Variational Calculations for (ns²) ¹Se, (np²) ¹D^e and (nd²) ¹G^e Resonance States for He Isoelectronic Sequences below the n = 2, 3 and 4 Hydrogenic Thresholds

Abstract

This work presents results of the different parameters which characterize the nonrelativistic Hamilton operator for the helium atoms allowing us to solve the Schr ö dinger equation. The total energy is decomposed into three terms allowing to separate the kinetic energy, the electrons-nucleus interaction energy and the electron-electron interaction energy of the (2s 2 , 3s 2 and 4s 2 ) 1 S e , (2p 2 , 3p 2 and 4p 2 ) 1 D e and (3d 2 and 4d 2 ) 1 G e resonance singlet states of the helium isoelectronic sequences. The states have been defined by using special forms of the Hylleraas type wave functions. The calculations have been carried out in the framework of the variational method using configuration interaction basis states with a real Hamiltonian. The agreement of the energy value of other states between the present theoretical values available in the literature is excellent. But as for the comparison of the kinetic energies, the electrons-nucleus energies interaction and the electron-electron interaction energies, we note a slight difference with the theoretical values common in literature.