Stochastic Variational Search for $^{4}_{ΛΛ}$H

Abstract

A four-body calculation of the $pnΛΛ$ bound state, $^{\ 4}_{ΛΛ}$H, is performed using the stochastic variational method and phenomenological potentials. The $NN$, $ΛN$, and $ΛΛ$ potentials are taken from a recent Letter by Filikhin and Gal, PRL{\bf 89}, 172502 (2002). Although their Faddeev-Yakubovsky calculation found no bound-state solution over a wide range of $ΛΛ$ interaction strengths, the present variational calculation gives a bound-state energy, which is clearly lower than the $_Λ^3{H}+Λ$ threshold, even for a weak $ΛΛ$ interaction strength deduced from a recent experimental $B_{ΛΛ}(^{6}_{ΛΛ}{He})$ value. The binding energies obtained are close to, and slightly larger than, the values obtained from the three-body $dΛΛ$ model in the Letter.