The elastic scattering of ${\mathrm{He}}^3$ by alpha particles in the energy range 0-20 MeV is considered using the method of resonating-group structure in the one-channel approximation. A two-body, central potential of Gaussian form which fits the low-energy nucleon-nucleon scattering data as well as possible is used. Saturation is taken approximately into account by choosing the radii of the clusters according to the experimental data. Phase shifts are computed up to $l=6\mathrm{}$. The presence of a $l=3\mathrm{}$ resonance is predicted with an excitation energy of about 6 MeV. Angular distributions at 1.7 and 16.6 MeV in the c.m. system are also calculated. At 1.7 MeV, the theoretical result agrees very well with the experimental data. At 16.6 MeV, the calculation predicts correctly the position of the diffraction minima and maxima, but the differential cross sections are somewhat larger than the experimental values in the forward angular region. An optical-model analysis is also performed at these two energies. It is found that at the higher energy, an imaginary optical potential of about 2 MeV is necessary to obtain the best fit with experiment. This indicates that in the resonating-group calculation, channels other than the ${\mathrm{He}}^3$-$\alpha$ channel are also important in determining the elastic scattering cross section at relatively high energies. Specifically, one can see from the existing reaction data that the other important channels are the $p$-${\mathrm{Li}}^6$ channels with ${\mathrm{Li}}^6$ in the ground and the first excited state. Calculations are also done with a second two-body potential which was extensively used in resonating-group calculations by the London-group of Massey and Collaborators.

• Received 3 May 1963

DOI:https://doi.org/10.1103/PhysRev.131.2631