Abstract
A variational trial wave function of the form ψ=f(r1)f(r2)g(r12) 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, —5.79613RHehc, 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, —5.78252RHehc, 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.
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