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A new method which enables us to transcribe the dynamics of the system of even number of fermions 'into that of the boson system is developed, with the purpose of analysing the " anharmonic effects " on the collective oscillations in spherical even nuclei from the standpoint of the microscopic theory of the collective excitations. In the "harmonic approximation", a pair of bound quasi-pa:I;ticles is replaced by the "phonon" as an ideal boson. This replacement inevitably leads to neglecting two main effects; the dynamical effect due to the residual interactions omitted under the "harmonic approximation" and the effect of the Pauli-principle among the quasi-particles composing the different pairs. According to our theory, the two effects which cause "anharmonic effects" can be evaluated correctly, in principle. It is not our purpose to go into detailed quantitative calculations, but rather to develop the basic idea. § 1. IntroductionRecently the microscopic theory of the collectiye oscillations of spherical even nuclei 1 ) has clarified that the "phonon" used in the Bohr-Mottelson model is a strongly correlated (bound) pair of quasi-particles with a definite total angular momentum. It was also confirmed by using the so-called "pairing plus quadrupole force" that this picture for the "phonon" reproduces the approximately correct energy of the first excited state (with spin and parity 2+) of spherical even nuclei and the E2 transition probability from this leveP)The essential approximation used in this theory is the "harmonic approximation" which is known under such various names as Sawada's approximation, random phase approximation, method of approximate second quantization, method of linearized equation of motion and Dyson's new Tamm-Dancoff method. Under this "harmonic approximation ", the second excited state of spherical even nuclei corresponds to the two-" phonon" state, which consists of a degenerate triplet (0+, 2+, 4+), and the E2 cross-over transition (2 2 + ---c)O) and the Ml transition (2 2 + ---c)2 1 +) are forbidden.As is well kno-vvn, actual properties of the second excited states of real nuclei show appreciable deviations from the simple regularities. Thus it has been desired to investigate the "anharmonic effects " giving rise to such deviations in the framework of the microscopic theory. 3 ) at colostateuniv on July 17, 2015 http://ptp.oxfordjournals.org/ Downloaded from T. Marumori, 1"'\d. Yamamura and A. TokunagaThe main purpose of this paper is to develop a new method which enables us to transcribe the dynamics of the system of even number of fermions into that of the boson system'correctly, with the purpose of analysing the "anharmonic effects". In .the "harmonic approximation", a pair of quasi-particles is replaced by an ideal boson. This replacement inevitably leads to neglecting two main effects; the dynamical effects due to the. residual interactions (in the original Hamiltonian) omitted under the " harmonic approximation " and the effect of the Pauli-principle among the quasi-particles comp...

Contents § 1. In traduction §2. Verification of realization of the alpha-correlations in Beryllium regwn §3. Indispensable role of alpha-like four-body correlations in the sd-shell region 3. 1 Our viewpoints in the joint discussions m 1966 3. 2 Alpha-cluster plus 16 0-core model 3. 3 Approach based on the dominance of the alpha-correlation mode 3. 4 Connection with the viewpoint of molecule~like structure §4. Viewpoint of molecule-like structure in nuclei §5. Dual roles of the Pauli principle §6. §7."Critical" region --Coexistence of "molecular phase" with "shell phase" and its growth--Justification of density localization through the Hartree-Fock approach §8. Connection with saturation property and nuclear forces §9. Remarks on present status and future problems §1. Introduction 1The nucleus is a many-body quantal system self-sustained by the strong interaction. Usually we can regard this system as an aggregate of nucleons by absorbing main effects of the meson fields in determining nuclear structure at NERL on May 30, 2015 http://ptps.oxfordjournals.org/ Downloaded from

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) .