest-energy line observed in Fig. 2(a). In addition, aγray with an energy of 810(15) keV is observed for counts/20 keV 10 2 10 3 10 Energy (keV) 500 1000 1500 2000 counts/20 keV 1 10 2 10 (a) (b) FIG. 2. (a) Doppler-shift corrected γ-ray spectrum from inelastic scattering of 136Te on the C target. The fit to the experimental spectrum is shown as a thick black line which is the sum of the background (blue dashed line) and the simulated DALI2 response for γrays with energies of 353, 423, 607, 810, and 962 keV (red dashed lines). No cut on the γ-ray multiplicity was applied. (b) Same as (a), but for the one-neutron transfer reaction C(137Te,136Te). Here, only events with multiplicity Mγ<4 are considered. In both parts of the figure add-back was applied. the first time in the present experiment. The background in the spectrum shown in Fig. 2(a) can be parametrized by the sum of two exponential functions cut off at low energy with an error function. The experimental spectrum is then nicely reproduced by the sum of this background and the simulated response function of the DALI2 array for γrays with energies of 353, 423, 607, 810, and 962 keV. Note that the feeding of the 2+ 1level from the 4+ 1state is simulated as a cascade because the finite lifetime of the 4+ 1state (see below) affects the position of the line corresponding to the 2+ 1→0+ 1transition. As shown in Fig. 2(b),thesamefiveγ transitions are also observed following the population of 136Te via the one-neutron knockout reaction from 137Te, although with different relative intensities. A comparison between the two spectra shown in Fig. 2nicely illustrates the very different shape of the background, in particular at low energy, in these two reaction channels leading to the same final nucleus. To obtain information about the placement of the new 810- keV transition in the level scheme of 136Te, γγ-coincidence spectra were produced using the data from inelastic scattering with a gate on either the 607-keV, 2+ 1→0+ 1transition or the 962-keV, (2+ 2)→2+ 1transition; see Fig. 3. Because the moderate energy resolution of DALI2 does not allow one to 034306-3 V. VAQ UERO et al. PHYSICAL REVIEW C 99, 034306 (2019) FIG. 3. γγ-coincidence spectra for 136Te on the C target with gate on (a) the 607-keV, 2+ 1→0+ 1transition and (b) the 962-keV, (2+ 2)→2+ 1transition. In both parts of the figure add-back was applied and only events with multiplicity Mγ<6 were considered. perform a clean background subtraction, in addition to the lines corresponding to the 353-, 423-, 810-, and 962-keV transitions, also one at 607 keV is observed in the spectrum shown in Fig. 3(a). This self-coincidence has its origin in the contributions from the Compton background of the higher-energy transitions to the energy gate on the 607-keV line (compare Fig. 2). The gate on the 962-keV transition, in contrast, is expected to be much cleaner because of the lower background at higher energies and the fact that no γrays are observed above 1 MeV. The coincidence spectrum in Fig. 3(b) shows that in addition to the 607-keV ground-state transition also the new 810-keV transition is observed in coincidence with the 962-keV line suggesting its placement on top of the (2+ 2) state as shown in Fig. 4. Included in Fig. 4is also the relative feeding of the excited states of 136Te populated via either inelastic scattering or one-neutron knockout. Note that the 4+ 1and 6+ 1yrast states are stronger populated relative to the 2+ 1state in the one-neutron knockout reaction while the population of the yrare (2+ 2) level is comparable in the two reactions. The Doppler-corrected γ-ray spectrum measured in coincidence with 136Te ions detected in both BigRIPS and the ZeroDegree spectrometer for the Au target is shown in Fig. 5(a). Only a single line corresponding to the decay of the first excited 2+state at 607 keV is observed in the energy range up to 2 MeV. Because for the relativistic beam energies used in the present experiment the probability for multistep Coulomb excitation is very small, the nonobservation of the transitions emitted in the decay of the 4+ 1and 6+ 1states is (2 + 2 ) 6 + 4 + 2 + 0 + 607(8) 423(7) 353(5) 962(18) 810(15) 0 607 1030 1383 1568 2378 C( 136 Te, 136 Te') C( 137 Te, 136 Te') 77(11) 54(5) 115(17) 59(6) 100(17) 100(8) 8(7) 7(4) 16(6) 22(3) FIG. 4. Level scheme of 136Te including the new transition with an energy of 810(15) keV (see text for details). All energies are quoted in keV. The feeding (normalized to that of the first excited 2+state) of all excited states of 136Te populated in the present experiment via the inelastic scattering (one-neutron knockout) reaction on a C target is quoted above (below) each level. expected. However, a second 2+state could have been excited and its decay observed in the present experiment if the B(E2) transition probability would have been sufficiently large. As mentioned in the introduction several theoretical calculations predict the existence of an excited 2+state with mixed proton-neutron symmetry in 136Te in the excitation energy range 1.5–2.2 MeV. Such a mixed-symmetry 2+ ms state is expected to decay via a strong M1 transition to the 2+ 1and a weak E2tothe0 + 1level. As illustrated by the difference between the experimental spectrum and the fitted DALI2 response shown in Fig. 5(b), in addition to the 607-keV ground-state transition no additional γray is observed in the energy range up to 2 MeV in the present experiment following the excitation of the 136Te beam on the Au target. In particular, we note that the 962-keV (2+ 2)→2+ 1transition, which was observed with the C target (see Fig. 2), is absent in the spectrum shown in Fig. 5(a). To optimize the resolution for the 607-keV line in this spectrum Doppler correction was performed using β=0.448 corresponding to the velocity of the 136Te ions behind the target. However, the search for additional lines in the spectrum was performed for a wide range of βvalues. Based on Monte Carlo simulations and the difference spectrum shown in Fig. 5(b) observational lower limits of 10% and 14% relative to the intensity of the 607-keV line have been determined for hypothetical γ-ray energies of 0.9 MeV and 1.6 MeV, respectively. The estimation of B(E2; 0+ 1→2+ ms) limits from these values will be discussed in Sec. VII. Finally, we note in passing that in the present experiment, in addition to the 607-keV 2+ 1→0+ 1transition, two γrays with energies of 3.6(1) and 4.2(1) MeV, respectively, have been observed for the first time. They depopulate a state at an excitation energy of 4.2(1) MeV and the 3.6(1) MeV γ ray corresponds to a decay branch to the 2+ 1state. This new excited state will be discussed in detail in a forthcoming publication. It is sufficient to mention here that this indirect feeding of the 2+ 1level will correctly be taken into account in the determination of the B(E2; 0+ 1→2+ 1) value presented in Sec. VI. 034306-4 IN-BEAM γ-RAY SPECTROSCOPY OF 136Te AT … PHYSICAL REVIEW C 99, 034306 (2019) counts/10 keV 1000 2000 3000 4000 5000 6000 Relat. Dev. Ener gy ( keV ) 400 600 800 1000 1200 1400 1600 1800 2000 1 0.5 0 0.5 1 (b) (a) FIG. 5. (a) Doppler-shift corrected γ-ray spectrum from inelastic scattering of 136Te on the Au target. The fit to the experimental spectrum is shown by the thick black line, which is composed of a two-exponential function describing the background (blue dashed line) and the simulated response function of DALI2 for the 607-keV 2+ 1→0+ 1transition (red dashed line). No cut on the γ-ray multiplicity and no add-back was applied. (b) Relative difference between the experimental and simulated spectra shown in (a). B. Direct lifetime determination based on the observed Doppler shifts Both the 2+ 1and 4+ 1states in 136Te are known to have lifetimes of tens of picoseconds [6]. This implies that the 607- and 423-keV γrays are emitted mainly after the ions already left the target. If Doppler correction is performed using the midtarget velocity and assuming emission from the center of the target, these lines are shifted to smaller energies as compared to the nominal values (all detectors are placed at θ<60◦). Therefore, as already was demonstrated in Ref. [17], estimates of the excited-state lifetimes can be obtained from a comparison between the experimental line shapes and Monte Carlo simulations. In Fig. 6(a) the experimental line shape of the 607-keV line measured with DALI2 for the Au target is compared to GEANT4 simulations assuming a prompt decay of the 2+ 1state. Clearly the experimental line shape is not reproduced by these simulations. Only when a finite lifetime around τ(2+ 1)=33 ps is assumed, a good agreement is obtained [see Fig. 6(b)]. In the spectrum taken with the C target in addition to the 607-keV line also the 423-keV transition emitted in the decay of the 4+ 1state is observed [compare Fig. 2(a)]. Keeping the lifetime of the 2+ 1state fixed, τ(2+ 1)=33 ps, and considering both a direct population of the 2+ 1state as well as a cascade of two γrays emitted following the population of the 4+ 1level a longer lifetime around 98 ps is needed for the 4+ 1state to describe the experimental spectrum [compare Figs. 6(c) and 6(d)]. This value has to be considered as effective lifetime of the 4+ 1state because the relative intensities quoted in Fig. 4 indicate significant feeding from the 6+ 1state. Unfortunately, 500 600 700 800 0 500 1000 1500 500 600 700 800 0 500 1000 1500 counts/5 keV (21+) = 0 ps (a) (b) (21+) = 33 ps 400 500 600 700 0 100 200 300 400 500 600 700 0 100 200 300 counts/10 keV (c) (d) eff (41+) = 0 ps eff (41+) = 98 ps Energy (keV) FIG. 6. (a) Comparison between the experimental shape of the 607-keV line for the Au target (black histogram) and GEANT4sim- ulations (black line) assuming τ(2+ 1)=0 ps; (b) same as (a) but assuming τ(2+ 1)=33 ps; (c) comparison between the experimental shapes of the 423- and 607-keV lines (black histogram) for the C target and GEANT4 simulations (black line) assuming τ(2+ 1)=33 ps and τeff (4+ 1)=0 ps, (d) same as (c) but assuming τeff (4+ 1)=98 ps. In parts (a) and (b) no add-back was applied and the γ-ray multiplicity was limited to Mγ=1 while in parts (c) and (d) add-back was applied and only events with Mγ=2 were considered. In all cases Doppler correction performed using the midtarget velocity. because of the increasing background in the low-energy region of the spectrum and the vicinity to the 423-keV line, it was not possible to deduce any information with respect to the unknown lifetime of the 6+ 1state from an analysis of the line corresponding to the 353-keV transition. Final values of τ(2+ 1)=33(15) ps and τeff (4+ 1)=98(50) ps were deduced from the experimental spectra shown in Fig. 6. From the fit of the simulated DALI2 response functions assuming vanishing excited state lifetimes to the two lines observed around 810 and 962 keV in Fig. 2(a),γ-ray energies of 810(15) and 962(18) keV have been deduced. The agreement of the latter value with the literature value of 961.72(5) keV [15] suggests that the lifetime of the (2+ 2) level at 1568 keV is short. Note that while the accuracy which can be achieved using this technique is obviously very limited when unsegmented scintillator arrays such as DALI2 are used for γ-ray detection as in the present experiment, it becomes a precision tool when position-sensitive Ge detectors are employed for in-beam spectroscopy at relativistic energies [18,19] and will show its full power with γ-ray tracking arrays such as AGATA [20] and GRETA [21]inthefuture. IV. DETERMINATION OF EXCLUSIVE SCATTERING CROSS SECTIONS To determine experimental differential inelastic scattering cross sections, the γ-ray yield has to be measured as a 034306-5 V. VAQ UERO et al. PHYSICAL REVIEW C 99, 034306 (2019) counts 5000 10000 15000 20000 gold Entries 4101786 Mean 0.6757 RMS 0.3854 (deg) lab θ 0 0.5 1 1.5 2 2.5 0 0.1 0.2 0.3 0.4 T(bin) x0.5 01234 1 10 2 10 3 10 4 10 counts (deg) lab θ tail (a) (b) FIG. 7. (a) Angular distributions of the ions which have been identified as 136Te in BigRIPS without target (red line) and for the C (blue area) and Au (gray area) targets, respectively. Note that the three curves have been scaled to the same height for better comparability. The inset shows the angular distribution of the 136Te ions for the C target [filled blue curve, same as blue curve in (a)] on a logarithmic scale in comparison to the one obtained when in addition the detection of a fully stripped 136Te ion in the ZeroDegree spectrometer is required (filled red curve). (b) Transmission curves for those 136Te ions which are detected in the ZeroDegree spectrometer in the fully stripped charge state for the C (black, multiplied by 0.5) and Au (red) targets, respectively, before (open circles) and after correction for reaction losses (bullets). Angular bins of θlab =0.15◦ were used. See text for details. function of the scattering angle. In the present experiment the latter is measured using the information from the three PPACs installed in front of and behind the target position. The proper alignment of all beam detectors used in the reconstruction of the incoming and outgoing beam trajectories was checked by confirming a flat distribution of the azimuthal scattering angle. In Fig. 7(a) the angular distributions of the 136Te ions identified in BigRIPS are shown for the runs without target (empty frame) and with the C and Au targets inserted at target position. Note that in the following the expression cross-section angular distribution always refers to dσ/dθlab [which includes the sin(θ) and corresponds to what is really measured], in contrast to the differential cross section dσ/d. All three distributions can be fitted with Gaussian curves multiplied by sin(θ) yielding width parameters σof 4.8 mrad, 5.4 mrad, and 8.8 mrad, respectively. The angular resolution measured without target reflects the uncertainty of the position measurements in the PPAC detectors. The measured value σ=4.8 mrad can be reproduced in Monte Carlo simulations assuming a position resolution of σx=σy=0.73 mm for all PPAC detectors involved in the measurement of the scattering angle. With the C and Au targets in the beam an additional contribution stemming from the angular straggling, mainly from multiple elastic scattering in the target material, leads to considerably worse angular resolutions. This angular straggling was estimated with the code ATIMA [22] based on the energy before the target and the target thickness to 2.3/8.0mradfor the C/Au targets. Combining the contributions from the position measurement and the straggling, values of 5.3/9.3 mrad are obtained in somewhat good agreement with the experimental observation. In the next step, separate γ-ray spectra were produced for different ranges of the scattering angle. To determine the cross-section angular distribution for the excitation of the 2+ 1 state, angular bins of θlab =0.15◦were used. Coincidence conditions were applied on 136Te ions in BigRIPS and on either the fully stripped or the hydrogenlike 136Te in the ZeroDegree spectrometer (compare Fig. 1). For each of these scattering-angle gated γ-ray spectra the intensity of the 607- keV line was deduced from a fit of the simulated DALI2 response function similar to the ones shown in Fig. 2for the case of the C target and Fig. 5for the case of the Au target. In the simulation of the DALI2 response 100% prolate (oblate) nuclear spin alignment was assumed for the Coulomb excitation on the Au target (the nuclear excitation on the C target) [23,24]. A systematic uncertainty of 5%, corresponding to half of the intensity difference obtained for the present detector geometry assuming either 100% prolate (oblate) alignment or no alignment at all, was considered to account for possible attenuation effects from charge state changes and γdecay behind the target. Before the cross section can be calculated for each angular bin, the absolute γyield has to be corrected for (i) the scattering-angle-dependent losses from the limited acceptance of the ZeroDegree spectrometer, (ii) losses from reactions which take place on any material in the beam line, both targets and beam detectors, between the identifications in BigRIPS and the ZeroDegree spectrometer, and (iii) the charge state fraction. An effective transmission which includes all three contributions can be extracted from the data by comparing the number of 136Te ions which are detected in the ZeroDegree spectrometer (separately for each of the charge states) to the number of 136Te ions identified in BigRIPS as a function of the scattering angle. The resulting transmission curves for the fully stripped component are shown for both the C and Au targets in Fig. 7(b). As illustrated in the inset of Fig. 7(a) for the C target, the angular distributions of the ions identified as 136Te in BigRIPS exhibit tails at large scattering angles which correspond to ions which had been identified as 136Te in BigRIPS but lost neutrons and/or protons before their scattering angle was measured in the PPACs. These tails have been parametrized, extrapolated to smaller scattering angles, and subtracted from the distributions (details are provided in Ref. [38]). Using these corrected angular distributions, new effective transmission curves have been determined as shown in Fig. 7(b). After removal of the tail, higher transmission 034306-6 IN-BEAM γ-RAY SPECTROSCOPY OF 136Te AT … PHYSICAL REVIEW C 99, 034306 (2019) 10 20 30 0.5 1 1.5 2 2.5 0 10 20 30 d /d lab lab (deg) (a) (b) FIG. 8. Experimental cross-section angular distributions measured in coincidence with the 607-keV transition in 136Te on the Au target (a) separately for the ions detected in the fully stripped (open circles) and hydrogenlike (open squares) charge states in the ZeroDegree spectrometer and (b) after averaging both components. was obtained, in particular for large scattering angles. To acknowledge the uncertainty involved in the subtraction process, an error was assumed for the experimental points at largest scattering angles which covers the full range between the lower limit of the transmission obtained before the subtraction of the tail and the maximum limit corresponding to the assumption of constant transmission over the whole angular range. Once the effective transmission T(bin) is determined, the cross-section angular distribution is obtained as dσ/dθlab(bin) =Nγ(bin) T(bin) ×Nions ×dθlab(bin) ×Ntarget , (1) where Nγ(bin) is the number of decays of the 2+ 1state (deduced from the fit to the spectrum for each angular bin), Nions is the number of 136Te ions impinging on the target (number of ions in the BigRIPS gate corrected for the downscaling factor used in the trigger), and Ntarget is the number of target atoms/area. Figure 8(a) shows the resulting crosssection angular distributions dσ/dθlab(bin) for the excitation of the 2+ 1state in 136Te on the Au target, separately for the ions detected in the fully stripped and hydrogenlike charge states, respectively, in the ZeroDegree spectrometer. A good agreement is observed so that finally for each angular bin an average value can be calculated leading to the final cross- TABLE I. Total cross sections measured in coincidence with γ rays in 136Te on C and Au targets (left) and exclusive inelastic scattering cross sections to individual excited states of 136Te (right). The quoted errors include the uncertainties related to the transmission, the number of γrays from the fit, the number of detected ions, the target thickness, and the down-scale factor of the trigger. Additional errors of 5% each are added to account for the uncertainties of the DALI2 efficiency calibration and the angular distribution (see text for details). EγσCσAu ExIπ iσCσAu (MeV) (mb) (mb) (MeV) (mb) (mb) 0.353 5.1(7) – 0.607 2+ 19.5(32) 219(23)a 0.423 10.7(11) – 1.030 4+ 15.6(13) – 0.607 23(3) 279(22) 1.383 6+ 15.1(7) – 0.810 2.1(3) – 1.568 (2+ 2) 0.7(5) – 0.962 2.8(4) – 2.378 – 2.1(3) – 3.6 –b21(3) 4.2 – – 42(4) 4.2 –b21(3) aAssuming 15(5)% feeding from high-lying 2+ xstates. bContaminated by C target excitations. section angular distribution shown in Fig. 8(b). The total cross section for the excitation of the 2+ 1state is calculated as sum over all bins, i.e., σtot =n bin=1dσ/dθlab(bin). A comparison between Figs. 7(b) and 8(b) shows that the uncertainty in the determination of the transmission in the angular range θlab >1.5◦does not significantly affect the total cross section because the cross-section angular distribution peaks at lower scattering angles. Note that because of the scattering-angle dependence of the effective transmission and the different shapes of the ion angular distributions and the cross-section angular distributions (see Figs. 7and 8), a too small cross section value is obtained when it is calculated in an integral way from the total number of γrays Nγ, and the total transmission T= NZD ions/NBR ions. In the case of the 2+ 1state in 136Te excited on the Au target, the difference amounts to 9% for the fully stripped component and 7% for the hydrogenlike ions. In cases in which the statistics is not sufficient to allow for a differential analysis according to Eq. (1), we anticipate that in view of the good agreement between experimental and theoretical crosssection angular distributions to be discussed in Sec. VI,the cross sections can be determined based on the experimental transmission curve and the calculated cross-section angular distribution. All cross-section values measured in coincidence with a discrete γtransition are summarized on the left-hand side of Table I. To deduce the exclusive excitation cross section to the 2+ 1 state from the cross sections measured in coincidence with the different γtransitions for the C and Au targets, the indirect population of this level from higher-lying excited states has to be considered. For the C target exclusive cross sections have been calculated on the basis of the level scheme presented in Fig. 4. The result is that only less than half of the observed yield of the 607-keV transition, namely σ(2+ 1)=9.5(32) mb, is from the direct excitation of the 2+ 1state, while the remaining intensity is because of feeding from the higher-lying 034306-7 V. VAQ UERO et al. PHYSICAL REVIEW C 99, 034306 (2019) states. As mentioned in the last section, two discrete γrays with energies above 3.5 MeV have been observed following the inelastic excitation of the 136Te ions on the Au target. One of them populates the 2+ 1state and consequently the cross section of 21(3) mb corresponding to this transition has to be subtracted from the 279(22) mb measured for the 607-keV γray(seeTableI). In this case the statistics was sufficient to subtract this feeding contribution in a differential way, i.e., separately for each bin of the cross-section angular distribution shown in Fig. 8(b). In addition, the contribution from unobserved feeding from higher-lying 2+states has to be taken into account. This feeding fraction was estimated in two different ways. First, this quantity was determined for the experimentally very well-studied stable N=84 isotones 142Ce and 144Nd [25]. In these nuclei, a total of 7 and 12 excited 2+states with known lifetimes, respectively, are reported in the energy range from 1.5 to 3.2 MeV. Taking into account measured half-lives and branching ratios, a feeding of 15% and 11% is obtained for the 2+ 1states in 142Ce and 144Nd, respectively. Alternatively, shell model calculations employing realistic effective interactions (see Sec. VII)have been performed to estimate the feeding from 2+ xstates to the 2+ 1level at 607 keV. In the same energy range quoted above, a total of 16 2+states are predicted to exist (see Table 5.6 of Ref. [38]) and from the calculated decay properties, a feeding fraction of 14% is deduced in nice agreement with the experimental numbers for 142Ce and 144Nd. Based on these estimates it is in the following assumed that 85(5)% of the remaining yield measured for the 607-keV γray, σ(2+ 1)= 0.85(5) ×258(22) mb =219(23) mb correspond to the direct excitation of the 2+ 1state in 136Te. V. EXTRACTION OF B(E2; 0+ 1→2+ 1)FROM THE MEASURED σ(2+ 1) In scattering off a high-Ztarget both electromagnetic and nuclear excitations can occur so that both processes, as well as the interference between them, contribute to the measured inelastic scattering cross section. Therefore, the determination of the B(E2) value from the measured cross section is not a trivial task. For Coulomb excitation experiments at intermediate or relativistic energies (with typical beam energies between 40 and 180 MeV/u) there are in general four different ways to determine the transition probability for the state of interest, e.g., B(E2; 0+→2+ 1) values, from the measured exclusive inelastic scattering cross section. In the first two, relative measurements are performed. The excitation strength is deduced either by comparison to target excitations with known transition probability (e.g., the 548-keV transition in 197Au; see examples in Ref. [26]) or relative to another nucleus excited under the same experimental conditions [27–29]. In these cases the quality of the obtained result relies mainly on the reliability of the experimental information from literature and the correct evaluation of experimental differences (with respect to transmission, feeding, efficiencies, etc.). In cases in which nuclear contributions cannot be neglected, in addition also possible differences with respect to the nuclear deformation length, δnucl,havetobe considered. Alternatively, two different approaches have been used in the literature which are based on the measurement of absolute inelastic scattering cross sections. In the analyses of experiments performed at NSCL, using beam energies in the range from 40 to 80 MeV/u, cuts on the scattering angle were applied to limit the analysis to peripheral collisions in which nuclear contributions are assumed to be negligible (“safe” impact parameter criterion touching spheres plus 2 fm); see Refs. [30,31] and overview tables in [32,33]. At the higher beam energies in the order of 150 MeV/u, which are usually employed for experiments at GSI and RIKEN [28,29,34–36], this technique is not valid any longer as will be illustrated below. In these cases, transition probabilities can only be deduced from the measured cross sections when the contributions from both the Coulomb and nuclear interactions to the total cross section are correctly accounted for. This latter approach will be discussed in detail in Sec. VI. A. The minimum impact parameter (maximum scattering angle) approach Once the angular resolution of the measurement is determined (see last section and Fig. 7) we can demonstrate why at least in the present case of 136Te measured at a midtarget energy of 139 MeV/u, but probably more in general in this energy domain, the approach to apply a cut on the scattering angle to suppress nuclear contributions to the measured cross section is no longer valid. Using the criterion which is commonly applied in the analysis of NSCL experiments, namely selecting a minimum impact parameter corresponding to touching spheres plus 2 fm, a maximum scattering angle of θmax =1.2◦in the laboratory system is calculated for the Au target. Figure 9(a) shows a schematic cross-section angular distribution, dσ/dθlab, in line with the Alder-Winther formalism [37]. Here it is assumed that all events with angles beyond θmax are absorbed, corresponding to a sharp angle cutoff in a simplistic black-disk model. In Figure 9(b),the corresponding cross-section angular distribution is shown for the case of 88Kr excited on a 209Bi target at a midtarget energy of 58.5 MeV/u which was recently discussed in Ref. [31]. In this case, a significantly larger maximum scattering angle of θmax =3.2◦is obtained. Now, to compare these theoretical curves with data, they have to be folded with the angular resolution of the experiment which in the present case amounts to σAu =8.8 mrad as discussed above. This folding is done in three dimensions taking into account independent vectors for the scattering and straggling processes (for more details see Ref. [38]). The comparison between the original and folded curves shown in Fig. 9legitimates the approach followed by the NSCL group to limit the comparison to angles below a certain limit and only consider the Coulomb part of the interaction (at least in cases in which the nuclear contributions are small; see Sec. VI). A comparison to the Fig. 3 of Ref. [31] indicates that the angular resolution in that experiment was similar to the one assumed here. Depending on the resolution indeed a maximum scattering angle can be chosen, here θ= 2.4◦[31], so that nuclear contributions and absorption effects are negligible [see green dashed line in Fig. 9(b)]. Although proven to be a valid analysis procedure it still has the drawback that for the determination of the transition probability 034306-8 IN-BEAM γ-RAY SPECTROSCOPY OF 136Te AT … PHYSICAL REVIEW C 99, 034306 (2019) 1 2 3 012345 0 2 4 6 8 lab (deg) d/d lab (a) (b) FIG. 9. Illustration of the effect of the limited experimental angular resolution on the measurement of cross-section angular distributions for (a) the reaction 136Te +197Au at 139 MeV/u discussed in the present work and (b) the reaction 88Kr +209Bi at 58.5 MeV/u[31]. The red lines correspond to cross-section angular distributions calculated within the relativistic Coulomb excitation model of Ref. [37]andcutatθmax, while the black lines show these theoretical curves after folding with the experimental angular resolution of σAu =8.8 mrad. The dashed green line indicates the more restrictive scattering-angle cut applied in the analysis presented in Ref. [31]. it takes advantage of only part of the statistics gathered in the experiment (roughly 50%). The same comparison for the case of 136Te as shown in Fig. 9(a), on the other hand, clearly demonstrates that this technique cannot be applied in the present case. To conclude, only when the safe scattering angle is large as compared to the angular resolution of the experiment, a cut on the cross-section angular distribution is a valid approach. However, for most of the experiments performed at higher beam energies around 150 MeV/uatGSI and RIKEN this is not the case. B. Consistent description of both nuclear and electromagnetic excitations with the reaction code FRESCO As was shown in the last section, in the present case it is not possible to determine a B(E2) value from the measured cross section without considering simultaneously the contributions from both Coulomb and nuclear excitations as well as possible interference effects between them. There are several reaction codes available which allow one to do that, among them ECIS [39], FRESCO [40,41], and DWEIKO [42]. ECIS and FRESCO are fully quantum-mechanical coupled-channels codes. DWEIKO is also a coupled channels code, designed for inelastic processes, which makes the additional eikonal (i.e., forward-angle, high-energy) approximation to the distorted waves to simplify its solution. The different versions of the ECIS code have widely been used in the past in the analysis of Coulomb excitation experiments [35,36,43–46], in some of these cases considering relativistic kinematics. In particular in the cases in which cross-section angular distributions have been measured with high angular resolution and thus high sensitivity to the interference pattern between the nuclear and Coulomb interactions, ECIS has proven to well describe the experimental data. Unfortunately, ECIS97 shows convergence problems when applied to heavier systems such as the reaction discussed in the present work and therefore had to be discarded. Before using instead the FRESCO code for the determination of the B(E2; 0+ 1→2+ 1) value in 136Te we investigated its capability to correctly describe some of the high-resolution measurements reported in the literature, in particular the cross-section angular distributions measured for excited states in 208Pb populated in collisions with a 17O beam at 84 MeV/u[43,46] as well as the data reported in Ref. [35]. Good agreement was found so that it seems legitimate to employ FRESCO instead of ECIS97 in the present analysis. Unfortunately no experimental information on the cross-section angular distributions for inelastic scattering were found in the literature for heavier systems and at higher beam energies. In the following results will be presented which have been obtained with a modified version of the FRESCO code [47] that takes into account relativistic kinematics. Before closing this section we would like to mention that we were not able to reproduce the cross-section angular distributions measured for the system 17O+208Pb [43,46]usingtheDWEIKO code. The analysis of both electric dipole and quadrupole states seems to indicate that, at least in the studied cases, neither the nuclear-Coulomb interferences nor the nuclear absorption are correctly treated. VI. DETERMINATION OF THE REDUCED TRANSITION PROBABILITY B(E2; 0+ 1→2+ 1) To deduce a reduced transition probability to the 2+ 1state in 136Te from the experimental exclusive cross section on the Au target determined as discussed in Sec. IV, both the nuclear and Coulomb contributions have to be considered. In all calculations presented in this section, optical potentials were used which were derived from the microscopic folding model with the complex G-matrix interaction CEG07 and a specific global density (for more details see [48]). For the Coulomb part the standard collective-model form factor was employed. Because in reactions on the C target Coulomb effects are negligible information about the nuclear deformation length can be deduced from the cross sections measured on this light target (compare Table I). The inclusive cross section of σC=23(3) mb measured for the 607-keV transition is reproduced with FRESCO using a value for the deformation length of δeff nucl =1.05(7) fm, while the exclusive cross section to the 2+ 1state, σC(2+ 1)=9.5(32) mb, is reproduced with a value of δnucl(2+ 1)=0.68(10) fm. As shown 034306-9