Cross-Shell Excitation in F and Ne Isotopes around N = 20
Abstract
:1. Introduction
2. Theories
2.1. SDPF-M
2.2. SDPF-MU
2.3. SDPF-U-SI
3. Results and Discussions
3.1. Ground-State Properties
3.2. Excitation Energies
3.3. Configuration Occupancies
3.4. Shell Structure and Evolution
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Haxel, O.; Jensen, J.H.D.; Suess, H.E. On the “magic numbers” in nuclear structure. Phys. Rev. 1949, 75, 1766. [Google Scholar] [CrossRef]
- Mayer, M.G. On closed shells in nuclei. II. Phys. Rev. 1949, 75, 1969–1970. [Google Scholar] [CrossRef]
- Revel, A.; Sorlin, O.; Marques, F.M.; Kondo, Y.; Kahlbow, J.; Nakamura, T.; Orr, N.A.; Nowacki, F.; Tostevin, J.A.; Yuan, C.X.; et al. Extending the southern shore of the island of inversion to 28F. Phys. Rev. Lett. 2020, 124, 152502. [Google Scholar] [CrossRef] [PubMed] [Green Version]
- Terry, J.R.; Bazin, D.; Brown, B.A.; Campbell, C.M.; Church, J.A.; Cook, J.M.; Davies, A.D.; Dinca, D.C.; Enders, J.; Gade, A.; et al. Direct evidence for the onset of intruder configurations in neutron-rich Ne isotopes. Phys. Lett. B 2006, 640, 86–90. [Google Scholar] [CrossRef] [Green Version]
- Dombradi, Z.; Elekes, Z.; Saito, A.; Aoi, N.; Baba, H.; Demichi, K.; Fulop, Z.; Gibelin, J.; Gomi, T.; Hasegawa, H.; et al. Vanishing N = 20 shell gap: Study of excited states in 27,28Ne. Phys. Rev. Lett. 2006, 96, 182501. [Google Scholar] [CrossRef]
- Liu, H.; Lee, J.; Doornenbal, P.; Scheit, H.; Takeuchi, S.; Aoi, N.; Li, K.; Matsushita, M.; Steppenbeck, D.; Wang, H.; et al. Single-neutron knockout reaction from 30Ne. JPS Conf. Proc. 2015, 6, 030003. [Google Scholar]
- Thibault, C.; Klapisch, R.; Rigaud, C.; Poskanzer, A.M.; Prieels, R.; Lessard, L.; Reisdorf, W. Direct measurement of the masses of 11Li and 26-32Na with an on-line mass spectrometer. Phys. Rev. C 1975, 12, 644–657. [Google Scholar] [CrossRef] [Green Version]
- Terry, J.R.; Brown, B.A.; Campbell, C.M.; Cook, J.M.; Davies, A.D.; Dinca, D.C.; Gade, A.; Glasmacher, T.; Hansen, P.G.; Sherrill, B.M.; et al. Single-neutron knockout from intermediate energy beams of 30,32Mg: Mapping the transition into the “island of inversion”. Phys. Rev. C 2008, 77, 014316. [Google Scholar] [CrossRef] [Green Version]
- Guillemaud-Mueller, D.; Jacmart, J.C.; Kashy, E.; Latimier, A.; Mueller, A.C.; Pougheon, F.; Richard, A.; Penionzhkevich, Y.E.; Artuhk, A.G.; Belozyorov, A.V.; et al. Particle stability of the isotopes 26O and 32Ne in the reaction 44 MeV/nucleon 48Ca+Ta. Phys. Rev. C Nucl. Phys. 1990, 41, 937–941. [Google Scholar] [CrossRef]
- Tarasov, O.; Allatt, R.; Angélique, J.C.; Anne, R.; Borcea, C.; Dlouhy, Z.; Donzaud, C.; Grévy, S.; Guillemaud-Mueller, D.; Lewitowicz, M.; et al. Search for 28O and study of neutron-rich nuclei near the N = 20 shell closure. Phys. Lett. B 1997, 409, 64–70. [Google Scholar] [CrossRef] [Green Version]
- Thoennessen, M. Reaching the limits of nuclear stability. Rep. Prog. Phys. 2004, 67, 1187–1232. [Google Scholar] [CrossRef] [Green Version]
- Ahn, D.S.; Fukuda, N.; Geissel, H.; Inabe, N.; Iwasa, N.; Kubo, T.; Kusaka, K.; Morrissey, D.J.; Murai, D.; Nakamura, T.; et al. Location of the neutron dripline at fluorine and neon. Phys. Rev. Lett. 2019, 123, 212501. [Google Scholar] [CrossRef]
- Sakurai, H.; Lukyanov, S.M.; Notani, M.; Aoi, N.; Beaumel, D.; Fukuda, N.; Hirai, M.; Ideguchi, E.; Imai, N.; Ishihara, M.; et al. Evidence for particle stability of F and particle instability of N and O. Phys. Lett. B 1999, 448, 180–184. [Google Scholar] [CrossRef]
- Wang, M.; Huang, W.J.; Kondev, F.G.; Audi, G.; Naimi, S. The AME 2020 atomic mass evaluation (II). Tables, graphs and references*. Chin. Phys. C 2021, 45, 030003. [Google Scholar] [CrossRef]
- Kobayashi, N.; Nakamura, T.; Kondo, Y.; Tostevin, J.A.; Aoi, N.; Baba, H.; Barthelemy, R.; Famiano, M.A.; Fukuda, N.; Inabe, N.; et al. One-neutron removal from 29Ne: Defining the lower limits of the island of inversion. Phys. Rev. C 2016, 93, 014613. [Google Scholar] [CrossRef] [Green Version]
- Nakamura, T.; Kobayashi, N.; Kondo, Y.; Satou, Y.; Aoi, N.; Baba, H.; Deguchi, S.; Fukuda, N.; Gibelin, J.; Inabe, N.; et al. Halo structure of the island of inversion nucleus 31Ne. Phys. Rev. Lett. 2009, 103, 262501. [Google Scholar] [CrossRef]
- Gaudefroy, L.; Mittig, W.; Orr, N.A.; Varet, S.; Chartier, M.; Roussel-Chomaz, P.; Ebran, J.P.; Fernandez-Dominguez, B.; Fremont, G.; Gangnant, P.; et al. Direct mass measurements of 19B, 22C, 29F, 31Ne, 34Na and other light exotic nuclei. Phys. Rev. Lett. 2012, 109, 202503. [Google Scholar] [CrossRef] [Green Version]
- Bagchi, S.; Kanungo, R.; Tanaka, Y.K.; Geissel, H.; Doornenbal, P.; Horiuchi, W.; Hagen, G.; Suzuki, T.; Tsunoda, N.; Ahn, D.S.; et al. Two-Neutron Halo is Unveiled in 29F. Phys. Rev. Lett. 2020, 124, 222504. [Google Scholar] [CrossRef]
- Chrisman, D.; Kuchera, A.N.; Baumann, T.; Blake, A.; Brown, B.A.; Brown, J.; Cochran, C.; DeYoung, P.A.; Finck, J.E.; Frank, N.; et al. Neutron-unbound states in 31Ne. Phys. Rev. C 2021, 104, 034313. [Google Scholar] [CrossRef]
- Jansen, G.R.; Engel, J.; Hagen, G.; Navratil, P.; Signoracci, A. Ab initio coupled-cluster effective interactions for the shell model: Application to neutron-rich oxygen and carbon isotopes. Phys. Rev. Lett. 2014, 113, 142502. [Google Scholar] [CrossRef] [Green Version]
- Sun, Z.; Wu, Q.; Xu, F. Green’s function calculations of light nuclei. Sci. China Phys. Mech. 2016, 59, 692013. [Google Scholar] [CrossRef]
- Bender, M.; Heenen, P.-H.; Reinhard, P.-G. Self-consistent mean-field models for nuclear structure. Rev. Mod. Phys. 2003, 75, 121–180. [Google Scholar] [CrossRef]
- Otsuka, T.; Honma, M.; Mizusaki, T.; Shimizu, N.; Utsuno, Y. Monte Carlo shell model for atomic nuclei. Prog. Part. Nucl. Phys. 2001, 47, 319–400. [Google Scholar] [CrossRef]
- Miyagi, T.; Stroberg, S.R.; Holt, J.D.; Shimizu, N. Ab initio multishell valence-space Hamiltonians and the island of inversion. Phys. Rev. C 2020, 102, 034320. [Google Scholar] [CrossRef]
- Luo, Y.-X.; Fossez, K.; Liu, Q.; Guo, J.-Y. Role of quadrupole deformation and continuum effects in the “island of inversion” nuclei F28,29,31. Phys. Rev. C 2021, 104, 014307. [Google Scholar] [CrossRef]
- Tripathi, V.; Tabor, S.L.; Mantica, P.F.; Utsuno, Y.; Bender, P.; Cook, J.; Hoffman, C.R.; Lee, S.; Otsuka, T.; Pereira, J.; et al. Competition between normal and intruder states inside the “island of inversion”. Phys. Rev. C 2007, 76, 021301. [Google Scholar] [CrossRef] [Green Version]
- Michel, N.; Li, J.G.; Xu, F.R.; Zuo, W. Two-neutron halo structure of 31F. Phys. Rev. C 2020, 101, 031301. [Google Scholar] [CrossRef] [Green Version]
- Masui, H.; Horiuchi, W.; Kimura, M. Two-neutron halo structure of 31F and a novel pairing antihalo effect. Phys. Rev. C 2020, 101, 041303. [Google Scholar] [CrossRef] [Green Version]
- Singh, J.; Casal, J.; Horiuchi, W.; Fortunato, L.; Vitturi, A. Exploring two-neutron halo formation in the ground state of 29F within a three-body model. Phys. Rev. C 2020, 101, 024310. [Google Scholar] [CrossRef] [Green Version]
- Lee, J.; Xu, X.X.; Kaneko, K.; Sun, Y.; Lin, C.J.; Sun, L.J.; Liang, P.F.; Li, Z.H.; Li, J.; Wu, H.Y.; et al. Large isospin asymmetry in 22Si/22O mirror Gamow-Teller transitions reveals the halo structure of 22Al. Phys. Rev. Lett. 2020, 125, 192503. [Google Scholar] [CrossRef]
- Liang, P.F.; Sun, L.J.; Lee, J.; Hou, S.Q.; Xu, X.X.; Lin, C.J.; Yuan, C.X.; He, J.J.; Li, Z.H.; Wang, J.S.; et al. Simultaneous measurement of β-delayed proton and γ emission of 26P for the 25Al(p,γ)26Si reaction rate. Phys. Rev. C 2020, 101, 024305. [Google Scholar] [CrossRef] [Green Version]
- Sun, L.J.; Xu, X.X.; Hou, S.Q.; Lin, C.J.; José, J.; Lee, J.; He, J.J.; Li, Z.H.; Wang, J.S.; Yuan, C.X.; et al. Experimentally well-constrained masses of 27P and 27S: Implications for studies of explosive binary systems. Phys. Lett. B 2020, 802, 135213. [Google Scholar] [CrossRef]
- Shi, G.Z.; Liu, J.J.; Lin, Z.Y.; Zhu, H.F.; Xu, X.X.; Sun, L.J.; Liang, P.F.; Lin, C.J.; Lee, J.; Yuan, C.X.; et al. β-delayed two-proton decay of 27S at the proton-drip line. Phys. Rev. C 2021, 103, L061301. [Google Scholar] [CrossRef]
- Chen, Z.Q.; Li, Z.H.; Hua, H.; Watanabe, H.; Yuan, C.X.; Zhang, S.Q.; Lorusso, G.; Nishimura, S.; Baba, H.; Browne, F.; et al. Proton shell evolution below 132Sn: First measurement of low-lying beta-emitting isomers in 123,125Ag. Phys. Rev. Lett. 2019, 122, 212502. [Google Scholar] [CrossRef] [Green Version]
- Xu, X.; Liu, J.H.; Yuan, C.X.; Xing, Y.M.; Wang, M.; Zhang, Y.H.; Zhou, X.H.; Litvinov, Y.A.; Blaum, K.; Chen, R.J.; et al. Masses of ground and isomeric states of 101In and configuration-dependent shell evolution in odd-A indium isotopes. Phys. Rev. C 2019, 100, 051303. [Google Scholar] [CrossRef] [Green Version]
- Yuan, C.X.; Liu, Z.; Xu, F.R.; Walker, P.M.; Podolyák, Z.; Xu, C.; Ren, Z.Z.; Ding, B.; Liu, M.L.; Liu, X.Y.; et al. Isomerism in the “south-east” of 132Sn and a predicted neutron-decaying isomer in 129Pd. Phys. Lett. B 2016, 762, 237–242. [Google Scholar] [CrossRef]
- Phong, V.H.; Lorusso, G.; Davinson, T.; Estrade, A.; Hall, O.; Liu, J.; Matsui, K.; Montes, F.; Nishimura, S.; Boso, A.; et al. Observation of a μs isomer in 134In: Proton-neutron coupling “southeast” of 132Sn. Phys. Rev. C 2019, 100, 011302. [Google Scholar] [CrossRef]
- Li, C.B.; Zhang, G.L.; Yuan, C.X.; Zhang, G.X.; Hu, S.P.; Qu, W.W.; Zheng, Y.; Zhang, H.Q.; Mengoni, D.; Testov, D.; et al. New level scheme and shell model description of 212Rn. Phys. Rev. C 2020, 101, 044313. [Google Scholar] [CrossRef]
- Zhang, M.M.; Yang, H.B.; Gan, Z.G.; Zhang, Z.Y.; Huang, M.H.; Ma, L.; Yang, C.L.; Yuan, C.X.; Wang, Y.S.; Tian, Y.L.; et al. A new isomeric state in 218Pa. Phys. Lett. B 2020, 800, 135102. [Google Scholar] [CrossRef]
- Zhou, H.B.; Gan, Z.G.; Wang, N.; Yang, H.B.; Ma, L.; Huang, M.H.; Yang, C.L.; Zhang, M.M.; Tian, Y.L.; Wang, Y.S.; et al. Lifetime measurement for the isomeric state in 213Th. Phys. Rev. C 2021, 103, 044314. [Google Scholar] [CrossRef]
- Cai, B.; Chen, G.; Xu, J.; Yuan, C.; Qi, C.; Yao, Y. α decay half-life estimation and uncertainty analysis. Phys. Rev. C 2020, 101, 054304. [Google Scholar] [CrossRef]
- Zhang, Z.Y.; Yang, H.B.; Huang, M.H.; Gan, Z.G.; Yuan, C.X.; Qi, C.; Andreyev, A.N.; Liu, M.L.; Ma, L.; Zhang, M.M.; et al. New alpha-emitting isotope 214U and abnormal enhancement of alpha-particle clustering in lightest uranium isotopes. Phys. Rev. Lett. 2021, 126, 152502. [Google Scholar] [CrossRef]
- Fukunishi, N.; Otsuka, T.; Sebe, T. Vanishing of the shell gap in N = 20 neutron-rich nuclei. Phys. Lett. B 1992, 296, 279–284. [Google Scholar] [CrossRef]
- Utsuno, Y.; Otsuka, T.; Mizusaki, T.; Honma, M. Varying shell gap and deformation in N~20 unstable nuclei studied by the Monte Carlo shell model. Phys. Rev. C 1999, 60, 054315. [Google Scholar] [CrossRef]
- Caurier, E.; Nowacki, F.; Poves, A. Merging of the islands of inversion at N = 20 and N = 28. Phys. Rev. C 2014, 90, 014302. [Google Scholar] [CrossRef] [Green Version]
- Chen, J.; Auranen, K.; Avila, M.L.; Back, B.B.; Caprio, M.A.; Hoffman, C.R.; Gorelov, D.; Kay, B.P.; Kuvin, S.A.; Liu, Q.; et al. Experimental study of the low-lying negative-parity states in 11Be using the 12B(d,3He)11Be reaction. Phys. Rev. C 2019, 100, 064314. [Google Scholar] [CrossRef]
- Chen, J.; Wang, S.M.; Fortune, H.T.; Lou, J.L.; Ye, Y.L.; Li, Z.H.; Michel, N.; Li, J.G.; Yuan, C.X.; Ge, Y.C.; et al. Observation of the near-threshold intruder 0− resonance in 12Be. Phys. Rev. C 2021, 103, L031302. [Google Scholar] [CrossRef]
- Yang, Z.H.; Kubota, Y.; Corsi, A.; Yoshida, K.; Sun, X.X.; Li, J.G.; Kimura, M.; Michel, N.; Ogata, K.; Yuan, C.X.; et al. Quasifree neutron knockout reaction reveals a small s-orbital component in the Borromean nucleus 17B. Phys. Rev. Lett. 2021, 126, 082501. [Google Scholar] [CrossRef]
- Yuan, C.X. Impact of off-diagonal cross-shell interaction on 14C. Chin. Phys. C 2017, 41, 104102. [Google Scholar] [CrossRef] [Green Version]
- Jiang, Y.; Lou, J.L.; Ye, Y.L.; Liu, Y.; Tan, Z.W.; Liu, W.; Yang, B.; Tao, L.C.; Ma, K.; Li, Z.H.; et al. Quadrupole deformation of 16C studied by proton and deuteron inelastic scattering. Phys. Rev. C 2020, 101, 024601. [Google Scholar] [CrossRef]
- Yuan, C.X.; Suzuki, T.; Otsuka, T.; Xu, F.; Tsunoda, N. Shell-model study of boron, carbon, nitrogen, and oxygen isotopes with a monopole-based universal interaction. Phys. Rev. C 2012, 85, 064324. [Google Scholar] [CrossRef] [Green Version]
- Wang, Y.B.; Su, J.; Han, Z.Y.; Tang, B.; Cui, B.Q.; Ge, T.; Lyu, Y.L.; Brown, B.A.; Yuan, C.X.; Chen, L.H. Direct observation of the exotic β−γ−α decay mode in the Tz = −1 nucleus 20Na. Phys. Rev. C 2021, 103, L011301. [Google Scholar] [CrossRef]
- Utsuno, Y.; Otsuka, T.; Brown, B.A.; Honma, M.; Mizusaki, T.; Shimizu, N. Shape transitions in exotic Si and S isotopes and tensor-force-driven Jahn-Teller effect. Phys. Rev. C 2012, 86, 051301. [Google Scholar] [CrossRef] [Green Version]
- Nowacki, F.; Poves, A. New effective interaction for 0ℏω shell-model calculations in the sd−pf valence space. Phys. Rev. C 2009, 79, 014310. [Google Scholar] [CrossRef] [Green Version]
- Bazin, D.; Aoi, N.; Baba, H.; Chen, J.; Crawford, H.; Doornenbal, P.; Fallon, P.; Li, K.; Lee, J.; Matsushita, M.; et al. Spectroscopy of 33Mg with knockout reactions. Phys. Rev. C 2021, 103, 064318. [Google Scholar] [CrossRef]
- Gade, A.; Brown, B.A.; Tostevin, J.A.; Bazin, D.; Bender, P.C.; Campbell, C.M.; Crawford, H.L.; Elman, B.; Kemper, K.W.; Longfellow, B.; et al. Is the structure of 42Si understood? Phys. Rev. Lett. 2019, 122, 222501. [Google Scholar] [CrossRef] [Green Version]
- Hjorth-Jensen, M.; Kuo, T.T.S.; Osnes, E. Realistic effective interactions for nuclear systems. Phys. Rep. 1995, 261, 125–270. [Google Scholar] [CrossRef]
- Brown, B.A. The nuclear shell model towards the drip lines. Prog. Part. Nucl. Phys. 2001, 47, 517–599. [Google Scholar] [CrossRef]
- Noritaka, S. Nuclear shell-model code for massive parallel computation, “KSHELL”. arXiv 2013, arXiv:1310.5431. [Google Scholar]
- Noritaka, S.; Takahiro, M.; Yutaka, U.; Yusuke, T. Thick-restart block Lanczos method for large-scale shell-model calculations. Comput. Phys. Commun. 2019, 244, 372–384. [Google Scholar]
- Available online: https://sites.google.com/a/cns.s.u-tokyo.ac.jp/kshell/ (accessed on 1 November 2021).
- Brown, B.A.; Richter, W.A.; Julies, R.E.; Wildenthal, B.H. Semi-empirical effective interactions for the 1s-0d shell. Ann. Phys. 1988, 182, 191–236. [Google Scholar] [CrossRef]
- Kuo, T.T.S.; Brown, G.E. Reaction matrix elements for the 0f-1p shell nuclei. Nucl. Phys. A 1968, 114, 241–279. [Google Scholar] [CrossRef]
- Millener, D.J.; Kurath, D. The particle-hole interaction and the beta decay of 14B. Nucl. Phys. A 1975, 255, 315–338. [Google Scholar] [CrossRef]
- Warburton, E.K.; Alburger, D.E.; Becker, J.A.; Brown, B.A.; Raman, S. Probe of the shell crossing at A=40 via beta decay: Experiment and theory. Phys. Rev. C 1986, 34, 1031–1051. [Google Scholar] [CrossRef] [Green Version]
- Bansal, R.K.; French, J.B. Even-parity-hole states in f7/2 -shell nuclei. Phys. Lett. 1964, 11, 145–148. [Google Scholar] [CrossRef]
- Doornenbal, P.; Scheit, H.; Takeuchi, S.; Utsuno, Y.; Aoi, N.; Li, K.; Matsushita, M.; Steppenbeck, D.; Wang, H.; Baba, H.; et al. Low-Z shore of the “island of inversion” and the reduced neutron magicity toward 28O. Phys. Rev. C 2017, 95, 041301. [Google Scholar] [CrossRef] [Green Version]
- Utsuno, Y.; Otsuka, T.; Glasmacher, T.; Mizusaki, T.; Honma, M. Onset of intruder ground state in exotic Na isotopes and evolution of the N = 20 shell gap. Phys. Rev. C 2004, 70, 044307. [Google Scholar] [CrossRef] [Green Version]
- Han, R.; Li, X.Q.; Jiang, W.G.; Li, Z.H.; Hua, H.; Zhang, S.Q.; Yuan, C.X.; Jiang, D.X.; Ye, Y.L.; Li, J.; et al. Northern boundary of the “island of inversion” and triaxiality in 34Si. Phys. Lett. B 2017, 772, 529–533. [Google Scholar] [CrossRef]
- Honma, M.; Otsuka, T.; Mizusaki, T.; Hjorthjensen, M. Shell-model description of beta-decays for pfg-shell nuclei. Riken Acce. Prog. Rep. 2009, 42, 43. [Google Scholar]
- Otsuka, T.; Suzuki, T.; Honma, M.; Utsuno, Y.; Tsunoda, N.; Tsukiyama, K.; Hjorth-Jensen, M. Novel features of nuclear forces and shell evolution in exotic nuclei. Phys. Rev. Lett. 2010, 104, 012501. [Google Scholar] [CrossRef] [Green Version]
- Poves, A.; Zuker, A. Theoretical spectroscopy and the fp shell. Phys. Rep. 1981, 70, 235–314. [Google Scholar] [CrossRef]
- Bertsch, G.; Borysowicz, J.; McManus, H.; Love, W.G. Interactions for inelastic scattering derived from realistic potentials. Nucl. Phys. A 1977, 284, 399–419. [Google Scholar] [CrossRef]
- Nummela, S.; Baumann, P.; Caurier, E.; Dessagne, P.; Jokinen, A.; Knipper, A.; Le Scornet, G.; Miehé, C.; Nowacki, F.; Oinonen, M.; et al. Spectroscopy of 34,35Si by β decay: Sd−fp shell gap and single-particle states. Phys. Rev. C 2001, 63, 044316. [Google Scholar] [CrossRef] [Green Version]
- Retamosa, J.; Caurier, E.; Nowacki, F.; Poves, A. Shell model study of the neutron-rich nuclei around N = 28. Phys. Rev. C 1997, 55, 1266–1274. [Google Scholar] [CrossRef] [Green Version]
- Kahana, S.; Lee, H.C.; Scott, C.K. Effect of Woods-Saxon wave functions on the calculation of A=18, 206, 210 spectra with a realistic interaction. Phys. Rev. 1969, 180, 956–966. [Google Scholar] [CrossRef]
- Gloeckner, D.H.; Lawson, R.D. Spurious center-of-mass motion. Phys. Lett. B 1974, 53, 313–318. [Google Scholar] [CrossRef]
- Kondev, F.G.; Wang, M.; Huang, W.J.; Naimi, S.; Audi, G. The NUBASE2020 evaluation of nuclear physics properties. Chin. Phys. C 2021, 45, 030001. [Google Scholar] [CrossRef]
- Available online: https://www.nndc.bnl.gov/nudat2/ (accessed on 1 November 2021).
- Umeya, A.; Muto, K. Single-particle energies in neutron-rich nuclei by shell model sum rule. Phys. Rev. C 2006, 74, 034330. [Google Scholar] [CrossRef]
- Yuan, C.X.; Qi, C.; Xu, F.R. Shell evolution in neutron-rich carbon isotopes: Unexpected enhanced role of neutron–neutron correlation. Nucl. Phys. A 2012, 883, 25–34. [Google Scholar] [CrossRef] [Green Version]
- Otsuka, T.; Tsunoda, Y.; Abe, T.; Shimizu, N.; Van Duppen, P. Underlying Structure of Collective Bands and Self-Organization in Quantum Systems. Phys. Rev. Lett. 2019, 123, 222502. [Google Scholar] [CrossRef] [Green Version]
- Yuan, C.X.; Liu, M.L.; Ge, Y.L. Shell-model explanation on some newly discovered isomers. Nucl. Phys. R 2020, 37, 447–454. [Google Scholar]
Exp. (Error) | SDPF-M (0–1)ħω | SDPF-M (0–3)ħω | SDPF-M (0–5)ħω | SDPF-MU (0–1)ħω | SDPF-MU (0–3)ħω | SDPF-MU (0–5)ħω | SDPF-U-SI (0–1)ħω | SDPF-U-SI (0–3)ħω | SDPF-U-SI (0–5)ħω | |
---|---|---|---|---|---|---|---|---|---|---|
Sn (27F) | 1.610 (0.060) | 0.886 | 2.437 | 2.659 | 1.114 | 3.200 | 3.934 | 2.402 | 3.027 | 3.154 |
Sn (28F) | −0.199 (0.006) | 0.157 | −0.479 | −0.584 | 0.003 | −0.796 | −1.113 | −0.090 | −0.541 | −0.622 |
Sn (29F) | 1.320 (0.540) | −1.762 | 0.116 | 1.498 | −0.980 | 0.908 | 2.619 | 0.152 | 1.465 | 2.016 |
Sn (30F) | / | 0.830 | −0.799 | −1.217 | 1.075 | −1.005 | −1.774 | 0.240 | −0.362 | −0.652 |
Sn (31F) | / | −0.502 | 0.999 | 1.005 | 0.117 | 1.491 | 1.845 | 1.325 | 1.232 | 1.200 |
Sn (32F) | / | 0.178 | −1.423 | −1.787 | −0.222 | −2.015 | −2.689 | −0.095 | −0.860 | −1.077 |
Sn (33F) | / | −0.851 | 0.535 | 0.564 | −0.140 | 0.895 | 1.067 | 0.537 | 0.636 | 0.675 |
Sn (28Ne) | 3.820 (0.160) | 2.607 | 4.477 | 4.824 | 2.500 | 5.328 | 6.359 | 4.086 | 4.861 | 5.060 |
Sn (29Ne) | 0.970 (0.200) | 0.908 | 0.005 | −0.091 | 1.111 | 0.137 | −0.410 | 0.592 | 0.059 | −0.081 |
Sn (30Ne) | 3.190 (0.290) | −0.771 | 2.225 | 3.562 | −0.274 | 1.757 | 3.987 | 1.032 | 2.532 | 3.663 |
Sn (31Ne) | 0.170 (0.130) | 2.864 | 0.304 | −0.474 | 3.657 | 0.998 | −1.179 | 2.441 | 0.681 | −0.478 |
Sn (32Ne) | / | 0.520 | 2.247 | 2.352 | 1.247 | 2.616 | 3.763 | 2.239 | 2.990 | 3.319 |
Sn (33Ne) | / | 1.495 | −0.969 | −1.334 | 1.598 | −1.216 | −2.224 | 0.723 | −0.127 | −0.446 |
Sn (34Ne) | / | −0.085 | 1.483 | 1.540 | 0.970 | 2.315 | 2.468 | 2.264 | 2.173 | 2.186 |
Sn (35Ne) | / | 0.067 | −1.629 | −1.902 | −1.514 | −2.470 | −3.016 | −0.512 | −0.943 | −1.032 |
Sn (36Ne) | / | −0.110 | 1.156 | 1.143 | 0.721 | 1.211 | 1.327 | 0.798 | 0.822 | 0.830 |
S2n (27F) | 2.340 (0.150) | 1.276 | 2.746 | 2.975 | 2.038 | 4.307 | 5.079 | 3.323 | 4.217 | 4.353 |
S2n (28F) | 1.410 (0.060) | 1.043 | 1.958 | 2.075 | 1.117 | 2.404 | 2.821 | 2.312 | 2.486 | 2.532 |
S2n (29F) | 1.130 (0.540) | −1.605 | −0.363 | 0.914 | −0.977 | 0.112 | 1.506 | 0.062 | 0.924 | 1.394 |
S2n (30F) | / | −0.932 | −0.683 | 0.281 | 0.095 | −0.097 | 0.845 | 0.392 | 1.103 | 1.364 |
S2n (31F) | / | 0.328 | 0.200 | −0.212 | 1.192 | 0.486 | 0.071 | 1.565 | 0.870 | 0.548 |
S2n (32F) | / | −0.324 | −0.424 | −0.782 | −0.105 | −0.524 | −0.844 | 1.230 | 0.372 | 0.123 |
S2n (33F) | / | −0.673 | −0.888 | −1.223 | −0.362 | −1.120 | −1.622 | 0.442 | −0.224 | −0.402 |
S2n (28Ne) | 5.320 (0.130) | 3.766 | 5.367 | 5.719 | 4.415 | 6.404 | 7.378 | 5.382 | 6.183 | 6.375 |
S2n (29Ne) | 4.790 (0.170) | 3.515 | 4.482 | 4.733 | 3.611 | 5.465 | 5.949 | 4.678 | 4.920 | 4.979 |
S2n (30Ne) | 4.160 (0.280) | 0.137 | 2.230 | 3.471 | 0.837 | 1.894 | 3.577 | 1.624 | 2.591 | 3.582 |
S2n (31Ne) | 3.360 (0.310) | 2.093 | 2.529 | 3.088 | 3.383 | 2.755 | 2.808 | 3.473 | 3.213 | 3.185 |
S2n (32Ne) | / | 3.384 | 2.551 | 1.878 | 4.904 | 3.614 | 2.584 | 4.680 | 3.671 | 2.841 |
S2n (33Ne) | / | 2.015 | 1.278 | 1.018 | 2.845 | 1.400 | 1.539 | 2.962 | 2.863 | 2.873 |
S2n (34Ne) | / | 1.410 | 0.514 | 0.206 | 2.568 | 1.099 | 0.244 | 2.987 | 2.046 | 1.740 |
S2n (35Ne) | / | −0.018 | −0.146 | −0.362 | −0.544 | −0.155 | −0.548 | 1.752 | 1.230 | 1.154 |
S2n (36Ne) | / | −0.043 | −0.473 | −0.759 | −0.793 | −1.259 | −1.689 | 0.286 | −0.121 | −0.202 |
Nucleus | Exp. | SDPF-M (0–1)ħω | SDPF-M (0–3)ħω | SDPF-M (0–5)ħω | SDPF-MU (0–1)ħω | SDPF-MU (0–3)ħω | SDPF-MU (0–5)ħω | SDPF-U-SI (0–1)ħω | SDPF-U-SI (0–3)ħω | SDPF-U-SI (0–5)ħω |
---|---|---|---|---|---|---|---|---|---|---|
27F | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ |
28F | 4− | 6– | 4– | 4– | 4– | 4– | 4– | 4– | 4– | 4– |
29F | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ |
30F | / | 3+ | 4– | 4– | 3+ | 3+ | 4– | 3+ | 4– | 4– |
31F | / | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ | 5/2+ |
28Ne | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ |
29Ne | 3/2– | 7/2– | 7/2– | 3/2+ | 3/2– | 3/2– | 3/2– | 3/2– | 3/2– | 3/2– |
30Ne | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ |
31Ne | 3/2– | 3/2+ | 3/2– | 3/2– | 3/2+ | 3/2+ | 3/2– | 3/2+ | 3/2+ | 3/2+ |
32Ne | 0+ | 3– | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ |
33Ne | / | 3/2+ | 3/2– | 3/2- | 3/2+ | 3/2+ | 3/2– | 3/2– | 3/2– | 3/2– |
34Ne | / | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ | 0+ |
Nucleus | State | Exp. | SDPF-M (0–1)ħω | SDPF-M (0–3)ħω | SDPF-M (0–5)ħω | SDPF-MU (0–1)ħω | SDPF-MU (0–3)ħω | SDPF-MU (0–5)ħω | SDPF-U-SI (0–1)ħω | SDPF-U-SI (0–3)ħω | SDPF-U-SI (0–5)ħω |
---|---|---|---|---|---|---|---|---|---|---|---|
27F | 1/21+ | 0.915 (0.012) | 1.980 | 1.297 | 1.184 | 2.176 | 1.952 | 1.482 | 1.923 | 1.770 | 1.715 |
3/21+ | / | 2.626 | 2.732 | 2.675 | 2.847 | 3.571 | 3.452 | 2.872 | 3.218 | 3.293 | |
29F | 1/21+ | 1.080 (0.018) | 3.553 | 0.952 | 0.797 | 3.669 | 2.833 | 1.515 | 2.736 | 2.116 | 1.294 |
3/21+ | / | 6.407 | 2.246 | 2.294 | 6.349 | 5.047 | 3.442 | 6.660 | 3.829 | 2.816 | |
31F | 1/21+ | / | 0.648 | 0.542 | 0.628 | 0.311 | 0.680 | 0.796 | 0.176 | 0.340 | 0.390 |
3/21+ | / | 1.868 | 1.701 | 2.019 | 1.821 | 2.342 | 2.618 | 1.447 | 1.681 | 1.764 | |
28Ne | 21+ | 1.304 (0.003) | 1.553 | 1.401 | 1.362 | 1.830 | 2.110 | 2.196 | 1.804 | 1.947 | 1.983 |
41+ | 3.010 (0.006) | 2.952 | 2.770 | 2.757 | 3.302 | 3.512 | 3.779 | 3.342 | 3.458 | 3.510 | |
30Ne | 21+ | 0.792 (0.004) | 1.531 | 0.873 | 1.028 | 1.912 | 1.997 | 1.808 | 1.901 | 1.760 | 1.201 |
41+ | 2.235 (0.012) | 2.444 | 1.945 | 2.364 | 2.817 | 2.954 | 3.359 | 2.879 | 2.935 | 2.535 | |
32Ne | 21+ | 0.722 (0.009) | 0.768 | 0.682 | 0.841 | 0.857 | 1.262 | 1.482 | 0.659 | 0.858 | 0.932 |
41+ | / | 1.763 | 1.778 | 2.086 | 2.120 | 2.784 | 3.253 | 1.762 | 2.092 | 2.241 | |
34Ne | 21+ | / | 0.521 | 0.838 | 0.969 | 0.690 | 1.110 | 1.403 | 0.476 | 0.616 | 0.655 |
41+ | / | 1.387 | 2.028 | 2.267 | 1.922 | 2.670 | 3.158 | 1.424 | 1.679 | 1.747 |
Nucleus | State | (0–1)ħω | (0–3)ħω SDPF-M | (0–3)ħω SDPF-MU | (0–3)ħω SDPF-U-SI | (0–5)ħω SDPF-M | (0–5)ħω SDPF-MU | (0–5)ħω SDPF-U-SI |
---|---|---|---|---|---|---|---|---|
27F | 5/21+ | 0 | 0.795 | 0.543 | 0.236 | 0.951 | 0.877 | 0.300 |
29F | 5/21+ | 0 | 1.497 | 0.646 | 0.457 | 2.354 | 1.660 | 0.930 |
29F | 1/21+ | 0 | 1.972 | 1.003 | 1.226 | 2.716 | 2.302 | 1.967 |
29F | 3/21+ | 0 | 1.994 | 1.356 | 1.971 | 2.730 | 2.330 | 2.127 |
31F | 5/21+ | 2 | 3.413 | 2.689 | 2.346 | 4.030 | 3.452 | 2.519 |
33F | 5/21+ | 4 | 5.337 | 4.669 | 4.234 | 5.745 | 5.214 | 4.298 |
28Ne | 01+ | 0 | 1.090 | 0.570 | 0.261 | 1.307 | 1.089 | 0.377 |
30Ne | 01+ | 0 | 1.857 | 0.700 | 0.669 | 2.479 | 1.958 | 1.619 |
30Ne | 21+ | 0 | 1.965 | 0.690 | 1.330 | 2.533 | 2.192 | 2.053 |
30Ne | 41+ | 0 | 1.981 | 0.589 | 1.016 | 2.404 | 1.953 | 2.050 |
32Ne | 01+ | 2 | 3.705 | 2.693 | 2.385 | 4.038 | 3.515 | 2.660 |
34Ne | 01+ | 4 | 5.344 | 4.566 | 4.204 | 5.654 | 5.101 | 4.268 |
Nucleus | Configuration | (0–1)ħω | (0–3)ħω SDPF-M | (0–3)ħω SDPF-MU | (0–3)ħω SDPF-U-SI | (0–5)ħω SDPF-M | (0–5)ħω SDPF-MU | (0–5)ħω SDPF-U-SI |
---|---|---|---|---|---|---|---|---|
29F | π0d5/2ν(0d3/2)4 | 1 | 24.98 | 65.81 | 76.24 | 8.53 | 30.65 | 56.14 |
π0d5/2ν(0d3/2)2 (0f7/2)2 | 0 | 43.65 | 13.83 | 9.53 | 36.16 | 20.56 | 15.91 | |
π0d5/2ν(0d3/2)2 (1p3/2)2 | 0 | 15.41 | 4.42 | 2.93 | 15.14 | 14.28 | 7.92 | |
30Ne | π(0d5/2)2 ν(0d3/2)4 | 1 | 6.55 | 57.88 | 59.73 | 2.98 | 17.45 | 22.58 |
π(0d5/2)2ν(0d3/2)2 (0f7/2)2 | 0 | 45.4 | 12.88 | 11.08 | 32.53 | 17.94 | 17.49 | |
π(0d5/2)2ν(0d3/2)2 (1p3/2)2 | 0 | 10.27 | 3.41 | 3.74 | 8.56 | 10.33 | 10.21 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Liu, M.; Yuan, C. Cross-Shell Excitation in F and Ne Isotopes around N = 20. Symmetry 2021, 13, 2167. https://doi.org/10.3390/sym13112167
Liu M, Yuan C. Cross-Shell Excitation in F and Ne Isotopes around N = 20. Symmetry. 2021; 13(11):2167. https://doi.org/10.3390/sym13112167
Chicago/Turabian StyleLiu, Menglan, and Cenxi Yuan. 2021. "Cross-Shell Excitation in F and Ne Isotopes around N = 20" Symmetry 13, no. 11: 2167. https://doi.org/10.3390/sym13112167
APA StyleLiu, M., & Yuan, C. (2021). Cross-Shell Excitation in F and Ne Isotopes around N = 20. Symmetry, 13(11), 2167. https://doi.org/10.3390/sym13112167