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-p hase approximation for spherical even-mass :imclei . 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

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... 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.