Enhanced Quadrupole and Octupole Strength in Doubly Magic 132Sn

© the Authors, 2018. Published version Rosiak, D.; Seidlitz, M.; Reiter, P.; Naïdja, H.; Tsunoda, Y.; Togashi, T.; Nowacki, F.; Otsuka, T.; Colò, G.; Arnswald, K.; Berry, T.; Blazhev, A.; Borge, M. J. G.; Cederkäll, J.; Cox, Daniel; De Witte, H.; Gaffney, L. P.; Henrich, C.; Hirsch, R.; Huyse, M.; Illana, A.; Johnston, K.; Kaya, L.; Kröll, Th.; Benito, M. L. Lozano; Ojala, Joonas; Pakarinen, Janne; Queiser, M.; Rainovski, G.; Rodriguez, J. A.; Siebeck, B.; Siesling, E.; Snäll, J.; Van Duppen, P.; Vogt, A.; von Schmid, M.; Warr, N.; Wenander, F.; Zell, K. O.

The first 2 þ and 3 − states of the doubly magic nucleus 132 Sn are populated via safe Coulomb excitation employing the recently commissioned HIE-ISOLDE accelerator at CERN in conjunction with the highly efficient MINIBALL array. The 132 Sn ions are accelerated to an energy of 5.49 MeV=nucleon and impinged on a 206 Pb target. Deexciting γ rays from the low-lying excited states of the target and the projectile are recorded in coincidence with scattered particles. The reduced transition strengths are determined for the transitions 0 þ g:s: → 2 þ 1 , 0 þ g:s: → 3 − 1 , and 2 þ 1 → 3 − 1 in 132 Sn. The results on these states provide crucial information on cross-shell configurations which are determined within large-scale shellmodel and Monte Carlo shell-model calculations as well as from random-phase approximation and relativistic random-phase approximation. The locally enhanced BðE2; 0 þ g:s: → 2 þ 1 Þ strength is consistent with the microscopic description of the structure of the respective states within all theoretical approaches. The presented results of experiment and theory can be considered to be the first direct verification of the sphericity and double magicity of 132 Sn. DOI: 10.1103/PhysRevLett.121.252501 Ten doubly magic atomic nuclei act as cornerstones along the whole chart of nuclei. Their basic properties like masses, binding energies, and excited states play an eminent role for a detailed understanding and theoretical description of the nuclear system. Tin has a magic number of protons (Z ¼ 50) and is the heaviest element to have two isotopes with a magic number of neutrons ( 100 Sn 50 and 132 Sn 82 ). The latter of these nuclei acts as an essential benchmark for theoretical approaches extending towards heavier and more neutron-rich systems. This region of the nuclear chart plays a critical role in the astrophysical r process, and understanding its path around 132 Sn is indispensable for the accurate description of elemental abundances in the Solar System [1]. Recent multimessenger astronomy of, e.g., kilonovae reported on observation of nucleosynthesis of medium-heavy and heavy neutronrich nuclei around N ¼ 50 and N ¼ 82 [2,3]. The persistence or disappearance of the N ¼ 82 shell in neutron-rich nuclei implies severe consequences for modeling the r-process nucleosynthesis. While the single-particle states of neighboring isotopes were studied in pioneering experiments recently [4][5][6][7][8][9], the complementary collective properties of 132 Sn are poorly understood, and experimental information on low-lying excitations is severely lacking. In particular, the collective behavior of nucleons giving rise to the simplest vibrational modes of quadrupole and octupole character is dependent on shell energies and effective interactions; thus, measuring these properties acts as a sensitive probe of shell-model (SM) calculations. Especially important are the constraints these properties provide on the extrapolation of theoretical models to neutron-rich nuclei. While nuclei around Z ¼ 50, N ¼ 82 could be treated within the SM, predictions for doubly magic 132 Sn, its excited 2 þ 1 and 3 − 1 states, and the respective electromagnetic properties were not accessible until now due to the huge valence space and computational complexity including several shells for protons and neutrons simultaneously. Models based on the (quasiparticle) random-phase approximation (RPA) have, however, been used for the description of tin isotopes, predicting a local increase of the quadrupole and octupole collectivity at 132 Sn [10][11][12]. This enhancement is explained by the excitation of a doubly magic core and the occupation of specific orbitals across a large shell gap and is a crucial feature of doubly magic nuclei. A similar behavior is observed along the lead isotopic chain [11,12] and is also expected for so far unreachable 78 Ni [13,14].
The huge experimental and theoretical interest in 132 Sn and its vicinity goes along with advanced detection techniques and new facilities for reaccelerated radioactive ion beams. The first preliminary results on Coulomb excitation of 130;132;134 Sn were obtained at HRIBF and published in conference proceedings [15][16][17][18]. The present Letter reports the results for the 2 þ 1 and 3 − 1 states in 132 Sn and their transition strengths obtained in a Coulombexcitation (CE) experiment performed at the newly commissioned HIE-ISOLDE facility at CERN [19,20]. Highresolution gamma-ray spectroscopy is employed for the unambiguous identification of the interesting transitions in 132 Sn in contrast to the former measurements. The radioactive 132 Sn was produced by irradiating a thick UC x target with 1.4-GeV protons provided by the CERN PS Booster. The average current of the pulsed proton beam amounted to 2 (μ)A. To reduce intense isobaric contamination, the isotope of interest 132 Sn was extracted as a positively charged ð 132 Sn 34 SÞ 1þ molecular beam (cf. Ref. [21]), which was then mass separated by the ISOLDE high-resolution separator (HRS). The molecular beam with A ¼ 166 was guided into a Penning trap (REXTRAP) [22], where it was accumulated, cooled, and bunched. Following break up of the molecules by charge exchange, the residual 132 Sn 1þ ions were injected into an electron-beam ion source (REXEBIS) [23] where they were charge bred for 194 ms. After a mass-overcharge separation with A=q ¼ 4.258, the 132 Sn 31þ beam was postaccelerated by the HIE-ISOLDE linear accelerator [20] and delivered with a final beam energy of 5.49 MeV=nucleon onto the secondary target inside the MINIBALL array [24]. The secondary target with a thickness of 3.1 mg=cm 2 consisted of 99.80%-enriched 206 Pb evaporated onto a 25-μg=cm 2 thin 12 C supporting foil. The average intensity of the postaccelerated ion beam amounted to approximately 3.0 × 10 5 ions=s, with an overall beamon-target time of 127 h. Scattered beam and target nuclei were detected by a highly segmented circular double-sided silicon strip detector (DSSSD), covering scattering angles between 16.2°and 52.9°in the laboratory system [24,25]. γ rays following CE of projectile and target nuclei were detected in coincidence by the MINIBALL γ-ray spectrometer, consisting of eight triple-cluster detectors in close geometry, each containing three sixfold-segmented HPGe crystals [24,26].
Accurate energy and efficiency calibrations of the HPGe detectors up to 5 MeV were achieved using 60 Co, 152 Eu, and 66 Ga sources yielding a γ-ray efficiency of 2.74(4)% at 4 MeV. The position of each individual segment of the HPGe detectors was determined utilizing Doppler-shifted γ rays of the reactions dð 22 Ne; 23 NeÞp and dð 22 Ne; 23 NeÞn. Combining the angular information of the γ rays with the momentum vector of the scattered nucleus that was detected in the DSSSD in coincidence, the final relative energy resolution of the γ-ray transitions from CE amounted to 1.1% (FWHM) after Doppler correction. This ensures a clean separation and identification of different γ-ray transitions of 132 Sn even at energies above 4 MeV.
The exact beam composition was determined using β-delayed γ-ray events as well as prompt γ-ray events after CE. No isobaric contaminations stemming from 132 Cs and 132 In were observed by studying β decays. Moreover, timedependent intensity ratios of decays of mother and daughter nuclei in the decay chain of 132 Sn during the beam time showed no evidence for 132 I in the beam. γ-ray spectra obtained from prompt CE events were particularly clean from 132 Te and 132 Xe [cf. Fig. 1(a)]. Considering their known transition probabilities [27], both isotopes were excluded from being beam contaminants. The contribution of 132 Ba to the beam composition was determined from the measured 2 þ 1 → 0 þ g:s: transition at 464 keV and its known BðE2Þ value [27]. The amount of 132 Sb in the beam was determined relative to the yield of 132 Sn via a dedicated implantation and subsequent decay measurement at the PHYSICAL REVIEW LETTERS 121, 252501 (2018) 252501-2 target position inside the MINIBALL setup. The calculated ratio amounted to Ið 132 SbÞ=Ið 132 SnÞ ¼ 0.16ð1Þ. As the mass number of 166 Yb equals the mass number of the extracted molecular 132 Sn 34 S beam, both ion species were transported through the HRS into the REXTRAP and the REXEBIS. Moreover, a similar A=q ratio of 4.256 for 166 Yb 39þ permitted injection into the postaccelerator. Accordingly, multiple yrast-band transitions of 166 Yb were observed in the CE spectra [see Fig. 1(a)] validated via mutual particle-γγ coincidences. The contribution of 166 Yb to the beam composition was determined using its known BðE2Þ values [28]. Overall, the radioactive ion beam was composed of 82(2)% 132 Sn, 13(1)% 132 Sb, 0.3(1)% 132 Ba, and 5(2)% 166 Yb.
To ensure pure electromagnetic excitation, the minimum distance between the nuclear surfaces must exceed 5 fm [29]. Thus, only scattering angles up to 67.6(1)°in the center-of-mass frame were included in the analysis. Doppler correction was employed for beamlike and targetlike nuclei using kinematic reconstruction. The Dopplercorrected, background-subtracted γ-ray spectra, which were detected in coincidence to scattered A ¼ 132, 166 particles, are shown in Figs. 1(a)-1(d). Pb, the error is less than 3%. The 3 − 1 → 2 þ 1 transition of 132 Sn at 310.7 keV was not observed in this work. Its low intensity was expected due to the small branching known from β-decay studies [27]. Reduced transition probabilities and the respective CE cross sections of 132 Sn were deduced relative to the established 0 þ g:s: → 2 þ 1 (E2) cross section of the target nucleus 206 Pb [30] using the coupled-channel code GOSIA2 [31,32]. In addition to the measured efficiency-corrected intensities, the detector geometries and the level schemes of 132 Sn up to 4.5 MeV and of 206 Pb up to 1.2 MeV were included in the calculations as well as the adopted BðE2; 0 þ g:s: → 2 þ 1 Þ value of 206 Pb [30] and the abovementioned branching ratio of 132 Sn. A spherical shape was assumed for 132 Sn with zero quadrupole moments. Transition matrix elements were fitted using a least-squares fit. Figure 2 shows a corresponding χ 2 surface within the 1σ range. The results obtained from GOSIA2 provide one global minimum for the set of reduced matrix elements. The final results are summarized in Table I. The present BðE2Þ value is consistent with the preliminary results from HRIBF [15][16][17][18]. However, the improved energy resolution of the HPGe array and the measured efficiency does allow unambiguous identification of the 2 þ 1 and 3 − 1 states and their respective excitation cross sections. Moreover, the new transition strengths related to the 3 − 1 state are compatible with the lower limits deduced from a lifetime measurement [33].
A novel MCSM calculation was performed recently in a unified way along the 100-138 Sn isotopic chain [37]. A large model space consisting of eight single-particle orbitals for protons and neutrons, i.e., the full sdg harmonic oscillator shell and the 0h 11=2 , 1f 7=2 , and 2p 3=2 orbitals, was used with a fixed Hamiltonian and effective charges (e π ¼ 1.25e, e ν ¼ 0.75e). Additional information on the 0 þ g:s: , 2 þ 1 , and 4 þ 1 states as well as E2 excitation probabilities in 132 Sn are deduced employing the same MCSM approach.
Skyrme RPA calculations are performed according to Ref. [38] (cf. also Ref. [9]). The model space is large enough so that appropriate energy-weighted sum rules are well fulfilled: All hole states of 132 Sn and particle states up to a maximum energy cutoff of 120 MeV were included, discretized in a spherical box of 20 fm. RPA is a proper theory to describe nuclear collective motion. However, while the results for giant resonances only depend on bulk properties of the Skyrme force, those for the low-lying excitations are quite sensitive to the details of the levels close to the Fermi surface. In this respect, measurements are instrumental to test the performance of the Skyrme parameter sets. Additional values derived from a study based on relativistic RPA (RRPA) were taken from Ref. [39].
The excitation energy of the 2 þ 1 state is well reproduced by most calculations [cf. Fig. 3(a)]. The BðE2; 0 þ g:s: → 2 þ 1 Þ values derived from LSSM, MCSM, and RRPA calculations compare well with the new experimental value within the error bars [cf. Fig. 3(b)]. Both SM approaches corroborate the locally enhanced quadrupole strength in doubly magic 132 Sn. The calculated BðE2Þ values from LSSM yield 0.028, 0.100, and 0.027 e 2 b 2 for 130;132;134 Sn, respectively, in agreement with experimental data (cf. Ref. [15] for 130;134 Sn). Corresponding values from MCSM are given in Ref. [37], yielding 0.085 e 2 b 2 for 132 Sn. Proton excitations πg −1 9=2 d 5=2 across the Z ¼ 50 shell gap with Δj ¼ Δl ¼ 2 are found to be crucial for the evolution of E2 strength along the Sn isotopic chain. According to the LSSM, these proton excitations amount to a fraction of approximately 14% of the total wave function of the 2 þ 1 state in 132 Sn, resulting in an occupation number of 0.21 for the πd 5=2 orbital. In neighboring 130;134 Sn, the occupation is reduced by a factor of about 3. The MCSM result yields a similar trend for the Sn isotopes with an average πd 5=2 occupation of 0.07 for the 2 þ 1 state in 132 Sn. Although this is not a large number, the contribution to the total E2 matrix element is approximately 25%. RPA calculations with, e.g., the SkX Skyrme force, yield an expectation value of 0.19 for the proton excitations (cf. Ref. [9]). The BðE2Þ value is overestimated by about 60% [cf. Fig. 3(b)].
Varying structures of the 0 þ g:s: and 2 þ 1 states of 130;132;134 Sn can be visualized by the T-plot, as shown in Fig. 4. The MCSM eigenstate is a superposition of J π projected MCSM basis vectors [40]. Each basis vector can be characterized by the quadrupole moments Q 0 and Q 2 , which is plotted as circle on top of the potential energy surface (PES) [41,42]. The area of each circle indicates the overlap probability of the respective MCSM basis vector with the eigenstate. The PES is obtained by constrained Hartree-Fock calculations for the same SM Hamiltonian. Although the PES exhibits a more pronounced spherical minimum for 132 Sn, the circles are spread outward in the 0 þ g:s: states of 130;132;134 Sn shown in Figs. 4(a), 4(c), and 4(e), indicating quantum fluctuations due to pairing correlations (cf. Ref. [41]). However, the major basis vectors of the ground state of 132 Sn in Fig. 4(c) are particularly concentrated towards the spherical limit, indicating the well-stabilized double magicity. Moreover, the MCSM calculations provide a high probability of 90% for the ground state of 132 Sn to be in the spherical doubly closed configuration. This value is significantly larger than the corresponding values for the doubly magic isotopes 56;68;78 Ni yielding only 60%, 53%, 75% [41]. Similar to the BðE2; 0 þ g:s: → 2 þ 1 Þ, an enhanced octupole transition strength is predicted for the 3 − 1 state in 132 Sn by theory [11,12] [33].
In summary, the new HIE-ISOLDE facility enabled a safe Coulomb-excitation experiment of 132 Sn yielding transition strength values for the first two excited states. Novel theoretical approaches allowed detailed insights into the structure of these excitations. For the first time, the doubly magic nucleus 132 Sn was explored by MCSM and LSSM calculations. The excitation energies of the 2 þ 1 and 4 þ 1 states and their BðE2Þ values were well reproduced. Although a dominant contribution is caused by the 1p1h neutron excitation across the N ¼ 82 shell gap, the contribution of the πg −1 9=2 d 5=2 excitation is crucial to reproduce the enhanced E2 strength of 132 Sn. As the T-plots of the 0 þ g:s: states of 130;132;134 Sn exhibited a strong confinement towards the spherical limit, the presented results of experiment and theory can be considered to be the first direct verification of the sphericity and double magicity of 132 Sn. This is not a trivial fact, as the N=Z ratio differs considerably from unity. Moreover, the MCSM calculations provide a high probability of 90% for the ground state to be in the doubly closed configuration. For the quadrupole excitation, a shape change from oblate to prolate deformation across the doubly magic configuration was deduced. The E3 transition strengths were well reproduced by the RPA and RRPA results. Future perspectives for experiment and SM theory include challenging measurements of the BðE3Þ transition strengths, also of the neighboring isotopes, and their calculation by the extension of the model space. Moreover, numerous experiments at HIE-ISOLDE will investigate nuclei in the vicinity of 132 Sn relevant to the astrophysical r process [43].
We thank the HIE-ISOLDE team for the professional support during the experiment. Moreover, we thank M. Zielińska and P. J. Napiorkowski for their support and discussion regarding the GOSIA2 analysis. The research leading to these results has received funding from the European Union's Horizon 2020 research and innovation program under Grant Agreement No. 654002. This work was supported by the German BMBF under Contract No. 05P15PKCIA and Verbundprojekt No. 05P2015, in part by the High Performance Computing Infrastructure Strategic Program (Grant No. hp150224), in part by MEXT and Joint Institute for Computational Fundamental Science and a priority issue (elucidation of the fundamental laws and evolution of the universe) to be tackled by using the Post "K" Computer (Grants No. hp160211 and