He I Ground-State Wave Function of the Form ψ=f(r1)f(r2)g(r12)*

A variational trial wave function of the form ${\mathrm{\psi =f(r}}_1{\mathrm{)f(r}}_2{\mathrm{)g(r}}_{12})$ has been applied to the ground state of He I. In Sec. I, f(r) is taken to be an arbitrary function and g(r₁₂) is taken as linear. The form of f(r) and the slope of g(r₁₂) are chosen to yield the minimum energy. The energy, —5.79613R_Hehc, and the form of f are compared with the results of earlier work and with the results obtained with analytic functions. A table of f(r) and the charge distribution is given. The charge distribution is compared with that obtained from a Hartree‐Fock wave function and the difference is discussed. In Sec. II, f(r) is taken as an exponential and g(r₁₂) is taken to be an arbitrary function. The coefficient in the exponent in f(r) and the form of g(r₁₂) are chosen to yield the minimum energy. The energy, —5.78252R_Hehc, and the form of f are compared with the results obtained with analytic wave functions. The behavior of g is shown in a table and by its asymptotic series. The probable effectiveness of ψ if both f(r) and g(r₁₂) are taken as arbi trary is discussed.