原子核结合能的协方差分析

Covariance Analysis of Nuclear Binding Energy

以Weizs?cker公式为基础,使用协方差分析的研究方法,重新计算了原子核结合能中的体积项、表面项等5个系数,使原子核的结合能平均误差降至最低。在此基础上,利用Fattoyev给出的协方差方法,给出了各项系数的误差范围、各项系数与原子核结合能之间的关联系数、各项系数之间的关联系数。研究表明,原子核的结合能与对称能、表面能、库仑能有很大关系,而且对称能系数的误差很大,这里隐含着3个重要的物理规律:原子核可能存在四极形变;库仑能的大小可能因为四极形变而改变;可能存在中子皮、质子皮等影响对称能的大小。可以通过该项研究,对比系数间的关联性,合并减少系数的个数;得到结合能与体积项、表面项、对称能之间的密切程度等信息,为得出更为精确的原子核质量提供理论依据。

Based on the Weizsacker formula,five coefficients of nuclear binding energy were recalculated by the covariance analysis method to minimize the average error of the nuclear binding energy.The covariance method given by Fattoyev was used to give out the error ranges of each coefficient,the correlation coefficient between each coefficient and the nuclear binding energy,and the coefficient of correlation between coefficients themselves.The research shows that the nuclear binding energy is closely related with the symmetry energy,surface energy and Coulomb energy.The error of the symmetry energy coefficient is large,which suggests that three important physical laws are involved here:the nucleus may have quadrupole deformation;the size of Coulomb energy may change because of the quadrupole deformation;there may exist neutron skins and proton skins that affect the size of the symmetry energy.By the study,the correlation between the coefficients can be compared,the number of coefficients can be reduced and the information of the binding energy and the close relationship between the volume term and surface item can be got.The results provide a theoretical basis for achieving a more accurate value of nuclear mass.