@phdthesis{oai:sucra.repo.nii.ac.jp:00017920,
 author = {照屋, 絵理},
 month = {},
 note = {117 p., Nuclei in the heavy mass region are attractive to study since neutron-rich nuclei in this mass region are important for understanding the r-process in the nucleosynthesis. Up to now many investigations of nuclear structure for neutron-rich nuclei in the heavy mass region have been carried out. In recent years, for example, nuclei in the superheavy mass region have been produced and intensively studied at Radioactive Isotope Beam Factory (RIBF) in RIKEN.
Theoretically, nuclear structure in the heavy mass region has been studied using various models. For example, these nuclei are studied using mean field theories, where each nucleon motion is treated in a mean field. The nucleus shows various characteristic features and aspects due to the collective motion of nucleons. On the other hand, it is important to investigate the nucleus by considering independent motion of nucleons in addition to the collective motion, since some features of nuclei are determined by specific motion of only one or a few nucleons.
One of the established models that treat motion of nucleons microscopically is the nuclear shell model. By treating the nucleon motion in a completely independent way, the shell model describes irregular patterns of energy spectra in even-even nuclei in the transitional region and structure of odd-mass and doubly-odd nuclei, which are generally difficult to be reproduced in other models. However, only a limited number of shell model calculations have been carried out in the heavy mass region since dimension of shell-model configurations in the calculation becomes huge, then the shell model calculations soon infeasible. In particular, open-shell nuclei with more than mass number 200 require a large dimension of shell-model configurations so that they have not been analyzed enough using the shell model until now. Moreover, in order to understand nuclei deeply, it is necessary to analyze not only each nucleus itself, but also nuclei in that mass region systematically within one framework. However, there are only a limited number of systematic studies in the heavy mass region.
Recently we have devised a new method to reduce the dimension of the shell model configurations by effectively excluding the high-lying states which do not affect the low-lying structure. It enables us to carry out the systematic shell model calculation in the heavy mass region.
The aim of this thesis is to study features, aspects, and systematics of nuclear structure of nuclei around 208Pb using the large scale nuclear shell model. The systematic study is performed for nuclei with less than 126 neutrons and more than 82 protons (nuclei around mass 210; 33 species) and for nuclei with more than 126 neutrons and more than 82 protons (nuclei around mass 220; 23 species). Pb, Bi, Po, At, Rn, and Fr isotopes for even-even, odd-mass, and doubly-odd nuclei are systematically investigated. The energy levels and electromagnetic properties are calculated and compared with experiment. Specific features of each nucleus are analyzed and discussed. Additionally, structure of isomeric states, whose half lives are more than several nanoseconds, are analyzed for each nucleus., 1 Introduction 7
2 Framework of the nuclear shell model 10
2.1 Basic concept of the nuclear shell model . . . . . . . . . . . . . . . . . . . 10
2.2 Procedure of the shell model calculation and truncation scheme . . . . . . 11
2.3 Shell model Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Framework of the pair-truncated shell model . . . . . . . . . . . . . . . . . 14
3 Analysis for nuclei around mass 210 16
3.1 Nuclei around mass 210 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2 Theoretical framework for nuclei around mass 210 . . . . . . . . . . . . . . 17
3.3 Theoretical results for nuclei around mass 210 . . . . . . . . . . . . . . . . 19
3.3.1 Pb isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3.2 Bi isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3.3 Po isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3.4 At isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.5 Rn isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.3.6 Fr isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.4 Discussions for nuclei around mass 210 . . . . . . . . . . . . . . . . . . . . 43
3.4.1 Validity of the truncation . . . . . . . . . . . . . . . . . . . . . . . 43
3.4.2 Magnetic moments and quadrupole moments . . . . . . . . . . . . . 43
3.4.3 The MP-8 interaction . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.4.4 The particle number dependence of the i13/2 orbitals . . . . . . . . 47
3.4.5 The vi-1 13/2⊗πi 13/2 band . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4.6 The necessity of other kinds of interactions . . . . . . . . . . . . . . 51
4 Analysis for nuclei around mass 220 53
4.1 Nuclei around mass 220 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.2 Theoretical framework for nuclei around mass 220 . . . . . . . . . . . . . . 54
4.3 Theoretical results for nuclei around mass 220 . . . . . . . . . . . . . . . . 55
4.3.1 Pb isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3.2 Bi isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.3.3 Po isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3.4 At isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.3.5 Rn isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
4.3.6 Fr isotopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.4 Discussions for nuclei around mass 220 . . . . . . . . . . . . . . . . . . . . 76
5 Summary 82
Appendix 88
A Hamiltonian 89
A.1 Matrix elements of two-body shell-model interactions . . . . . . . . . . . . 89
A.2 Derivation of the shell model Hamiltonian . . . . . . . . . . . . . . . . . . 90
A.2.1 Quadrupole-pairing interaction . . . . . . . . . . . . . . . . . . . . 90
A.2.2 Quadrupole-quadrupole interaction . . . . . . . . . . . . . . . . . . 91
A.2.3 Octupole-pairing interaction . . . . . . . . . . . . . . . . . . . . . . 93
A.2.4 Octupole-octupole interaction . . . . . . . . . . . . . . . . . . . . . 94
A.3 Neutron-proton interactions for single-j shells . . . . . . . . . . . . . . . . 95
B Operators 97
B.1 The E2 transition rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
B.2 The M1 transition rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
B.3 The magnetic dipole moment . . . . . . . . . . . . . . . . . . . . . . . . . 98
B.4 The electric quadrupole moment . . . . . . . . . . . . . . . . . . . . . . . . 98
B.5 The occupation number . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
B.6 The ladder operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
C Particle-hole conversion 100
C.1 Denition of the hole-operator . . . . . . . . . . . . . . . . . . . . . . . . . 101
C.2 Matrix elements of the hole-operator . . . . . . . . . . . . . . . . . . . . . 102
C.3 Particle-hole conversions of operators . . . . . . . . . . . . . . . . . . . . . 103
C.3.1 Electromagnetic operators . . . . . . . . . . . . . . . . . . . . . . . 103
C.3.2 Operators which mix neutrons and protons . . . . . . . . . . . . . . 104
D Formulas 105
D.1 Matrix elements of radial part . . . . . . . . . . . . . . . . . . . . . . . . . 105
D.2 Clebsh Gordan coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
D.3 Six-j and nine-j . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
D.4 Spherical tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
D.5 Reduced matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110, 指導教員 : 吉永尚孝, text, application/pdf},
 school = {埼玉大学},
 title = {Systematic Shell-Model Study of Nuclei around 208Pb},
 year = {2017},
 yomi = {テルヤ, エリ}
}