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論文

System of radiological protection; Towards a consistent framework on earth and in space

R$"u$hm, W.*; 伴 信彦*; Chen, J.*; Li, C.*; Dobynde, M.*; Durante, M.*; El-Jaby, S.*; 込山 立人*; 小笹 晃太郎*; 佐藤 達彦; et al.

Journal of Medical Physics - Zeitschrift f$"u$r medizinische Physik -, 10 Pages, 2024/00

国際放射線防護委員会(ICRP)は、過去90年間に渡って世界各国や国際的な放射線防護の枠組み作りに貢献してきた。2019年、ICRPは宇宙飛行士の放射線防護に関わる様々な問題に対応したタスクグループ(TG115)を立ち上げ、地上の放射線防護体系と宇宙の放射線防護体系との共通の枠組み作りに取り組んでいる。本論文では、現時点でICRPが定めている宇宙放射線防護体系についてとりまとめて報告する。

論文

Electromagnetic moments of the antimony isotopes $$^{112-133}$$Sb

Lechner, S.*; 宮城 宇志*; Xu, Z. Y.*; Bissell, M. L.*; Blaum, K.*; Cheal, B.*; Devlin, C. S.*; Garcia Ruiz, R. F.*; Ginges, J. S. M.*; Heylen, H.*; et al.

Physics Letters B, 847, p.138278_1 - 138278_9, 2023/12

 被引用回数:0 パーセンタイル:0.02(Astronomy & Astrophysics)

不安定核を含むアンチモン同位体$$^{112-133}$$Sbの磁気モーメントと電気的四重極モーメントをレーザー分光を用いて測定した。現象論的な相互作用と有効演算子を用いた殻模型計算によって測定値をよく再現することができた。第一原理に基づいたVS-IMSRG法による殻模型計算では、磁気モーメントは現象論的な有効演算子を用いればよく実験値を再現するものの、電気的四重極モーメントについては有効電荷を用いても現象論的な相互作用を用いた計算ほどには実験値を再現することができなかった。

論文

Level structures of $$^{56,58}$$Ca cast doubt on a doubly magic $$^{60}$$Ca

Chen, S.*; Browne, F.*; Doornenbal, P.*; Lee, J.*; Obertelli, A.*; 角田 佑介*; 大塚 孝治*; 茶園 亮樹*; Hagen, G.*; Holt, J. D.*; et al.

Physics Letters B, 843, p.138025_1 - 138025_7, 2023/08

 被引用回数:1 パーセンタイル:0.02(Astronomy & Astrophysics)

$$^{57,59}$$Scからの1陽子ノックアウト反応を用いて、$$^{56}$$Caと$$^{58}$$Caのガンマ崩壊を観測した。$$^{56}$$Caでは1456(12)keVの$$gamma$$線遷移が、$$^{58}$$Caでは1115(34)keVの遷移が観測された。どちらの遷移も暫定的に$$2^{+}_{1} rightarrow 0^{+}_{gs}$$と割り当てられた。有効核子間相互作用をわずかに修正した広い模型空間での殻模型計算では、$$2^{+}_{1}$$準位エネルギー、2中性子分離エネルギー、反応断面積が実験とよく一致し、N=34閉殻の上に新しい殻が形成されていることを裏付けた。その構成要素である$$0_{f5/2}$$$$0_{g9/2}$$軌道はほぼ縮退しており、これは$$^{60}$$Caが二重魔法核である可能性を排除し、Ca同位体のドリップラインを$$^{70}$$Caあるいはそれ以上にまで広げる可能性がある。

論文

Corrosion fatigue crack growth behavior of a structurally gradient steel for high-speed railway axles

Ao, N.*; Zhang, H.*; Xu, H. H.*; Wu, S. C.*; Liu, D.*; 徐 平光; Su, Y. H.; Kang, Q. H.*; Kang, G. Z.*

Engineering Fracture Mechanics, 281, p.109166_1 - 109166_14, 2023/03

 被引用回数:4 パーセンタイル:85.05(Mechanics)

Considering the complex service environments that high-speed railway axles are subjected to, the fatigue crack growth (FCG) behavior of a structurally gradient axle steel with different pre-crack depths both in air and corrosive medium was investigated at a frequency of 5 Hz. The results indicated that in the high $$Delta$$$$K$$ region, FCG rate was dramatically accelerated by corrosion, but the gap narrows as $$Delta$$$$K$$ decreased. The accelerated corrosion FCG rate was a comprehensive result of the acceleration effect of the anodic dissolution, hydrogen-enhanced localized plasticity and the retardation effect of corrosion-induced crack-tip blunting. Despite the fact that the corrosion resistance gradually decreased as the pre-crack depth increased, the FCG rate in the corrosive medium gradually decreased. This was because fatigue loading played a more important role than corrosion in accelerating the corrosion FCG rate.

論文

The $$^{59}$$Fe(n,$$gamma$$)$$^{60}$$Fe cross section from the surrogate ratio method and its effect on the $$^{60}$$Fe nucleosynthesis

Yan, S. Q.*; Li, X. Y.*; 西尾 勝久; Lugaro, M.*; Li, Z. H.*; 牧井 宏之; Pignatari, M.*; Wang, Y. B.*; Orlandi, R.; 廣瀬 健太郎; et al.

Astrophysical Journal, 919(2), p.84_1 - 84_7, 2021/10

 被引用回数:1 パーセンタイル:8.87(Astronomy & Astrophysics)

The long-lived $$^{60}$$Fe (with a half-life of 2.62 Myr) is a crucial diagnostic of active nucleosynthesis in the Milky Way galaxy and in supernovae near the solar system. The neutron-capture reaction $$^{59}$$Fe(n,$$gamma$$)$$^{60}$$Fe on $$^{59}$$Fe (half-life=44.5 days) is the key reaction for the production of $$^{60}$$Fe in massive stars. This reaction cross section has been previously constrained by the Coulomb dissociation experiment, which offered partial constraint on the E1 $$gamma$$-ray strength function but a negligible constraint on the M1 and E2 components. In this work, for the first time, we use the surrogate ratio method to experimentally determine the $$^{59}$$Fe(n,$$gamma$$)$$^{60}$$Fe cross sections in which all the components are included. We derived a Maxwellian-averaged cross section of 27.5$$pm$$3.5 mb at $$kT$$ = 30 keV and 13.4$$pm$$1.7 mb at $$kT$$ = 90 keV, roughly 10%-20% higher than previous estimates. We analyzed the impact of our new reaction rates in nucleosynthesis models of massive stars and found that uncertainties in the production of $$^{60}$$Fe from the $$^{59}$$Fe(n,$$gamma$$)$$^{60}$$Fe rate are at most 25$$%$$. We conclude that stellar physics uncertainties now play a major role in the accurate evaluation of the stellar production of $$^{60}$$Fe.

論文

Field-tuned magnetic structure and phase diagram of the honeycomb magnet YbCl$$_3$$

Hao, Y. Q.*; Wo, H. L.*; Gu, Y. M.*; Zhang, X. W.*; Gu, Y. Q.*; Zheng, S. Y.*; Zhao, Y.*; Xu, G. Y.*; Lynn, J. W.*; 中島 健次; et al.

Science China; Physics, Mechanics & Astronomy, 64(3), p.237411_1 - 237411_6, 2021/03

 被引用回数:6 パーセンタイル:61.42(Physics, Multidisciplinary)

We report thermodynamic and neutron diffraction measurements on the magnetic ordering properties of the honeycomb lattice magnet YbCl$$_3$$. We find YbCl$$_3$$ exhibits a N${'e}$el type long-range magnetic order at the wavevector (0, 0, 0) below T$$_N$$ = 600 mK. This magnetic order is associated with a small sharp peak in heat capacity and most magnetic entropy release occurs above the magnetic ordering temperature. The magnetic moment lies in-plane, parallel to the monoclinic a-axis, whose magnitude m$$_{rm Yb}$$ = 0.86(3) $$mu_B$$ is considerably smaller than the expected fully ordered moment of 2.24 $$mu_B$$ for the doublet crystal-field ground state. The magnetic ordering moment gradually increases with increasing magnetic field perpendicular to the ab-plane, reaching a maximum value of 1.6(2) $$mu_B$$ at 4 T, before it is completely suppressed above $$sim$$9 T. These results indicate the presence of strong quantum fluctuations in YbCl$$_3$$.

論文

Quasifree neutron knockout reaction reveals a small $$s$$-Orbital component in the Borromean nucleus $$^{17}$$B

Yang, Z. H.*; 久保田 悠樹*; Corsi, A.*; 吉田 数貴; Sun, X.-X.*; Li, J. G.*; 木村 真明*; Michel, N.*; 緒方 一介*; Yuan, C. X.*; et al.

Physical Review Letters, 126(8), p.082501_1 - 082501_8, 2021/02

AA2020-0819.pdf:1.29MB

 被引用回数:43 パーセンタイル:96.7(Physics, Multidisciplinary)

ボロミアン核であり中性子ハロー構造が期待される$$^{17}$$Bに対する($$p$$,$$pn$$)反応実験を行った。断面積の運動量分布を分析することで、$$1s_{1/2}$$$$0d_{5/2}$$軌道の分光学的因子を決定した。驚くべきことに、$$1s_{1/2}$$の分光学的因子は9(2)%と小さいことが明らかになった。この結果は、連続状態を含むdeformed relativistic Hartree-Bogoliubov理論によってよく説明された。本研究の結果によると、現在知られているハロー構造を持つとされる原子核の中で$$^{17}$$Bは$$s$$および$$p$$軌道の成分が最も小さく、$$s$$または$$p$$軌道成分が支配的であることが必ずしもハロー構造の前提条件ではない可能性を示唆している。

論文

Shell structure of the neutron-rich isotopes $$^{69,71,73}$$Co

Lokotko, T.*; Leblond, S.*; Lee, J.*; Doornenbal, P.*; Obertelli, A.*; Poves, A.*; Nowacki, F.*; 緒方 一介*; 吉田 数貴; Authelet, G.*; et al.

Physical Review C, 101(3), p.034314_1 - 034314_7, 2020/03

 被引用回数:10 パーセンタイル:69.78(Physics, Nuclear)

中性子過剰核である$$^{69,71,73}$$Coに対する($$p,2p$$)ノックアウト反応が理化学研究所RIBFで測定された。$$gamma-gamma$$ coincidenceの方法で準位構造が決定され、測定された包括的断面積および排他的断面積から暫定的ではあるがスピン・パリティが決定された。殻模型計算との比較により、$$^{69,71,73}$$Coの低励起状態には球形核と変形核が共存することが示唆された。

論文

IAEA Photonuclear Data Library 2019

河野 俊彦*; Cho, Y. S.*; Dimitriou, P.*; Filipescu, D.*; 岩本 信之; Plujko, V.*; Tao, X.*; 宇都宮 弘章*; Varlamov, V.*; Xu, R.*; et al.

Nuclear Data Sheets, 163, p.109 - 162, 2020/01

 被引用回数:80 パーセンタイル:99.62(Physics, Nuclear)

We report our coordinated efforts to address these data needs such as radiation shielding design and radiation transport analyses, and present the results of the new evaluations of more than 200 nuclides included in the new updated IAEA Photonuclear Data Library, where the photon energy goes up to 200 MeV. We discuss the new assessment method and make recommendations to the user community in cases where the experimental data are discrepant and the assessments disagree. In addition, in the absence of experimental data, we present model predictions for photon-induced reaction cross section on nuclides of potential interest to medical radioisotope production.

論文

Fine structure in the $$alpha$$ decay of $$^{223}$$U

Sun, M. D.*; Liu, Z.*; Huang, T. H.*; Zhang, W. Q.*; Andreyev, A. N.; Ding, B.*; Wang, J. G.*; Liu, X. Y.*; Lu, H. Y.*; Hou, D. S.*; et al.

Physics Letters B, 800, p.135096_1 - 135096_5, 2020/01

 被引用回数:11 パーセンタイル:79.42(Astronomy & Astrophysics)

Fine structure in the $$alpha$$ decay of $$^{223}$$U was observed in the fusion-evaporation reaction $$^{187}$$Re($$^{40}$$Ar,p3n) by using fast digital pulse processing technique. Two $$alpha$$-decay branches of $$^{223}$$U feeding the ground state and 244 keV excited state of $$^{219}$$Th were identified by establishing the decay chain $$^{223}$$U$$rightarrow$$$$^{219}$$Th$$rightarrow$$$$^{215}$$Ra$$rightarrow$$$$^{211}$$Rn. The $$alpha$$-particle energy for the ground-state to ground-state transition of $$^{223}$$U was determined to be 8993(17) keV, 213 keV higher than the previous value, the half-life was updated to be 62$$^{+14}_{-10} mu$$s. Evolution of nuclear structure for $$N$$=131 even-$$Z$$ isotones from Po to U was discussed in the frameworks of nuclear mass and reduced $$alpha$$-decay width, a weakening octupole deformation in the ground state of $$^{223}$$U relative to its lighter isotones $$^{219}$$Ra and $$^{211}$$Th was suggested.

論文

Negative Te spin polarization responsible for ferromagnetic order in the doped topological insulator V$$_{0.04}$$(Sb$$_{1-x}$$Bi$$_{x}$$)$$_{1.96}$$Te$$_{3}$$

Ye, M.*; Xu, T.*; Li, G.*; Qiao, S.*; 竹田 幸治; 斎藤 祐児; Zhu, S.-Y.*; Nurmamat, M.*; 角田 一樹*; 石田 行章*; et al.

Physical Review B, 99(14), p.144413_1 - 144413_7, 2019/04

AA2018-0697.pdf:1.89MB

 被引用回数:12 パーセンタイル:56.27(Materials Science, Multidisciplinary)

We investigate the microscopic origin of ferromagnetism coupled with topological insulators in V-doped (Sb,Bi)$$_{2}$$Te$$_{3}$$ employing X-ray magnetic circular dichroism and angle-resolved two-photon photoemission spectroscopies, combined with first-principles calculations. We found an magnetic moment at the Te site anti-parallel to that of the V and Sb sites, which plays a key role in the ferromagnetic order. We ascribe it to the hybridization between Te 5${it p}$ and V 3${it d}$ majority spin states at the Fermi energy, consistent with the Zener-type ${it p}$-${it d}$ exchange interaction scenario. The substitution of Bi for Sb suppresses the bulk ferromagnetism by introducing extra electron carriers in the majority spin channel of the Te ${it p}$ states that compensates the antiparallel magnetic moment on the Te site. Our findings reveal important clues to designing magnetic topological insulators with higher Curie temperature that work under ambient conditions.

論文

Nuclear structure of $$^{76}$$Ni from the ($$p$$,$$2p$$) reaction

Elekes, Z.*; Kripk$'o$, $'A$*; Sohler, D.*; Sieja, K.*; 緒方 一介*; 吉田 数貴; Doornenbal, P.*; Obertelli, A.*; Authelet, G.*; 馬場 秀忠*; et al.

Physical Review C, 99(1), p.014312_1 - 014312_7, 2019/01

 被引用回数:10 パーセンタイル:64.15(Physics, Nuclear)

($$p$$,$$2p$$)反応による$$^{76}$$Niの核構造の探索実験を行った。Lenzi, Nowacki, Poves, Sieja相互作用を用いた殻模型計算では実験結果を説明しうる陽子空孔状態が得られており、理論的な断面積計算は実験値とよい一致を与えた。実験で得られたすべての状態を理論的に一意に決定することはできなかったが、過去の実験結果と同様にNi同位体でのZ = 28の大きなshell gapを示す結果が得られた。

論文

Shell evolution beyond $$Z$$=28 and $$N$$=50; Spectroscopy of $$^{81,82,83,84}$$Zn

Shand, C. M.*; Podoly$'a$k, Zs.*; G$'o$rska, M.*; Doornenbal, P.*; Obertelli, A.*; Nowacki, F.*; Otsuka, T.*; Sieja, K.*; Tostevin, J. A.*; Tsunoda, T.*; et al.

Physics Letters B, 773, p.492 - 497, 2017/10

 被引用回数:25 パーセンタイル:87.36(Astronomy & Astrophysics)

Low-lying states in neutron-rich $$^{81,82.83.84}$$Zn nuclei were measured for the first time via in-beam $$gamma$$-ray spectroscopy at RIKEN. These include the 4$$_1^+$$ to 2$$_1^+$$ in $$^{82}$$Zn and the 2$$_1^+$$ to 0$$_1^+$$ and 4$$_1^+$$ to 2$$_1^+$$ in $$^{84}$$Zn. The reduced E($$2^+$$) energies and increased E(4$$^+$$)/E(2$$^+$$) ratios at $$N$$=52,54 compared to $$^{80}$$Zn attest that the magicity is confined just on the neutron number $$N$$=50 only. The levels observed in $$^{84}$$Zn suggest the onset of deformation towards heavier Zn isotopes. The data were compared to state-of-the-art shell model calculations.

論文

Observation of a $$gamma$$-decaying millisecond isomeric state in $$^{128}$$Cd$$_{80}$$

Jungclaus, A.*; Grawe, H.*; 西村 俊二*; Doornenbal, P.*; Lorusso, G.*; Simpson, G. S.*; S$"o$derstr$"o$m, P.-A.*; 炭竃 聡之*; Taprogge, J.*; Xu, Z. Y.*; et al.

Physics Letters B, 772, p.483 - 488, 2017/09

 被引用回数:8 パーセンタイル:55.37(Astronomy & Astrophysics)

A new high-spin isomer in the neutron-rich nucleus $$^{128}$$Cd was populated in the projectile fission of a $$^{238}$$U beam at the Radioactive Isotope Beam Factory at RIKEN. A half-life of T$$_{1/2}$$ = 6.3(8) ms was measured for the new state which was tentatively assigned a spin/parity of (15$$^-$$). The isomeric state decays via the emission of a 309-keV $$gamma$$ ray with $$E3$$ multipolarity. The experimental results are compared to shell model calculations performed using state-of-the-art realistic effective interactions and to the neighbouring nucleus $$^{129}$$Cd. The comparison with calculations shows that adjustments of the pairing and multipole parts of the effective interaction derived from the CD-Bonn nucleon-nucleon potential are required in order to describe the properties of nuclei in the region around $$^{132}$$Sn.

論文

Shape evolution in neutron-rich krypton isotopes beyond N=60; First spectroscopy of $$^{98,100}$$Kr

Flavigny, F.*; Doornenbal, P.*; Obertelli, A.*; Delaroche, J.-P.*; Girod, M.*; Libert, J.*; Rodriguez, T. R.*; Authelet, G.*; 馬場 秀忠*; Calvet, D.*; et al.

Physical Review Letters, 118(24), p.242501_1 - 242501_6, 2017/06

 被引用回数:38 パーセンタイル:86.73(Physics, Multidisciplinary)

The first $$gamma$$-ray spectroscopy of very neutron rich $$^{98,100}$$Kr isotopes was carried out at the RIBF at RIKEN Nishina center. Excited states in these isotopes were populated via (p,2p) reactions using radioactive $$^{99,101}$$Rb beams accelerated to 220 MeV/nucleon. The new data show a significant increase in deformation beyond N=60, as well as competing configurations (shape-coexistence) at low energy. The data were compared with beyond-mean-field calculations which predict level energies in good agreement with observation, and suggest oblate-prolate shape coexistence.

論文

$$gamma$$ decay of unbound neutron-hole states in $$^{133}$$Sn

Vaquero, V.*; Jungclaus, A.*; Doornenbal, P.*; Wimmer, K.*; Gargano, A.*; Tostevin, J. A.*; Chen, S.*; N$'a$cher, E.*; Sahin, E.*; 志賀 慶明*; et al.

Physical Review Letters, 118(20), p.202502_1 - 202502_5, 2017/05

 被引用回数:21 パーセンタイル:77.24(Physics, Multidisciplinary)

Excited states in $$^{133}$$Sn were populated following one-neutron knockout reaction from an unstable $$^{134}$$Sn beam at the RIBF laboratory in RIKEN. In addition to the already known $$gamma$$ rays, additional $$gamma$$ strength was observed for the first time in the excitation-energy range 3.5-5.5 MeV. Since the neutron separation energy of $$^{133}$$Sn is low, this observation provides direct evidence for the radioactive decay of neutron-unbound states in this nucleus. The ability of $$gamma$$ decay to compete with neutron emission was attributed to a mismatch between the wave functions of the initial and final states in the neutron emission case. These findings suggest that in the region south-east of $$^{132}$$Sn, nuclear structure effects play a significant role in the decay of unbound states, which are instead usually ignored in the evaluation of neutron-emission probabilities in astrophysical simulations.

論文

Low-lying structure and shape evolution in neutron-rich Se isotopes

Chen, S.*; Doornenbal, P.*; Obertelli, A.*; Rodriguez, T. R.*; Authelet, G.*; 馬場 秀忠*; Calvet, D.*; Ch$^a$teau, F.*; Corsi, A.*; Delbart, A.*; et al.

Physical Review C, 95(4), p.041302_1 - 041302_6, 2017/04

 被引用回数:26 パーセンタイル:88.02(Physics, Nuclear)

Neutron-rich isotopes of selenium, $$^{88,90,92,94}$$Se, where studied via in beam $$gamma$$-ray spectroscopy after nucleon removal reactions at RIBF in RIKEN. The low-energy excitations of these nuclei were investigated using $$gamma$$-$$gamma$$ coincidences, and the first and second excited 2$$^+$$ states were found at remarkably low energies. The analysis and comparison with self-consistent beyond-mean field calculations suggest that both shape coexistence and triaxiality are needed to describe these isotopes.

論文

Type II shell evolution in $$A=70$$ isobars from the $$N geq 40$$ island of inversion

Morales, A. I.*; Benzoni, G.*; Watanabe, H.*; 角田 佑介*; Otsuka, T.*; 西村 俊二*; Browne, F.*; Daido, R.*; Doornenbal, P.*; Fang, Y.*; et al.

Physics Letters B, 765, p.328 - 333, 2017/02

 被引用回数:34 パーセンタイル:91.97(Astronomy & Astrophysics)

The level schemes of neutron-rich isotopes $$^{70}$$Co and $$^{70}$$Ni were populated in the $$beta$$ decay of $$^{70}$$Fe and studied using $$beta$$-delayed $$gamma$$-ray spectroscopy of the $$beta$$ decay, at the RIBF in RIKEN, Japan. The experimental results were compared to state-of-the-art shell-model calculations, and indicate a dominance of prolate deformation in the low-lying states, coexisting with spherical states. The $$beta$$ decay of the $$A=70$$ isobars is shown to progress in accordance to a new type of shell evolution, the so-called Type II, which involves many particle-hole excitations across energy gaps.

論文

Are there signatures of harmonic oscillator shells far from stability?; First spectroscopy of $$^{110}$$Zr

Paul, N.*; Corsi, A.*; Obertelli, A.*; Doornenbal, P.*; Authelet, G.*; 馬場 秀忠*; Bally, B.*; Bender, M.*; Calvet, D.*; Ch$^a$teau, F.*; et al.

Physical Review Letters, 118(3), p.032501_1 - 032501_7, 2017/01

 被引用回数:43 パーセンタイル:88.64(Physics, Multidisciplinary)

The first measurement of $$gamma$$ rays emitted by the very neutron rich nuclei $$^{112}$$Mo (Z=42) and $$^{110}$$Zr (Z=40) was carried out at the RIBF facility at RIKEN. These data shine light on the postulated N=70 harmonic oscillator shell. If the spin-orbit splitting which gives rise to the N=82 shell gap is reduced in very neutron-rich nuclei, the harmonic oscillator gap at N=70 should open instead. However, both the measured energy of the first excited state $$^{112}$$Mo and $$^{110}$$Zr, respectively 235(7) keV and 185(11) keV, and their E(4$$^+$$)/E(2$$^+$$) ratio, indicate that these nuclei are good rotors, and exclude the shell stabilization scenario at Z=40 and N=70. These results were compared to state-of-the-art density functional theoretical calculations using Gogny and Skyrme effective interactions.

論文

$$beta$$ decay of semi-magic $$^{130}$$Cd; Revision and extension of the level scheme of $$^{130}$$In

Jungclaus, A.*; Grawe, H.*; 西村 俊二*; Doornenbal, P.*; Lorusso, G.*; Simpson, G. S.*; S$"o$derstr$"o$m, P. A.*; 炭竃 聡之*; Taprogge, J.*; Xu, Z. Y.*; et al.

Physical Review C, 94(2), p.024303_1 - 024303_8, 2016/08

 被引用回数:18 パーセンタイル:77.39(Physics, Nuclear)

The $$beta$$ decay of the semi-magic nucleus $$^{130}$$Cd has been studied at the RIBF facility at the RIKEN Nishina Center. The high statistics of the present experiment allowed for a revision of the established level scheme of $$^{130}$$In and the observation of additional $$beta$$ feeding to high lying core-excited states in $$^{130}$$In. The experimental results are compared to shell-model calculations employing a model space consisting of the full major $$N=50-82$$ neutron and $$Z=28-50$$ proton shells, and good agreement is found.

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