arXiv 2303.009452023-03-02nucl-thnucl-ex

球核库仑势的实在计算及对传统方法的检验

Realistic evaluation of Coulomb potential in spherical nuclei and test of the traditional approach

L. Xayavong, Y. Lim

备注：: 13 pages, 2 figures

摘要：

一个现实的评价库仑势已选定的一些核使用现有的模型无关的数据的电荷密度和最近发展的库仑能量密度泛函。在伍兹-撒克逊潜力作为一个核组件，我们能够量化质子单粒子能量的差异，由于从模型无关的数据的均匀分布，两个参数的费米函数，以及从微观Hartree-Fock计算使用有效的Skyrme相互作用获得的电荷密度的差异。如果适当地确定电荷密度模型的参数，则所获得的能量差通常在量值上很小，即约100 keV或更小。当最后一个被占据的状态被高度填充时，会出现相当大的差异，同时具有小的轨道角动量。硫同位素（$Z=16$）是这些原子核的一个很好的例子。不幸的是，尽管它的简单性，均匀分布不能用于评估库仑交换项在一个既定的方法，因为它是不可微的表面的一个核。传统上，交换项的缺失通过简单地排除最后一个质子对直接项的贡献来校正。%%我们还调查了这种方法，发现它的效果是简单地介绍了因素$(Z-1)/Z$到库仑直接项。从中到重核（通常在$sd$壳层之外），得到的质子能级比用精确的Fock项得到的高300-800 keV。对于较轻的核，结果往往相反，因为因子$(Z-1)/Z$向$Z\to 1$的极限迅速减小。因此，为了精确计算原子核结构，应避免这种传统方法。

英文摘要：

A realistic evaluation of Coulomb potential has been made for some selected nuclei using the available model-independent data for the charge density and the recent development of Coulomb energy-density functional. Within the Woods-Saxon potential as a nuclear component, we are able to quantify the differences in proton single-particle energies due to the differences from the model-independent data of the uniform distribution, the two-parameter Fermi function, as well as the charge density obtained from a microscopic Hartree-Fock calculation using the effective Skyrme interaction. The obtained energy differences are generally small in magnitude, namely about 100~keV or less if the parameters of the charge density models are appropriately determined. Considerable larger differences appear when the last occupied state is highly filled and, at the same time, has a small orbital angular momentum. Sulfur isotopes ($Z=16$) are a perfect example of these nuclei. Unfortunately, despite its simplicity, the uniform distribution cannot be used for evaluating the Coulomb exchange term within a well-established method because it is not differentiable at the surface of a nucleus. Traditionally, the missing of exchange term is corrected for by simply excluding the last-proton contribution to the direct term. %% We also investigate this approach and find that its effect is simply an introduction of the factor $(Z-1)/Z$ into the Coulomb direct term. From medium to heavy nuclei (typically beyond the $sd$ shell) the resulting proton levels are 300-800~keV higher than those obtained with the exact Fock term. The result for lighter nuclei tends to be opposite because the factor $(Z-1)/Z$ decreases rapidly towards the limit of $Z\to 1$. Therefore, this traditional approach should be avoided for a precision nuclear structure calculation.

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