# Neutron-proton pairing correction in the extended isovector and isoscalar pairing model

#### Abstract

An extended OST(8) model with multi-j orbits is constructed based on the angular momentum decomposition with "pseudo"-spin S for valence nucleons in a j orbit. It is shown that the isovector S=0 and T=1 pairs are exactly the J=0 and T=1 pairs in a given j orbit, while the isoscalar S=1 pairs are linear combinations of J=odd pairs, with which the pairing Hamiltonian can be used to estimate isovector and isoscalar pairing interactions. As an example of the model application, some low-lying J=0+ level energies of even-even and odd-odd A=18-28 nuclei up to the half-filling in the ds shell above the O16 core are fit by the model and compared with the fitting results of the same Hamiltonian in the OLST(8) form. It has been verified from the fitting of both the models that the isoscalar pairing interaction can be neglected in the lower-energy part of the spectra of these ds-shell nuclei as far as binding energies and a few J=0+ excited levels of these nuclei are concerned. With the mean-field plus isovector pairing interaction only, neutron-neutron, proton-proton, and neutron-proton pairing contributions at the ground or the lowest J=0+ state of these nuclei are estimated. It is shown that the isovector np pairing contribution to the binding in the odd-odd N=Z nuclei is systematically larger than that in the even-even nuclei. Furthermore, the isoscalar np pair content at the lowest J=0+ state of these nuclei is also estimated. In both the OST(8) and OLST(8) models, it is clearly shown that the isoscalar pair content in the lowest J=0+ state of the N=Z and N=Z±2 nuclei increases with increasing of the valence nucleons, especially in those even-even nuclei, which indicates the isoscalar pairing correlation to be of importance at low-lying states of N=Z and N=Z±2 nuclei, especially in those even-even nuclei with more valence nucleons up to the half-filling, even though the isoscalar pairing interaction is negligible.

*This paper has been withdrawn.*