NUCLEON PAIR APPROXIMATION OF THE SHELL MODEL: A REVIEW AND PERSPECTIVE

Abstract

The nuclear shell model (SM) provides a firm framework to study low-lying states in nuclei. However, the configuration space of the SM truncated to a single major shell for neutrons and protons is too huge to handle for medium-mass and heavy nuclei. In order to study properties of low-lying states, one must truncate the shell model space. Pair approximation is among one of the practical approaches along this line. The wave functions of a given nucleus can be constructed in arbitrary basis of the assumed configuration spaces. They can be built by coupling the valence particles stepwise, and this can be easily realized via the wellknown procedure of the Coefficients of Fractional Parentage (cfps). The configuration spaces can be also constructed by coupling the valence nucleon pairs with given spins. If all possible pairs are considered in the pair basis, the calculated results in the pair basis are equivalent to those of the exact shell model calculations. The Nucleon pair approximation (NPA) of the shell model refers to calculation in the nucleon pair basis with truncations of pairs, i.e., in the NPA only limited pairs are assumed to play important roles while others are neglected. The NPA is found to be very good and