An analysis of the $\Lambda$-hypernuclear three-body systems is made by a variational method with a six-parameter trial function. An upper bound for the strength of the $\Lambda$-nucleon interaction required to account for the observed binding of the $T=0\mathrm{}$ hypertriton ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$ is obtained. This upper bound is 10-20% (depending upon the value taken for the binding energy) lower than the previous estimate by the same authors. An improved quantitative estimate of the spin dependence of the $\Lambda$-nucleon interaction (neglecting the possible influence of three-body forces) is obtained from the results of this analysis and those of a previous analysis of ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{He}_{}^5{}_{}{}^{}$; from this estimate it follows that the existence of a bound $\Lambda$-nucleon system is strongly excluded. The analysis of the $T=1\mathrm{}$ triplet ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{He}_{}^3{}_{}{}^{}$, ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^3{}_{}{}^{}$, ${}_{\Lambda }{}^{}{}_{}{}^{}n_{}^3{}_{}{}^{}$ indicates that these systems are not expected to form bound states. It appears that the essential conclusions of this work would not be seriously affected if there exist moderately strong three-body forces arising from pion exchange processes.

• Received 17 November 1958

DOI:https://doi.org/10.1103/PhysRev.114.593