The Study Of The Nucleon Pair Approximation

In this article we first study structure coefficients of collective pairs with spinzero and spin two (SD) in a number of configurations by a few realistic nuclei. Weinvestigate the robustness of these structure coefficients. Second, we study the va-lidity of pair truncation of the nuclear shell model by using the semi-magic nucleus⁴⁶Ca. We present low-lying states based on both nucleon pair approximation (NPA)and exact shell-model (SM) calculations. We also calculate overlaps between wavefunctions of low-lying states calculated by using the NPA and those calculated by us-ing the SM. Third, we perform systematic calculations on low-lying states of nucleiwith A = 202 ? 212, using the NPA. We use a phenomenological shell-model Hamil-tonian. The building blocks of our model space include one J = 4 valence neutronpair, and one J = 4, 6, 8 valence proton pair, in addition to the usual S and D pairs.We calculate binding energies, excitation energies, electric quadrupole and magneticdipole moments of low-lying states, and E2 transition rates between low-lying states.Our calculated results are reasonably consistent with available experimental data. Thecalculated quadrupole moments and magnetic moments, many of which have not yetbeen measured for these nuclei, are useful for future experimental measurements.