  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.
