H2(p,pp)nreaction as a probe of the short-range nuclear force

We examine the feasibility of using the ${}_{}{}^2{}_{}{}^{}\mathrm{H}\mathrm{}(p,pp)n$ reaction as a means of extracting information about the short-range behavior of the nuclear force not obtainable from $N$-$N$ scattering experiments. To do this we use several separable potentials and examine the predicted cross section in various regions of phase space and for beam energies between 14 and 65 MeV. The questions that we address are likely to be insensitive to Coulomb effects. Both the form factor and the energy dependence of the potentials have been modified from the usual Yamaguchi form. The form of the energy dependence is chosen to obtain phase-shift equivalence for two different form factors while guaranteeing a unitary two-body scattering amplitude. The sensitivity of breakup results to the on-shell and off-shell aspects of the nuclear force is examined and discussed. Significant on-shell sensitivity occurs for breakup amplitudes in all states and for cross sections over all regions of phase space. Off-shell sensitivity appears only in the $S=\frac{1}{2}$, $L=0\mathrm{}$ breakup amplitudes, with all $S=\frac{3}{2}$ and all $L>\mathrm{}0\mathrm{}$ amplitudes exhibiting negligible off-shell dependence. This result leads to only a very small (≤5%) off-shell sensitivity for quasifree scattering. However, cross sections far from quasifree scattering, and in particular cross sections in the final-state interaction region of phase space, exhibit as much as a 50% variation for phase-shift-equivalent potentials. This sensitivity is small at low beam energy and increases with increasing energy. The energy dependence at negative energies of one potential is also altered to adjust the triton binding energy. This enables us to compare phase-shift-equivalent potentials differing off shell but predicting the same triton binding energy. The energy dependence of this potential is somewhat unconventional. Fixing of the triton binding energy reduces the off-shell sensitivity appreciably only for $E\lesssim 20$ MeV.