Three-Nucleon Systems

We have made a preliminary calculation of the bare form factor $F_B\left(q^2\right)$ for the three-nucleon systems ${\mathrm{H}}^3$ and ${\mathrm{He}}^3$ with the wave function $\psi =N\exp [-(\frac{\kappa }{2}\left)\right(r_{12}+r_{23}+r_{13}\left)\right]$. It is found that if we adjust $\kappa$ so as to fit the experimental value of the Coulomb energy for ${\mathrm{He}}^3$, or to fit the bremsstrahlung-weighted integral cross section for the photoeffect of ${\mathrm{He}}^3$, the agreement with experimental results for $F_B\left(q^2\right)$ is quite good. Also, we have made a variational calculation of the binding energy of the triton using two-body velocity-dependent central potentials and $\psi$ as a trial function with $\kappa$ as the adjustable parameter. Our preliminary results show that the binding energy is much lower than the experimental value and that given by a static well-behaved potential, though it is in fairly good agreement with similar calculations using repulsive hard core potentials.