中文摘要：

以多电子原子塞曼哈密顿的球张量形式为基础，借助单体和双体算符在Slater表象中的矩阵元公式，利用不可约张量理论和角动量耦合理论推导出了包含磁场二次项的塞曼哈密顿在｜^3PJMJ〉表象中矩阵元的一般表达式。以氦原子1s4p组态为例，计算了氦原子4^3P态的精细结构裂距，并绘出了能级分裂图。

英文摘要：

Based on the spherical tensor form of the Zeeman Hamiltonian of multi-electron atom and by using the matrix elements of one-particle and two-particle operators in the Slater scheme, the matrix elements of the Zeeman Hamiltonian （including the quadratic field-dependent terms） for ｜^3PJMJ〉 scheme are carried out in virtue of angular momentum coupling theory and irreducible tensor theory. Take ls4p configuration of helium for example, fine structure splitting on the 4^3P state of helium has been calculated and the energy levels are plotted as a function of the magnetic field.