Nucleon-pair approximation of low-lying states forN=Znuclei

Abstract

In this paper the nucleon-pair approximation is studied for two typical cases of $N=Z$ nuclei, by using both schematic and effective interactions. The first case is given by four nucleons in a single-$j$ shell, for which we study the relevance of the seniority scheme, the spin-aligned isoscalar pair approximation, and the pair approximation of isoscalar pairs with spin 1, under different interactions. The nonorthogonality between wave functions with the lowest seniority quantum number and those of the spin-aligned pair approximation are studied with examples. In the second case we study low-lying states of two realistic nuclei, $^{20}\mathrm{Ne}$ and $^{24}\mathrm{Mg}$. In this case we find that, interestingly, the ground band states of these two nuclei are well described by both isovector and isoscalar pair approximations.