Formulation of a shell–cluster overlap integral with the Gaussian expansion method

Abstract

Abstract We formulate a computational method to evaluate the overlap integral of the shell-model and cluster-model wave functions. The framework is applied to the system of the core plus two neutrons, and the magnitude of the overlap of the shell-model configuration (core + $n$ + $n$) and the di-neutron cluster one (core + $2n$) is explored. We have found that the magnitude of the overlap integral is prominently enhanced when two neutrons occupy shell-model orbits with low orbital angular momenta, such as $s$- and $p$-wave orbits. The shell–cluster overlap is calculated in systems with $jj$-closed cores plus two neutrons, and the enhancement due to occupation of the $s$ or $p$ orbit also occurs in the systematic calculation. The effect of the configuration interaction on the shell–cluster overlap integrals is also discussed.