We present the nuclear matrix element for the neutrinoless double-beta decay of ${}^{48}\mathrm{Ca}$ based on large-scale shell-model calculations including two harmonic oscillator shells ($sd$ and $pf$ shells). The excitation spectra of ${}^{48}\mathrm{Ca}$ and ${}^{48}\mathrm{Ti}$, and the two-neutrino double-beta decay of ${}^{48}\mathrm{Ca}$ are reproduced in good agreement to the experimental data. We find that the neutrinoless double-beta decay nuclear matrix element is enhanced by about 30% compared to $pf$-shell calculations. This reduces the decay lifetime by almost a factor of 2. The matrix-element increase is mostly due to pairing correlations associated with cross-shell $sd\text{−}pf$ excitations. We also investigate possible implications for heavier neutrinoless double-beta decay candidates.

The stable existence of rod-shaped structures in highly excited states of ${}^{24}\mathrm{Mg}$ is studied based on a systematic cranked Hartree-Fock calculation with various Skyrme-type interactions. Its stability is examined by allowing the transition of the clusterlike structure to the shell-model-like structure. Especially, the rod-shaped state is exposed to two major instabilities: the bending motion, which is the main path for the transition to low-lying states, and the spin-orbit interaction, which is the driving force to break the $\alpha$ clusters and enhance the independent motion of the nucleons. The rod-shaped structure with large angular momentum is obtained as a metastable stationary state.

The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.

Miura transform is known as the transformation between Korweg de-Vries equation and modified Korweg de-Vries equation. Its formal similarity to the Cole-Hopf transform has been noticed. This fact sheds light on the logarithmic type transformations as an origin of a certain kind of nonlinearity in the soliton equations. In this article, based on the logarithmic representation of operators in infinite-dimensional Banach spaces, a structure common to both Miura and Cole-Hopf transforms is discussed. In conclusion, the Miura transform is generalized as the transform in abstract Banach spaces, and it is applied to the higher order abstract evolution equations.

The soliton existence in sub-atomic many-nucleon systems will be discussed. In many nucleon dynamics represented by the nuclear time-dependent density functional formalism, much attention is paid to energy and mass dependence of the soliton existence. In conclusion, the existence of nuclear soliton is clarified if the temperature of nuclear system ranges from 10 to 30 MeV. With respect to the mass dependence ⁴He and ¹⁶O are suggested to be the candidates for the self-bound states exhibiting the property of nuclear soliton.