Generator coordinate method with a conjugate momentum: application to the particle number projection

TL;DR

This paper extends the generator coordinate method by including a conjugate momentum, applying it to particle number projection, and demonstrating its effectiveness as a simpler alternative to the variation after projection method.

Contribution

It introduces a novel extension of the GCM using a conjugate momentum, applied to particle number projection, improving energy calculations for nuclei.

Findings

Ground state energy significantly lowered with the new method.

Effective for magic nuclei with zero pairing gap.

Offers a simpler alternative to VAP method.

Abstract

We discuss an extension of the generator coordinate method (GCM) by taking simultaneously a collective coordinate and its conjugate momentum as generator coordinates. To this end, we follow the idea of the dynamical GCM (DGCM) proposed by Goeke and Reinhard. We first show that the DGCM method can be regarded as an extension of the double projection method for the center of mass motion. As an application of DGCM, we then investigate the particle number projection, for which we not only carry out an integral over the gauge angle as in the usual particle number projection but also take a linear superposition of BCS states which have different mean particle numbers. We show that the ground state energy is significantly lowered by such effect, especially for magic nuclei for which the pairing gap is zero in the BCS approximation. This suggests that the present method makes a good alternative to the variation after projection (VAP) method, as the method is much simpler than the VAP.