Cluster Expansion Method in Light Nuclei

The convergence of the Van Kampen cluster expansion for evaluating the binding energies of light nuclei using a hard-core potential has been studied for different forms of the correlation function $f$. A Jastrow-type trial function was used with a Slater determinant of harmonic-oscillator wave functions. The variational calculations were performed on ${\mathrm{H}}^3$ and ${\mathrm{He}}^4$. For ${\mathrm{H}}^3$, where all terms in the expansion were included, good convergence was obtained and the binding energy was in good agreement with the results of the Monte Carlo calculation of Tang et al., indicating a good trial function. In the case of ${\mathrm{He}}^4$, the variation with all terms up to and including three-particle correlation gave a binding energy in agreement with the Monte Carlo results and the same convergence as in ${\mathrm{H}}^3$. In all the calculations, no subsidiary conditions on the correlation function $f\left(r\right)\mathrm{}$ were necessary, provided the contribution to the energy from three-particle correlation was included in the variation. Also, the contribution from four-particle correlation was found in all cases to be very small.