Finite-Mass Helium Atoms. I. The2P1State

The $2{}_{}{}^1{}_{}{}^{}P$ states of the helium isoelectronic series are investigated via 50-term variational wave functions containing two nonlinear parameters. The Hamiltonian, spin-free and nonrelativistic, is written directly in center-of-mass coordinates so that no adiabatic approximation is required. The expectation values of the Hamiltonian and of moments of the interparticle separations are reported. Isotope shifts are found and, as noted in a preliminary report, are in excellent agreement with experiment. In order to compare the results with previous theoretical results, the systems were similarly studied in the infinite-nuclear-mass limit (adiabatic approximation). The energies so obtained are the deepest thus far obtained by a direct calculation with a variational wave function. The expectation values of the operators were subjected to a differencing process to obtain estimates of the perturbation expansion coefficients for them, and the results are in good agreement with the directly calculated results of Knight and Scherr.