Calculations of the spin–orbit coupling constants and slater integrals for the 7snp (n = 7, 8, 9), 7snd (n = 6, 7, 8, 9) and 7snf (n = 5, 6, 7, 8) states in radium atom via an alternative way

Abstract

We present an alternative method suitable for the calculation of the spin–orbit coupling constants ζ and Slater integrals F(0) and G(k) in any atoms and ions which contain two valence electrons outside a closed p or d shells. This approach is based on the matrix elements of the spin–orbit and two-electron Coulomb interaction Hamiltonians as well as the matrix elements of the relativistic effective Dirac-Breit Hamiltonian for an N-electron atomic system. The application of this method on radium atom produced the spin–orbit coupling constants and Slater integrals for the 7s7p, 7s8p, 7s9p,7s6d, 7s7d, 7s8d, 7s9d, 7s5f, 7s6f, 7s7f, and 7s8f atomic states. In such a case, the various matrix elements were calculated in an intermediate spin–orbit coupling scheme. These matrix elements were then used to produce the numerical values of spin–orbit coupling constants and Slater integrals. The present results should provide the theoretical background that has heretofore been lacking in literature.