Residual Interactions in Nuclear Shell Model and Pairing Energies

Abstract

An effective residual interaction of the shell model is investigated by maing use of the experimental values of the pairing energies P(j) = B E.(Z, N) + B E.(Z, N - 2) - 2B E.(Z, N - 1), and II(j) = 2B E.(Z, N) - B E.(N, N + 1) - B E.(Z, N - 1). It is assumed that the effective interactions between paired like nucleons (n-n, p-p) in the same orbit are central forces and have the form V_ij = [V₀ + V₁(σ_i · σ_j)]f(r_ij), and the Gaussian and Yukawa types are used for f(r_ij). The strength parameters V₀ and V₁ are determined from P(j)_exp and Π(j)_exp in the pure configurations. The results are V₁/V₀ ∼ 2, then the effective residual interactions are near upon the Rosenfeld force. The effects of tensor force and configuration mixing on V₀ and V₁ obtained in the case of central force and pure configurations are investigated. The parameters to give nuclear binding energies are evaluated and these values are compared with those given by several authors. A discussion for the effective residual interactions thus obtained are made in this paper.

Author notes

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Now at University of Tokyo, Department of Applied Physics, Faculty of Engineering, Tokyo