The connection between the surface rigidity of the nuclear core, which has been accounted for in tenns of the surface tension of liquid drop nuclei, and its proper shell structure is discussed by using the method of the quantum mechanical description of the collective motion, which has been proposed by one of the present authors and others (§ 2). On the basis of such a consideration the surface rigidity of the core can be calculated, provided that the shell model is valid for the behaviour of particles forming the core (§ 3 and § 4). The noticeable features of our results obtained are that the calculated values of rigidity of cores are, in general, considerably larger than those due to the hydrodynamical estimation, and are closely related to the proper shell structures of cores (§ 4). Such a characteristic variation of the rigidity of cores is discussed in detail by comparing with the quadrupole moments of the " core±one extra-particle type " nuclei. Theoretical quadrupole moments thus obtained finely explain the observed values which have been noticed to depend on the shell structure (§ 5). Some discussions are devoted to the rigidity of a core with large defonnation (§ 6) .

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