The [formula omitted] state of 3H and 3He below the break-up threshold : (I). Hamada-Johnston potential

Abstract

We describe a series of accurate calculations on the J π = 1 2 + state of 3H and 3He with the Hamada-Johnston potential, below the threshold for break-up. Quantities calculated for the bound states include the binding energy, percentages of various angular states, charge and mass radii, electric form factors, and Coulomb energies for both point and extended protons. The charge form factors show a typical diffraction minimum at a momentum transfer of around 12.6 fm -2, in rather good agreement with the recent experimental values of McCarthy et al. For n-d elastic scattering we compute the complete (2x2) scattering matrix up to a c.m. energy of 4 MeV. To test the sensitivity of the results to the interaction used, the effects of an additional three-body potential, and of a change in the strength of the potential component 1 V c + are also investigated. We find that, when either of these additional terms is adjusted to fit the triton energy E( 3 H) , reasonable overall agreement with experiment is obtained for those parameters, such as the charge radius, which are expected to depend chiefly on the overall size of the triton and not on its detailed structure. Discrepancies remain in the doublet scattering length, and particularly in the Coulomb energy Ec; moreover, the diffraction minimum in the form factors moves to 14 fm -2, in poorer agreement with experiment. It remains a moot point whether an alternative fit to the two-body data would remove the discrepancy in these parameters; our results appear to give some support for a potential containing a softer but larger radius core than that of the HJ potential.