AverageΛ-Nucleon Interaction in the Hypertriton

Upper bounds on the strength of the average $\Lambda$-nucleon interaction required to account for the observed binding of the hypertriton have been established in a variation calculation with a ten-parameter trial function. Central two-body potentials having hard-core radii 0.2, 0.4, and 0.6 F and ranges suggested by consideration of the two-pion-exchange mechanism were used. These calculations led to improvements of 3-6% (depending upon the hard-core radius) in the required strengths over the results of previous calculations with a four-parameter function. The results cannot be used to rule out the existence of a bound hyperdeuteron of spin 0 for a hard-core radius as large as 0.6 F. A partial variation calculation is described, in which only two of the ten parameters of the trial function are varied. When the remaining parameters are fixed by consideration of the two-body subsystems of which the hypertriton is composed, variation of two appropriate parameters leads to required strengths within 3% of the values obtained by varying all ten parameters.