POLARIZABILITIES OF 2-ELECTRON POSITIVE-IONS AND RYDBERG LEVELS OF LITHIUM

We have carried out precision calculations of various second-order sums for the two-electron positive ions Li+, Be2+, and B3+. These have the form SIGMA(N)[0\V\N][N\V\0]/(E(N)-E0)k, where k = 1,2,3. The perturbation V is in each case a multipole-potential term, and for k = 1 the sum corresponds to the usual definition of multipole polarizability. The initial state 0 and the intermediate states N are constructed from two-particle Hylleraas basis sets of the appropriate symmetry and angular momentum. Although the set N does not contain any true continuum functions, the pseudostates represent the continuum very well, and excellent convergence is obtained. These two-body quantities are then used to evaluate the energy levels of three-electron systems in high Rydberg states by the asymptotic-optical-potential method previously used for two-electron systems, retaining all terms up to order x(-6). The results are good, but they can be still further improved by including higher-order terms, which will require multiple summation over intermediate states.