Electric polarizabilities of two-electron atoms by a lower-bound procedure

Abstract

A method is described for calculating rigorous lower bounds to polarizabilities and other second-order properties even when, as usual, the field-free (unperturbed) problem cannot be solved exactly. This method has been applied to calculate dipole polarizabilities for the low-lying singlet and triplet S states of the two-electron ions H - , He, and Li + , using well-correlated variational trial functions up to 104 terms in length. As a byproduct of the rigorous bounds we obtain new high-accuracy estimates, based on the conventional variation-perturbation procedure, which largely supplant previous calculations on these ions. The lower bounds are accurate to within a small fraction of a per cent for all species except H - and the metastable 2 1 S state of He (where the accuracy is about 2 and 1% respectively), and this accuracy is sufficient to rule out many previous theoretical and experimental results. The calculated values are then employed to evaluate the leading unknown terms in the Z -1 expansion of the polarizability, thereby extending the high-accuracy treatment to all members of the isoelectronic sequence.