Variational Monte Carlo method for shell-model calculations in odd-mass nuclei and restoration of symmetry

TL;DR

This paper extends the variational Monte Carlo method with Pfaffian to odd-mass nuclei and incorporates angular-momentum projection, enabling accurate and efficient nuclear shell-model calculations for both even and odd nuclei.

Contribution

It introduces a new Pfaffian expression for odd-mass nuclei and implements a full angular-momentum projected trial state in VMC, enhancing accuracy and efficiency.

Findings

Unified VMC framework for even and odd nuclei.

Successful implementation of angular-momentum projection.

Accurate estimation of yrast energies via energy-variance extrapolation.

Abstract

We investigate two kinds of extensions for the variational Monte Carlo (VMC) method with the Pfaffian in the nuclear shell-model calculations. One is the extension to odd-mass nuclei, for which we find a new Pfaffian expression of the VMC matrix elements. We can, thereby, give a unified VMC framework both for even and odd mass nuclei. The other is the extension of the variation after angular-momentum projection. We successfully implement the full angular-momentum projected trial state into the VMC method, which can provide us with the precise yrast energies. We also find a unique characteristic, namely that this angular-momentum projection in the VMC can be even "approximately" performed. This characteristic is useful not only for efficient computation but also for precise estimation of the yrast energies through the energy-variance extrapolation.