关于液滴模型质量公式的系数和核半径
On the coefficients of the liquid drop model mass formulae and nuclear radii
摘要：
本文用最小二乘法拟合了2027个实验原子质量，确定了由液滴模型导出的不同质量公式的系数，这些公式中包括或不包括曲率能、库仑能的扩散修正、电荷交换修正项、不同形式的Wigner项和不同幂次的相对中子过剩量$I=(N-Z)/A$。库仑扩散修正$Z^2/A$项或电荷交换修正$Z^{4/3}/A^{1/3}$项对提高质量公式的精度起主要作用。维格纳项和曲率能量也可以分别用于相同的目的。在表面能和体积能中引入$|I|$依赖性略微提高了膨胀的效率，并且比$I^4$依赖性更有效。给出了再现实验核电荷半径的不同表达式。不同的拟合导致约17-18 MeV的表面能系数和1.22-1.23 fm的相对等效均方根电荷半径r $_0$。
英文摘要：
The coefficients of different mass formulae derived from the liquid drop model and including or not the curvature energy, the diffuseness correction to the Coulomb energy, the charge exchange correction term, different forms of the Wigner term and different powers of the relative neutron excess $I=(N-Z)/A$ have been determined by a least square fitting procedure to 2027 experimental atomic masses. The Coulomb diffuseness correction $Z^2/A$ term or the charge exchange correction $Z^{4/3}/A^{1/3}$ term plays the main role to improve the accuracy of the mass formula. The Wigner term and the curvature energy can also be used separately for the same purpose. The introduction of an $|I|$ dependence in the surface and volume energies improves slightly the efficiency of the expansion and is more effective than an $I^4$ dependence. Different expressions reproducing the experimental nuclear charge radius are provided. The different fits lead to a surface energy coefficient of around 17-18 MeV and a relative equivalent rms charge radius r$_0$ of 1.22-1.23 fm.
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