Upper and Lower Bounds to Atomic and Molecular Properties. II. Electric Polarizabilities of Four-Electron Atoms by a Lower-Bound Procedure

Abstract

Wave functions, which include interelectron coordinates $r_{\mathrm{ij}}$ explicitly, are employed for the $1s^{ 2}2s^{ 2}{}_{}{}^1{}_{}{}^{}S$ and $1s^{ 2}2s 2p {}_{}{}^1{}_{}{}^{}P_1^{}{}_{}{}^{}$ states of Be I, C III, and O V in obtaining lower bounds and Hylleraas variation-perturbation estimates of dipole polarizabilities for the lowest ${}_{}{}^1{}_{}{}^{}S$ states of Be I, C III, and O V. Interpolation techniques are used to make a graphical study of the polarizability behavior along the entire isoelectronic sequence. The results of this study are polarizabilities for the lowest ${}_{}{}^1{}_{}{}^{}S$ state of Be I with probable accuracy ≤ 2%, and the rest of the isoelectronic sequence with probable accuracy of (2-5)%.