Binding Energy of Helium with a Velocity-Dependent Potential

Abstract

We make a variational calculation of the binding energy of helium, using a two-body central velocity-dependent potential both in the ${}_{}{}^1{}_{}{}^{}S$ and in the ${}_{}{}^3{}_{}{}^{}S$ states. We have used the two-parameter Irving wave function, and its suitable modifications with three and four parameters, as trial functions. Our results show that the convergence is rather slow. Obviously the maximum binding energy is obtained for the four-parameter wave function. Our maximum value for the binding energy of helium is somewhat greater than the experimental value of 28.2 MeV, but is in reasonable agreement with similar calculations using hard-core potentials.