Nucleon-pair approximations for low-lying states of even-evenN=Znuclei

Abstract

In this paper we study nucleon-pair correlations of low-lying states for two typical cases of even-even $N=Z$ nuclei. The first case is a single ${g}_{9/2}$ shell with eight valence nucleons. In this case we study $S$-pair, isoscalar spin-aligned-pair, isoscalar spin-one-pair approximations, with both schematic and realistic interactions. We find that electric quadrupole transition rates and electric quadrupole moments exhibit different patterns depending on the pair-truncated scheme. In the second case we study ground states of $^{20}\mathrm{Ne},^{24}\mathrm{Mg},^{32}\mathrm{S},^{36}\mathrm{Ar},^{44}\mathrm{Ti},^{48}\mathrm{Cr},^{60}\mathrm{Zn},^{64}\mathrm{Ge},^{92}\mathrm{Pd}$, and $^{96}\mathrm{Cd}$. For ground states of these nuclei, the $S$-pair approximation is reasonably good (though not as good as for semimagic nuclei); the isoscalar spin-one-pair approximation is not very good. The isoscalar spin-aligned pair approximation is good for ground states of $^{44}\mathrm{Ti}$ and $^{96}\mathrm{Cd}$, and not very good for $^{48}\mathrm{Cr}$ and $^{92}\mathrm{Pd}$. The effect of the spin-orbit coupling strength on pairing correlations is studied. Our calculations suggests that the spin-orbit coupling favors the $S$-pair correlation in ground states of $N=Z$ nuclei.