How have they started? – A brief guide for pedestrians

Abstract

I shall present a very brief summary of subjects selected from what Prof. Akito Arima has done in the past years. I will focus on the initial works on the configuration mixing and on the Interacting Boson Model. Since there are many literatures on these subjects, I shall concentrate what have been done at the initial or at the pre-history stages. By doing this, we shall see how Prof. Akito Arima started from the scratch.

Keywords

shell model / configuration mixing / magnetic moment / interacting boson model

References

[1] A. Arima and H. Horie, Configuration mixing and magnetic moments of nuclei, Prog. Theor. Phys. 11(4), 509 (1954)

[2] A. Arima and H. Horie, Configuration mixing and magnetic moments of odd nuclei, Prog. Theor. Phys. 12(5), 623 (1954)

[3] M. G. Mayer, On closed shells in nuclei (II), Phys. Rev. 75(12), 1969 (1949)

[4] O. Haxel, J. H. D. Jensen, and H. E. Suess, On the “magic numbers” in nuclear structure, Phys. Rev. 75(11), 1766 (1949)

[5] M. G. Mayer and J. H. D. Jensen, Elementary Theory of Nuclear Shell Structure, New York: Wiley, 1955

[6] H. Noya, A. Arima and H. Horie, Prog. Theor. Phys. Suppl. 8, 33 (1959)

[7] A. Bohr and B. R. Mottelson, Nuclear Structure (I), W. A. Benjamin, New York, 1969 and World Scientific, Singapore, 1998

[8] R. J. Blin-Stoyle and M. A. Perks, The deviations of nuclear magnetic moments from the Schmidt lines, Proc. Phys. Soc. Lond. A 67(10), 885 (1954)

[9] T. Inoue, T. Sebe, H. Hagiwara, and A. Arima, The structure of the sd-shell nuclei (I): ¹⁸C, ¹⁸F, ¹⁹O, ¹⁹F, and ²⁰Ne, Nucl. Phys. 59(1), 1 (1964)

[10] A. Arima, H. Horiuchi, and T. Sebe, Weak coupling model of particles and holes in the sdshell nuclei, Phys. Lett. B 24(3), 129 (1967)

[11] A. Arima, S. Cohen, R. D. Lawson, and M. H. Macfarlane, A shell-model study of the isotopes of O, F and Ne, Nucl. Phys. A 108(1), 94 (1968)

[12] Y. Akiyama, A. Arima, and T. Sebe, The structure of the sdshell nuclei, Nucl. Phys. A 138(2), 273 (1969)

[13] A. Arima, M. Harvey, and K. Shimizu, Pseudo LS coupling and pseudo SU(3) coupling schemes, Phys. Lett. B 30(8), 517 (1969)

[14] A. Arima, V. Gillet, and J. Ginocchio, Energies of quartet structures in even-even N= Znuclei, Phys. Rev. Lett. 25(15), 1043 (1970)

[15] M. Ichimura, A. Arima, E. C. Halbert, and T. Terasawa, Alpha-particle spectroscopic amplitudes and the SU(3) model, Nucl. Phys. A 204(2), 225 (1973)

[16] I. Tonozuka and A. Arima, Surface a-clustering and adecays of ²¹²Po, Nucl. Phys. A 323(1), 45 (1979)

[17] A. Arima, G. E. Brown, H. Hyuga, and M. Ichimura, Effect of exchange currents on orbital g-factors and E1 sum rule for photoabsorption, Nucl. Phys. A 205(1), 27 (1973)

[18] K. Shimizu, M. Ichimura, and A. Arima, Magnetic moments and GT-type β-decay matrix elements in nuclei with a LS doubly closed shell plus or minus one nucleon, Nucl. Phys. A 226(2), 282 (1974)

[19] A. de-Shalit and I. Talmi, Nuclear Shell Theory, Academic Press, New York, 1963; Dover, Mineola, New York, 2004

[20] 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(2), 427 (2005)

[21] T. Otsuka, M. Honma, T. Mizusaki, N. Shimizu, and Y. Utsuno, Monte Carlo shell model for atomic nuclei, Prog. Part. Nucl. Phys. 47(1), 319 (2001)

[22] N. Shimizu, T. Abe, Y. Tsunoda, Y. Utsuno, T. Yoshida, T. Mizusaki, M. Honma, and T. Otsuka, Prog. Theor. Exp. Phys. 2012, 01A205 (2012)

[23] A. Arima, Soryushiron Kenkyu (素粒子论研究) 35, E47 (1996) https://www.jstage.jst.go.jp/article/soken/ 35/5/35 KJ00004813701/ article/-char/ja

[24] A. Arima, Three comments, Prog. Theor. Phys. Suppl. 125, 1 (1996) (Translated by T. Otsuka)

[25] A. Arima and F. Iachello, Collective nuclear states as representations of a SU(6) group, Phys. Rev. Lett. 35(16), 1069 (1975)

[26] A. Bohr and B. R. Mottelson, Nuclear Structure (II), W. A. Benjamin, New York, 1975 and World Scientific, Singapore, 1998

[27] R. F. Casten, Nuclear Structure from a Simple Perspective, Oxford: Oxford University Press, 2001

[28] L. Wilets and M. Jean, Surface oscillations in even-even nuclei, Phys. Rev. 102(3), 788 (1956)

[29] A. Klein and E. R. Marshalek, Boson realizations of Lie algebras with applications to nuclear physics, Rev. Mod. Phys. 63(2), 375 (1991)

[30] J. P. Elliott, Collective motion in the nuclear shell model (I): Classification schemes for states of mixed configurations, Proc. R. Soc. Lond.A 245(1240), 128 (1958)

[31] A. Arima and F. Iachello, Interacting boson model of collective states (I): The vibrational limit, Ann. Phys. 99(2), 253 (1976)

[32] A. Arima and F. Iachello, Interacting boson model of collective nuclear states (II): The rotational limit, Ann. Phys. 111(1), 201 (1978)

[33] F. Iachello and A. Arima, The Interacting Boson Model, Cambridge: Cambridge University Press, 1987

[34] A. Arima and F. Iachello, New symmetry in the sd boson model of nuclei: The group O(6), Phys. Rev. Lett. 40(6), 385 (1978)

[35] A. Arima and F. Iachello, Interacting boson model of collective nuclear states (IV): The O(6) limit, Ann. Phys. 123(2), 468 (1979)

[36] O. Scholten, F. Iachello, and A. Arima, Interacting boson model of collective nuclear states (III): The transition from SU(5) to SU(3), Ann. Phys. 115(2), 325 (1978)

[37] A. Arima, T. Ohtsuka, F. Iachello, and I. Talmi, Collective nuclear states as symmetric couplings of proton and neutron excitations, Phys. Lett. B 66(3), 205 (1977)

[38] T. Otsuka, A. Arima, F. Iachello, and I. Talmi, Shell model description of interacting bosons, Phys. Lett. B 76(2), 139 (1978)

[39] T. Otsuka, A. Arima, and F. Iachello, Nuclear shell model and interacting bosons, Nucl. Phys. A 309(1–2), 1 (1978)

[40] T. Mizusaki and T. Otsuka, Microscopic calculations for O(6) nuclei by the interacting boson model, Prog. Theor. Phys. Suppl. 125, 97 (1996)

[41] K. Nomura, N. Shimizu, and T. Otsuka, Mean-field derivation of the interacting boson model Hamiltonian and exotic nuclei, Phys. Rev. Lett. 101(14), 142501 (2008)

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