[en] A method for solving the shell-model equations in terms of a basis which includes correlated subsystems is presented. It is shown that the method allows drastic truncations of the basis to be made. The corresponding calculations are easy to perform and can be carried out rapidly

[en] The spin-tensor decomposition method has been used to analyze the shell model effective interactions in sd shell systematically. Almost all the interactions have been studied, including the microscopic interactions and phenomenological ones. It can be noticed that the discrepancies between the central forces of microscopic interactions with the ones of empirical interactions are remarkable. (authors)

[en] We review two off-shell models for spontaneously broken $\mathcal{N}=1$ and $\mathcal{N}=2$ supergravity proposed in arXiv:1702.02423 and arXiv:1707.07390. New results on nilpotent $\mathcal{N}=1$ supergravity are also included.

No abstract available

[en] We perform shell model calculations using a quadrupole-quadrupole interaction (Q.Q) in a single j shell space. We show that this one-parameter interaction is a good predictor of where nuclear isomerism occurs and where it does not occur. The limitations of this interaction are also discussed. We then include other interactions, e.g. in the ${\mathrm{f}}_{7/2}$ shell those obtained from the (local) spectrum of a two particle system and then from a two hole system. In the ${\mathrm{g}}_{9/2}$ where there is insufficient empirical data from the two hole system and so various empirical interactions are used. (paper)

[en] One body levels for a harmonic potential are computed during the fission process using two-center shell model. The parametrization of the nuclear shape is obtained by smoothly joining two spheres with a third spherical surface. Both corrections due to mass-asymmetry and the necking-in and also that due the spin interactions are determined to agree with this special case. (Author)

[en] The procedure to transfer the description of a fermion system from the truncated shell model space built in terms of collective pairs onto a space of corresponding bosons has been discussed. The procedure has been applied to systems of six nucleons in the 1p0f shell under the assumption that valence nucleons occupy the 1p_3_/_2, 1p_1_/_2 and 0f_5_/_2 orbitals while the 0f_7_/_2 subshell is closed. The boson Hamiltonian has been deduced from the shell-model one. The effects of the truncation of the boson Hamiltonian to one- and two-body terms have been examined. (author)

[en] Projection operators for the use within the ab initio no-core shell model are suggested

[en] In this article I first discuss collaborations between France and Japan on nuclear physics in the past, at present and in future. Next I present some recent results of my own research on eigenvalue problems. (author)

[en] We propose some new, efficient, and practical extrapolation methods to obtain a few low-lying eigenenergies of a large-dimensional Hamiltonian matrix in the nuclear shell model. We obtain those energies at the desired accuracy by extrapolation after diagonalizing small-dimensional submatrices of the sorted Hamiltonian matrix.