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

Background: While a large-scale shell model calculation (LSSM) is a powerful model to describe the nuclear spectroscopic information, it requires a huge amount of computational resources. As an efficient approximation framework to the LSSM, we have introduced the variational Monte Carlo (VMC) method [T. Mizusaki et al., Phys. Rev. C 85, 021301(R) (2012)]. However, this framework was applicable only to even-mass nuclei. Purpose: We aim to extend the VMC method for better precision and to make it applicable to odd-mass nuclei. Methods: We investigate two kinds of extensions for the 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. The other is the extension of the variation after angular-momentum projection. Results: We successfully implement the full angular-momentum projected trial state into the VMC method, which can provide us with precise yrast energies. We also find a unique characteristic, namely that this angular-momentum projection in the VMC can be even "approximately" performed. Conclusions: A unified VMC framework with the variation after projection is given both for even and odd-mass nuclei. The approximate angular-momentum projection is useful not only for efficient computation but also for precise estimation of the yrast energies through the energy-variance extrapolation.