An extended O$_{{\cal S}{\rm T}}$(8) model with multi $j$-orbits is constructed based on the angular momentum decomposition with "pseudo’’-spin ${ \cal S}$ for valence nucleons in a $j$-orbit. It is shown that the isovector ${\cal S}=0$ and T=1 pairs are exactly the J=0 and T=1 pairs in a given $j$-orbit, while the isoscalar ${\cal S}=1$ 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 ${\rm J}=0^{+}$ level energies of even-even and odd-odd A=18,{–},28 nuclei up to the half-filling in the $ds$-shell above the ${}^{16}$O core are fit by the model and compared with the fitting results of the same Hamiltonian in the O$_{\rm LST}$(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 O$_{{\cal S}{\rm T}}$(8) and O$_{\rm LST}$(8) models, it is clearly shown that the isoscalar-pair content in the lowest J=0${}^{+}$ state of the N=Z and N=Z$\pm 2$ 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$\pm 2$ nuclei, especially in those even-even nuclei with more valence nucleons up to the half-filling, even though the isoscalar pairing interaction is negligible.

中文翻译：

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扩展等矢量和等标量配对模型中的中子-质子配对校正

扩展的O $ _ {{\ cal S} {\ rm T}} $（8）模型具有多个$Ĵ$-轨道是基于角动量分解构造的，其中“ pseudo”自旋$ {\ cal S} $用于原子中的价核子$Ĵ$-轨道。结果表明，等值向量$ {\ cal S} = 0 $和T = 1对正好是给定的J = 0和T = 1对$Ĵ$-轨道，而等标量$ {\ cal S} = 1 $对是J =奇数对的线性组合，配对的哈密顿量可用于估计等矢量和等标量配对相互作用。作为模型应用的示例，一些低洼的$ {\ rm J} = 0 ^ {+} $能级能量为偶数和奇数A = 18，{–}，28个核，直至半个填写$ds$壳上方 ${}^{16}$O芯由模型拟合，并与相同哈密顿量的拟合结果以O $ {\ rm LST} $（8）形式进行比较。通过两个模型的拟合已经证明，等标量配对相互作用可以在这些光谱的较低能量部分中被忽略。$ds$壳核的结合能和几个J = 0${}^{+}$这些细胞核的兴奋水平受到关注。仅通过平均场加等矢量配对相互作用，地面或最低J = 0的中子-中子，质子-质子和中子-质子对的贡献${}^{+}$这些核的状态被估计。结果表明，在奇数N = Z核中，等位向量np配对对结合的贡献系统地大于在偶数-偶核中。此外，最低J = 0时的等量np对含量${}^{+}$这些核的状态也被估计。在O $ _ {{\ cal S} {\ rm T}} $（8）和O $ _ {\ rm LST} $（8）模型中，清楚地显示出等标量对含量最低J = 0${}^{+}$ N = Z和N = Z的状态$\pm 2$ 原子核随着价原子核数目的增加而增加，尤其是在那些偶数核原子中，这表明等量配对对在低位N = Z和N = Z时很重要$\pm 2$ 核，特别是在等价核中，价核子最多到半填充的偶数核，即使等比例配对相互作用可以忽略不计。