The binding energy of the $\alpha$ particle is calculated to provide an example of the properties of the refined Brillouin-Wigner perturbation procedure. The potential consists of a series of Gaussian functions which are fitted to the Reid soft core potential. The terms in the perturbation series are evaluated in closed form, allowing critical tests of the number of oscillator states needed for precise calculations and the importance of multiparticle terms. The resulting formalism is similar to the separation method of Moszkowski and Scott, but in this case the nuclear force is separated into three parts. The divergent part of the strong short range repulsion is deducted from the perturbation series, even with the multiparticle terms. The relatively weak long range attractive part of the force is well adapted to ordinary perturbation theory. Finally one has an intermediate range component of the interaction which provides most of the binding energy in nuclear bound states.

NUCLEAR STRUCTURE Variational perturbation method. Reid soft core potential. ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.

• Received 22 December 1980

DOI:https://doi.org/10.1103/PhysRevC.23.2700