Theory of Collective Excitations in Spherical Odd-Mass Nuclei. I

Abstract

A new systematic theory of describing the collective excitations in spherical odd-mass nuclei is developed. The theory can be regarded as a direct extension of the conventional quasi-particle-new-Tamm-Dancoff method (i.e. the quasi-particle-random phase approximation) for spherical even-mass nuclei into the case of spherical odd-mass nuclei. In order to construct properly the theory within the framework of the quasi-particle-new-Tamm-Dancoff method, it is shown to be decisive to introduce a new concept which precisely specifies the “dressed” three-quasi-particle modes. The new concept is recognized in connection with the “quasi-spin space” which has been introduced through the quasi-spin formalism for the pairing correlations. It is not the purpose of this paper, part I, to go into a clear-cut formulation of the theory and into detailed quantitative calculations, but rather to put an emphasis on the explanation of basic ideas.