Brueckner calculations in harmonic oscillator basis

The binding energy (b.e.), r.m.s. radius and charge form factor of the⁴He nucleus are calculated for the Hamada-Johnston potential using the method developed in part I of this study. The single-particle spectrum is derived from that of a harmonic oscillator by means of an overall shiftC and state-dependent shifts _h of occupied levels. The's are chosen self-consistently and the dependence of results onC and oscillator frequency is examined. Third-order diagrams in the BG expansion for energy are explicitly calculated (except those belonging to the three-particle cluster) and their importance for getting a weak dependence of the b.e. onC is demonstrated. Dependence on remains rather strong; arguments are given in favour of the choice of that minimizes second-order diagrams. Effects due to the motion of the centre of mass of the nucleus are eliminated by subtracting T _CM calculated up to the second order, the usual zero-order approximation of T _CM being shown to overestimate the b.e. by 3–5 MeV. The computed b.e. and r.m.s. radius represent about 50% and 110% of experimental values respectively. The form factorF _ch(q) was computed for 0q ²20 fm^–2; the first-order approximation is a good fit to experimental data, while in the second order diagrams appear that worsen the fit forq ² > >10 fm^–2.The author thanks Professor I. Úlehla for stimulating discussions. The help of dr. J.Hoejí, who calculated a part of higher order diagrams, is gratefully acknowledged.