Atomic fine-structure calculations performed with a finite-nuclear-mass approach and with all-electron explicitly correlated Gaussian functions

A general algorithm for calculating an atomic fine structure is developed and implemented. All-electron explicitly correlated Gaussian functions and a finite-nuclear-mass (FNM) variational method are used in the approach. The leading alpha(2) relativistic and alpha(3) (and approximate alpha(4)) QED corrections are accounted for (alpha is the fine-structure constant). The approach is tested in calculations of P-3 states of the helium and beryllium atoms. The results are compared with experimental data and the systematic deviations -0.002 cm(-1) and -0.7 cm(-1) are found for P-3(J=0,1,2) excitation energies of He-4 and Be-9, respectively.