On the "Anharmonic Effects" on the Collective Oscillation in Spherical Even Nuclei. II

Abstract

On the basis of a kind of perturbation theory starting with the solutions of the “harmonic approximation” (the random phase approximation) as the zeroth-order approximation, a method to evaluate the correction to the first 2⁺ state and the splitting of the triplet (0⁺, 2⁺, 4⁺) in the spherical even nuclei is presented. An essential difficulty that the states obtained under the “harmonic approximation” do not form an orthogonal set in rigorous sense is overcome by transcribing the original quasi-particle system into the “ideal boson space” according to the theory proposed in a previous paper. In this “ideal boson space”, the states obtained under the “harmonic approximation” form a complete orthogonal set, so that we can safely use them as the zeroth-order approxiation. By adopting the Hamiltonian with “pairing plus quadrupole force”, our results are compared with those obtained by Do Dang and Klein with their “spectral decomposition method”. It is shown that our results are very similar to theirs in so far as the “phonon-quasi-particle coupling” is neglected. The advantage of our method in evaluating the effects of “phonon-quari-particle coupling” is emphasized.