Off-Shell Effects in the Three-Nucleon System

Results of calculations on the three-nucleon system are presented for two potentials: a spin-dependent square well potential acting in $s$ waves, and a spin-dependent rank-one separable potential, which gives exactly the same $s$-wave phase shifts and deuteron binding energy as the square well. Significant differences between the $T$ matrices arising from these potentials occur as soon as one goes off the energy shell by 40 or 50 MeV (c.m.). In the three-nucleon system the square well produces a triton binding energy of 9.11 MeV, a doublet scattering length of 0.414 fm, and quartet scattering length of 6.31 fm. The corresponding parameters for the separable potential are 9.92 MeV, -0.165 fm, and 6.33 fm. The results of calculations on the doublet and quartet $s$-wave elastic scattering amplitudes are presented for neutron lab energies up to 14.1 MeV. It is found that the doublet amplitudes are quite sensitive to off-shell effects, while the quartet amplitudes are not. A previously developed off-shell effective range theory for the half-off-shell $T$ matrix is extended to the fully-off-shell case.