Coupled Hartree–Fock calculation of the electric dipole hyper-polarizabilities: He sequence

The variation perturbation method in the coupled Hartree-Fock (HF) scheme has been used to calculate the fourth-order energies of He, Li⁺ and Be²⁺ ions subjected to a uniform external electric field. The hyper-polarizabilities γ_h which are related to the fourthorder energies have been calculated neglecting intra-atomic correlation. For He the observed value is γ_h = 53.6 ± 4.0 a.u. The present estimate in the coupled and uncoupled HF schemes yield 36.2 and 45.3 a.u. respectively. The other calculations using correlated ground state wave function gave values in the range 42-44 a.u. The discrepancies between our result and those of others have been discussed.