Generator coordinate kernels between zero- and two-quasiparticle BCS states

Abstract

We give a method with which the matrix elements of operators between BCS states can be evaluated with the generalized Wick's theorem even when the excitation of a pair of quasiparticles leads to a vanishing of the overlap. We analyze the behavior of the mean field and the pairing contributions to the matrix elements of two-body operators versus the gauge angle of the orbital and find that each of them diverges as the overlap vanishes while their sum remains finite. A new definition of these quantities is proposed which removes the divergence occurring at zero overlap. A numerical application to a deformed heavy nucleus is done, which tests the feasibility of our prescription.