The Binding Energy ofH3

Abstract

A calculation has been made of the constants in the meson type of potential by fitting the scattering data for the scattering of slow neutrons by protons and the binding energies of ${\mathrm{H}}^2$ and ${\mathrm{H}}^3$. Assuming the interaction between any two particles to be $(P_{\mathrm{ij}}+g{P}_{\mathrm{ij}}{Q}_{\mathrm{ij}})\left(\frac{C{e}^{-\lambda r_{\mathrm{ij}}}}{r_{\mathrm{ij}}\lambda }\right)$ one gets $C=49.54\mathrm{} m{c}^2$, $g=0.2667\mathrm{}$, $\lambda =1.536\mathrm{} \left(\frac{m{c}^2}{e^2}\right)$. This potential gives results which will be very little different from those given by the spherically symmetrical parts of the interaction obtained from meson field theory. The use of the coordinates introduced by James and Coolidge allows sufficient simplification so that the results can be easily modified to take account of other types of spin dependence. The possibility of $\lambda$ and $C$ being different for different particle interactions may also be taken into account.