The variation after projection shell model

In this paper, we review a recently developed approximated shell model method called as the variation after projection shell model (VAPSM). Some novel features in the VAPSM are presented. First of all, the VAPSM wave function can be considerably simplified by adopting just one projected basis state rather than previously adopting all [Formula: see text] angular-momentum projected basis states for each selected reference state. This is crucial in application of the VAPSM to the study of high-spin states. Second, the wave functions of the yrast and nonyrast states can be optimized simultaneously based on the Hylleraas–Undheim–MacDonald (HUM) theorem, which is famous in the field of quantum chemistry. Finally, the wave functions with different spins generated from the same reference state can be varied simultaneously. This makes it very convenient to study the rotational bands in deformed nuclei. In this sense, the VAPSM is also a microscopic collective model, but based on the shell model foundation.