Must Neutron-Neutron Forces Exist in theH3Nucleus?

Abstract

A wave function in the form of a series in the three interparticle distances with coefficients to be determined by the variational method is used to solve the ${\mathrm{H}}^3$ problem for a Wigner neutron-proton interaction of the form B $e^{-\frac{2r}{b}}$. For interaction radii $b$ of 1.0 and 2.0 × ${10}^{-13\mathrm{}}$ cm the best energies obtained are -11.0 and -9.5 $m{c}^2$, respectively, and the convergence of the energies obtained from successive improvements in the wave function is so rapid that the eigenvalues may be estimated to occur at -11.5±0.3 and -9.6±0.1 $m{c}^2$: Both pure and mixed exchange operators must give a higher total energy. It is shown that the narrower interaction radius is too small to be compatible with the known mass defects of ${\mathrm{H}}^2$ and ${\mathrm{He}}^4$ and that, accordingly, the value of 11.5 $m{c}^2$ is a very safe upper limit for the binding energy. From this we can conclude the existence of direct like-particle forces in the nucleus. Possible modification of the experimental data is considered and a comparison is made with the results of the equivalent two-body method.