Theory of Collective Excitations in Spherical Odd-Mass Nuclei. IV: Formulation in the General Many-j-Shell Model

The aim of this paper is to give a systematic formulation of microscopic description of the collective excitations in spherical odd-mass nuclei. The theory can be regarded as a natural extension of the conventional quasi-particle-random-phase approximation for spherical even-mass nuclei into the case of spherical odd-mass nuclei. In the same manner as the conventional random-phase approximation for even-mass nuclei leads us to the concept of “phonon”, the theory necessarily leads us to the concept of a new kind of fermion-type collective excitation mode. Recent rapid accumulation of experimental data seems to be revealing the systematic presence of this kind of collective mode in many odd-mass nuclei.