Charles W. Scherr

Two‐Electron Atoms. IV. Some Sixth‐Order Expectation Values

The sixth‐order perturbation ground‐state wavefunction for two electrons about a nucleus of charge Z obtained in Paper III of this series is used to compute perturbation expectation expansion coefficients 〈Ω〉p for 34 operators Ω through p = 6 where the total expectation value of an operator 〈Ω〉 is given by 〈Ω〉 = ΣpZ—p〈Ω〉p in appropriate units. Estimates of the accuracy of the calculation are obtained by comparison with exactly known values, by comparison with total values obtained from the accurate variational calculations of Pekeris, and by comparison with calculations based on Eqs. (V.1) and (V.2) of Paper III of this series. The function of the higher order correction terms is discussed.

Simple Configuration‐Interaction Wave Functions. II. Two‐Electron Ions: An Analytic Study

An analytical study of the 1S ground state of helium‐like ions employing the open‐shell function (1s1s′) and the angularly correlated configuration‐interaction function (1s1s′)+λ(2p)2 has been made. Expressions for the wave function parameters, energy values, and certain other expectation values in terms of the nuclear charge Z have been obtained. These are asymptotic expressions for large Z, but they reproduce numerically obtained results for small Z with sufficient accuracy to be useful for many purposes.

Relativistic corrections for variational wavefunctions

A consistent procedure based on a suggestion of Boys and Price is recommended for the simple inclusion of relativistic corrections in the Breit approximation into variational wavefunctions. A previous discussion is criticized as introducing error terms of the same order as the quantities being studied.

Isotope Shifts in the 21P and 23P States of the He and Li+ Systems

Energy values and isotopic shifts were calculated for the 2/sup 1/P and 2/sup 3/P states of the Re and Li/sup +/ systems. The results were obtained by applying the variational procedure to 50term wavefunctions. The discrepancy between theory and experiment was brought within the limits of experimental accuracy. (P.C.H.)

Some First‐Order Perturbation Energy Values

Computational formulas for first-order perturbation energy correction for singly excited singlet and triplet states of helium isoelectronic sequence

Simple Configuration Interaction Wave Functions. III. Three‐Electron Atomic System: An Analytic Study

An analytical study of the 2S ground state of lithium like ions employing Slater‐type orbitals to form the open‐shell function (1s1s′2s) and the angularly correlated configuration‐interaction functions (1s1s′2s)+λ1s(2p)2 and (1s1s′2s)+λ2s(2p)2 has been made. Expressions for the wave function parameters and energy values in terms of the nuclear charge Z have been obtained. These are asymptotic expansions for large Z, but they reproduce numerically obtained results for small Z with sufficient accuracy to be useful for many purposes. An unusual result is that, for large Z, the computed energy values are lowest if the orbitals 1s and 1s′ are allowed to have complex orbital exponents.