Based on the tensor expression for the Breit-Pauli Hamiltonian, and with the aid of irreducible tensor theory, the theory of relativistic corrections to the non-relativistic energies of many-electron atoms has been generalized to the case in which Racah wave functions are the linear combinations of multi-Slater wave functions, analytic formulism for calculating the relativistic corrections, which include mass correction, one-and two-body Darwin correction and spin-spin contact interaction, has been derived, all the angular interactions and spin sums involved in the problem have been worked out explicitly by using irreducible theory. The theory is applied to the ground state of carbon-like atoms.%以Breit-Pauli哈密顿的球张量形式为基础,借助不可约张量理论,将多电子原子能量的相对论修正理论拓展到了原子的拉卡波函数为多个Slater基函数的线性组合的情形,导出了此情形下多电子原子能量相对论修正(包括相对论质量修正项、单体和双体迭尔文修正项、自旋-自旋接触相互作用项)的解析表达式,完成了所有角向积分和自旋求和计算.利用所建立的理论,对类碳体系基态能量的相对论修正进行了具体计算.
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