The nuclear shell model: Simplicity from complexity

doi:10.1007/s11467-018-0847-2

Front. Phys.

2018, Vol. 13

Issue (6) : 132103 https://doi.org/10.1007/s11467-018-0847-2

PERSPECTIVE

The nuclear shell model: Simplicity from complexity

Igal Talmi(

)

Department of Particle Physics and Astrophysics, The Weizmann Institute of Science, Rehovot 76100, Israel

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Abstract

The shell model of atomic nuclei has been in intensive use since the middle of the previous century. This simple model of very complex nuclei, offers a quantitative description of its many features. Other features follow from small deviations from the extreme picture. Our friend and colleague Akito Arima made seminal contributions to this field starting with his famous paper with Horie on the magnetic moments of nuclei [Prog. Theor. Phys. 11, 509 (1954)]. In the following, a detailed description of a simple example is considered. It is the 1f_7/2 shell of the neutrons in the nuclei between ⁴⁰Ca and ⁴⁸Ca and of the protons in the nuclei between ⁴⁸Ca and ⁵⁶Ni. The results demonstrate the power and elegance of the shell model. They show how simplicity arises out of complexity. It is also shown how small deviations from the simple shell model lead to effects, in which valence neutrons act as if they carry electric charge.

Keywords shell model effective interactions seniority binding energies effective charges nuclear radii

Corresponding Author(s): Igal Talmi

Issue Date: 13 December 2018

Cite this article:

Igal Talmi. The nuclear shell model: Simplicity from complexity[J]. Front. Phys. , 2018, 13(6): 132103.

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https://academic.hep.com.cn/fop/EN/10.1007/s11467-018-0847-2
https://academic.hep.com.cn/fop/EN/Y2018/V13/I6/132103

1	A. Arima and H. Horie, Configuration mixing and magnetic moments of odd nuclei, Prog. Theor. Phys. 11, 509 (1954) https://doi.org/10.1143/PTP.11.509
2	W. Heisenberg, Ueber den Bau der Atom Kerne, Zeits. F. Physik. 77, 1 (1932) https://doi.org/10.1007/BF01342433
3	J. H. Bartlett, Nuclear structure, Nature 130, 165, Structure of atomic nuclei, Phys. Rev. 41, 370 (1932) https://doi.org/10.1103/PhysRev.41.370.2
4	W. M. Elsasser, Sur le principe de Pauli dans les noyaux, J. de phys. et radium 4, 549; II 5, 389; III 635 (1934); Energies de liaison des noyaux lourds, 6, 473 (1935)
5	N. Bohr, Neutron Capture and nuclear Constitution, Nature 137, 344 (1936) https://doi.org/10.1038/137344a0
6	G. Racah, Theory of complex spectra (I), Phys. Rev. 61, 186; Theory of complex spectra (II), Phys. Rev. 62, 438 (1942); Theory of complex spectra (III), Phys. Rev. 63, 367 (1943) https://doi.org/10.1103/PhysRev.62.438
7	M. G. Mayer, On closed shells in nuclei, Phys. Rev. 74, 235 (1948) https://doi.org/10.1103/PhysRev.74.235
8	E. Feenberg and K. C. Hammack, Nuclear shell structure, Phys. Rev. 75, 1877 (1949) https://doi.org/10.1103/PhysRev.75.1877
9	L. Nordheim, On spins, moments and shells in nuclei, Phys. Rev. 75, 1894 (1949) https://doi.org/10.1103/PhysRev.75.1894
10	M. G. Mayer, On closed shells in nuclei (II), Phys. Rev. 75, 1969
11	O. Haxel, J. H. D. Jensen and H. E. Suess, On the “magic numbers” in nuclear structure, Phys. Rev. 75, 1766 (1949), where earlier references are listed. https://doi.org/10.1103/PhysRev.75.1766.2
12	M. G. Mayer, Nuclear configurations in the spin-orbit coupling model (I): Empirical evidence, Phys. Rev. 78, 16 (1950) https://doi.org/10.1103/PhysRev.78.16
13	M. G. Mayer, Nuclear configurations in the spin-orbit coupling model (II): Theoretical considerations, Phys. Rev. 78, 22 (1950) https://doi.org/10.1103/PhysRev.78.22
14	G. Racah, Nuclear coupling and shell model, Phys. Rev. 78, 622 (1950) https://doi.org/10.1103/PhysRev.78.622
15	D. Kurath, Effect of finite range interactions in the (jj) coupling shell model, Phys. Rev. 80, 98 (1950) https://doi.org/10.1103/PhysRev.80.98
16	I. Talmi, On the spin of the nuclear ground state in the jj-coupling scheme, Phys. Rev. 82, 101 (1951) https://doi.org/10.1103/PhysRev.82.101
17	I. Talmi, nuclear spectroscopy with harmonic oscillator wave functions, Helv. Phys. Acta 25, 185 (1952)
18	K. Ford and C. A. Levinson, Independent-particle model of the nucleus (I): Inter particle forces and configuration mixing, Phys. Rev. 99, 742 (1955); Independent-particle model of The nucleus (III): The calcium isotopes, Phys. Rev. 100, 13 (1955)
19	S. Goldstein and I. Talmi, Related jj-coupling configurations in 38Cl and 40K, Phys. Rev. 102, 589 (1956) https://doi.org/10.1103/PhysRev.102.589
20	S. P. Pandya, Nucleon-hole interaction in jj-coupling, Phys. Rev. 103, 956 (1956) https://doi.org/10.1103/PhysRev.103.956
21	I. Talmi and I. Unna, Theoretical interpretation of energy levels of light nuclei, Ann. Rev. Nucl. Sci. 10, 426 (1961)
22	R. D. Lawson and J. L. Uretsky, Excited states in the proton f7/2 shell, Phys. Rev. 106, 1369 (1957) https://doi.org/10.1103/PhysRev.106.1369
23	I. Talmi, Energies of fn7/2 nuclear configurations, Phys. Rev. 107, 326 (1957) https://doi.org/10.1103/PhysRev.107.326
24	D. Amit and A. Katz, Effective interaction calculations of energy levels and wave functions in the nuclear 1pshell, Nucl. Phys. 58, 388 (1964) https://doi.org/10.1016/0029-5582(64)90549-8
25	S. Cohen and D. Kurath, Effective interaction for the 1pshell, Nucl. Phys. 73, 1 (1965) https://doi.org/10.1016/0029-5582(65)90148-3
26	B. H. Wildenthal, Empirical strengths of spin operators in nuclei, Prog. Part. Nucl. Phys. 11, 5 (1984), where earlier references are listed. https://doi.org/10.1016/0146-6410(84)90011-5
27	B. A. Brown and B. H. Wildenthal, Status of the nuclear shell model, Ann. Rev. Nucl. Sci. 38, 29 (1988) https://doi.org/10.1146/annurev.ns.38.120188.000333
28	E. Caurier, G. Martinez-Pinedo, F. Nowacki, A. Poves, and A. P. Zuker, The shell model as a unified view of nuclear structure,Rev. Mod. Phys. 77, 427 (2005) https://doi.org/10.1103/RevModPhys.77.427
29	T. Otsuka, et al., Monte Carlo shell model for atomic nuclei, Prog. Part. Nucl. Phys. 47, 319 (2001); N. Shimizu, et al., New-generation Monte Carlo shell model for the K computer era, Prog. Theor. Exp. Phys. 2012, 01A205 (2012) https://doi.org/10.1016/S0146-6410(01)00157-0
30	B. H. Flowers, Studies in jj-coupling (I): Classification of nuclear and atomic states, Proc. Roy. Soc. A 212, 248 (1952) https://doi.org/10.1098/rspa.1952.0079
31	G. Racah, Nuclear levels and Casimir operator, in: Farkas Memorial Volume, Res. Council of Israel, Jerusalem, 1952
32	A. de Shalit and I. Talmi, Nuclear Shell Theory, Academic Press, 1963, reprinted by Dover Publications, 2004
33	I. Talmi, Simple Models of Complex Nuclei, Harwood, 1993
34	E. P. Wigner, Group Theory and Its Application to the Quantum Mechanics of Atomic Spectra, Academic Press, 1959
35	G. Racah, Theory of complex spectra (II), Phys. Rev. 62, 438 (1942) https://doi.org/10.1103/PhysRev.62.438
36	E. P. Wigner, Unpublished widely circulated MS. Reprinted in: Quantum Theory of Angular Momentum, Eds. L. C. Biedenharn and H. van Dam, Academic Press, 1965
37	I. Talmi, Effective interactions and nuclear models, in: Proc. Int. School Phys. Enrico Fermi, Varenna (1984)
38	A. Volya. Manifestation of three-body forces in f7/2- shell nuclei, Europhys. Lett. 86, 52001 (2009) https://doi.org/10.1209/0295-5075/86/52001
39	P. Van Isacker and I. Talmi, Effective three-body interactions in nuclei, Europhys. Lett. 90, 32001 (2010) https://doi.org/10.1209/0295-5075/90/32001
40	R. F. Garcia Ruiz, et al., M. L. Bissell, K. Blaum, Ground-state electromagnetic moments of calcium isotopes, Phys Rev. C 91, 041304(R) (2015)
41	L. Zamick, Two-body contribution to the effective radius operator, Ann. Phys. 66, 784 (1971) https://doi.org/10.1016/0003-4916(71)90080-7
42	I. Talmi, On the odd-even effect in the charge radii of isotopes, Nucl. Phys. A 423, 189 (1982)
43	A. Andl, K. Bekk, S. Göring, et al., Isotope shifts and hyperfine structure of the 4s21S0–4s4p1P1 transition in calcium isotopes, Phys. Rev. C 26, 2194 (1982) https://doi.org/10.1103/PhysRevC.26.2194
44	A. Arima and F. Iachello, Collective nuclear states as representations of a SU(6) group, Phys. Rev. Lett. 35, 1064 (1975)
45	E. U. Condon and G. H. Shortley, The Theory of Atomic Spectra, Cambridge University Press, 1951
46	G. Racah, Model interactions in atomic spectroscopy, J. Quant. Spectroscop. Radiat. Transfer 4, 617 (1964) https://doi.org/10.1016/0022-4073(64)90022-6
47	I. Talmi, Generalized seniority and structure of semimagic nuclei, Nucl. Phys. A 172, 1 (1971) https://doi.org/10.1016/0375-9474(71)90112-6

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