Off-Energy-Shell Effects in the Triton with the Boundary-Condition Interaction

The boundary-condition model of the two-nucleon interaction due to Feshbach and Lomon is used without an external potential tail to determine the ground-state properties of the three-nucleon system for the purpose of studying the off-energy-shell properties of the two-body $T$ matrix. Calculations are performed using an average singlet-triplet $s$-wave interaction giving a completely symmetric triton wave function. The $T$ matrix is separable and depends on three energy-independent parameters — the boundary radius $r_0$ and the boundary condition $f$ at $r_0+\epsilon$ which are determined from the two-nucleon phase shifts, and the boundary condition $b$ at $r_0-\epsilon$ which is specifically an off-shell parameter that does not appear in the on-shell $T$ matrix. With $f=0.11\mathrm{}$ and $r_0=0.95\mathrm{}$ F, the Faddeev equations are solved for the triton energy eigenvalues and spectator functions for several values of $b$. It is found that the binding energy varies from 3.9 to 19.4 MeV for $b$ between 0.5 and 0.6, with a value of 8.5 MeV at $r=0.537\mathrm{}$. The average kinetic energy and charge form factor are determined as a function of $b$, and qualitative agreement of the charge radius with experiment is obtained for $b=0.5-0.6\mathrm{}$. The charge form factor, compared with experiment, does not drop off rapidly enough with $q^2$, indicating the presence of relatively too much large $q$ component in the spectator functions. The changes to be expected from the inclusion of tensor coupling in the boundary parameters are discussed.