Extrapolation method in shell model calculations with a deformed basis

Abstract

An extrapolation method in shell model calculations with a deformed basis is presented, which uses a scaling property of energy and energy variance for a series of systematically approximated wave functions to the true one. Such approximated wave functions are given by the variation-after-projection method concerning the full angular momentum projection. This extrapolation needs energy variance, which amounts to calculation of the expectation value of the square of the Hamiltonian ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}^{2}$. We present a method to evaluate this matrix element and show that a large reduction of its numerical computation can be done by taking advantage of time-reversal symmetry. The numerical tests are presented for $fp$-shell calculations with a realistic residual interaction.