Abstract
The structure of exotic nuclei sheds new light on the linkage of the nuclear structure to the nucleonic interaction. The self-consistent mean-field (SCMF) theories are useful to investigate this linkage, which are applicable to many nuclei covering almost the whole range of the nuclear chart without artificial truncation of model space. For this purpose, it is desired to develop effective interaction for the SCMF calculations well connected to the bare nucleonic interaction. Focusing on ground-state properties, I show the results of SCMF calculations primarily with the Michigan-three-range-Yukawa (M3Y)-type semi-realistic interaction, M3Y-P6 and M3Y-P6a to be precise, and discuss in detail how the nucleonic interaction affects the structure of nuclei including those far off the [Formula: see text]-stability. The central channels of the effective interaction are examined by the properties of the infinite nuclear matter up to the spin dependence and the isospin dependence. While experimental information of the infinite matter is obtained by extrapolating systematic data on finite nuclei in principle, it is not easy to constrain the spin dependence and the isospin dependence without connection to the bare nucleonic interaction. The noncentral channels play important roles in the shell structure of the finite nuclei. The tensor force is demonstrated to affect [Formula: see text]- or [Formula: see text]-dependence of the shell structure and the magic numbers, on which the spin–isospin channel in the central force often acts cooperatively. By using the M3Y-P6 interaction, the prediction of magic numbers is given in a wide range of the nuclear chart, which is consistent with almost all the available data. In relation to the erosion of magic numbers in unstable nuclei, effects of the tensor force on the nuclear deformation are also argued, being opposite between nuclei at the [Formula: see text]- and the [Formula: see text]-closed magicities. Qualitatively consistent with the [Formula: see text]-force effect on the [Formula: see text]-splitting suggested from the chiral effective field theory, the density-dependent LS channel, which is newly introduced in M3Y-P6a, reproduces the observed kinks in the differential charge radii at the [Formula: see text]-closed magic numbers and predicts anti-kinks at the [Formula: see text]-closed magic numbers. The pairing correlation has significant effects on the halos near the neutron drip line. A new mechanism called “unpaired-particle haloing” is disclosed.
Highlights
Atomic nuclei are quantum many-body systems in which a finite number of nucleons are bound by themselves, showing a variety of interesting and nontrivial properties
It is of interest whether and how well the self-consistent mean-field (SCMF) frame with a specific effective interaction can describe the magic numbers indicated by experiments, and what numbers are predicted to be magic in the region where experiments have not reached
The SCMF theories are useful for this purpose, which give nuclear wave functions from scratch: the input of the SCMF approaches is only the effective Hamiltonian, and no artificial truncation of model space is required in the SCMF calculations
Summary
Atomic nuclei are quantum many-body systems in which a finite number of nucleons are bound by themselves, showing a variety of interesting and nontrivial properties. The G-matrix may work as an effective two-nucleon (2N ) interaction It is still questioned whether these manybody calculations are fully convergent, it seems close.[10] These problems prevent us from fully understanding basic properties concerning nuclear structure, e.g., the saturation, from microscopic standpoints, despite significant progress.[11,12,13,14,15,16,17,18] In atomic systems, which are composed of electrons, an approach using the energydensity functional (EDF) has been established to be a standard theoretical framework in describing their ground-state (g.s.) properties. I shall discuss the properties of exotic nuclei based on the SCMF approaches, constraining to g.s. properties and mainly focusing on their linkage to the nucleonic interaction For this purpose, I shall employ the Michigan-three-range-Yukawa (M3Y)-type semi-realistic nucleonic interaction,[22,23] which is based on the G-matrix but is partly modified from phenomenological standpoints. Though it cannot be exhaustive, I expect that this review sheds light on their relationship and stimulates future studies in this line
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