Analytical Derivations of Single-Particle Matrix Elements in Nuclear Shell Model

Abstract

We present analytical method to calculate single particle matrix elements used in atomic and nuclear physics. We show seven different formulas of matrix elements of the operator f(r)drm where f(r) = rμ, rμ jJ(qr), V(r) corresponding to the Gaussian and the Yukawa potentials used in nuclear shell models and nuclear structure. In addition, we take into account a general integral formula of the matrix element 〈n′ l′|f(r) dr(m)|nl〉 that covers all seven matrix elements obtained analytically.