Energy levels for Be I calculated using a model potential and cores approximations

Abstract

A two-electron model Hamiltonian, used for Be I, includes a core polarization potential V_pol(1,2) which has asymptotic form V_pol approximately - alpha ((r₁/r₁ ²)+(r₂/r₂ ²))² where alpha is the polarizability of Be III 1s¹. Solutions are obtained using a frozen-cores method. Two approximations are considered: (a) uses an expansion with core states Be II 2s and 2p; (b) includes in addition a 3d core orbital with a parameter determined variationally. For the series ¹S, ³S, ¹P⁰, ³P⁰, ¹D, ³D, ¹F⁰ and ³F⁰, results are obtained for all bound states ( epsilon 1P, ³P, ¹D⁰, ³D⁰ converging to Be II 2p, results are obtained for n<or=10 and for n= infinity . The calculated ionization energies are more accurate than those obtained in previous theoretical work.