Study ofp+He3andn+H3Systems with the Resonating-Group Method

The $p+{\mathrm{He}}^3$ and $n+{\mathrm{H}}^3$ systems are considered with the resonating-group method in the one-channel approximation. A purely central nucleon-nucleon potential which has different ranges in the singlet and triplet states is employed. The internal wave function of the three-nucleon cluster is a sum of two Gaussian functions, with its parameters adjusted to reproduce quite well the properties of the cluster. From the results obtained it is found that the agreement with experiment is quite satisfactory, although in the very low-energy region, detailed fit is not obtained, which is most probably due to the omission of the specific distortion effect in our calculation. An effective interaction between the clusters is also constructed. From this effective interaction it is concluded that the requirement of antisymmetry for the total wave function is very important. In particular, it creates an odd-even feature, wherein the effective potentials in the odd-$l$ and even-$l$ states are quite different.