On Applicability of the Random Phase Approximation to the Collective Excitation in Spherical Even Nuclei. I

Abstract

In order to check the applicability of the random phase approximation (the RPA), the correction to the RPA for the first 2⁺ state in spherical even nuclei is evaluated using a kind of perturbation theory (starting with the solutions of the RPA as zeroth-order approximation). According to our method, in so far as the first-order correction is concerned, some ambiguities depending on various methods (presented by several authors) to transcribe the system into the boson space are avoidable. Physical implication of the correction is considered. Numerical results for Ni-isotopes (Ni⁶⁰ and Ni⁶²) and for the single j = 15/2 shell model show that the correction to the RPA is unexpectedly large in the region of “phonon” energy which we are interested in. We are thus forced to conclude that the conventional approach in terms of the RPA should be modified since in nuclear problems the total number of states in the shell under consideration, Ω, is not so large to guarantee the RPA and, as a result, the magnitude of correction in that region becomes highly sensitive to the force-strength χ.