Analysis of the Hypertriton in Terms of Hard-Core Potentials

The variation method was used to set upper bounds on the strength of the average $\Lambda$-nucleon potential in the hypertriton (${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$) required to reproduce the observed binding energy of that system for assumed hard-core radii of 0.2 F, 0.4 F, and 0.6 F. Only two-body A-nucleon potentials were considered. Although the well-depth parameter of the required potential increases as the assumed hard-core radius is increased, it seems unlikely that even the largest of the hard-core radii considered here would imply a bound state for the hyperdeuteron (${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^2{}_{}{}^{}$). The possibility that the scattering length and the effective range of the required potential may be insensitive to the value of the hard-core radius is discussed.