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.作者简介：黄时中.E-mail: huangsz@mail.ahnu.edu.cn.通讯作者