Stochastic Variational Search for ${}_{\Lambda \Lambda }^4$H

Abstract

A four-body calculation of the $pn\Lambda \Lambda$ bound state, ${}_{\Lambda \Lambda }^4$H, is performed using the stochastic variational method and phenomenological potentials. The $NN$, $\Lambda N$, and $\Lambda \Lambda$ 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 $\Lambda \Lambda$ interaction strengths, the present variational calculation gives a bound-state energy, which is clearly lower than the ${}_{\Lambda }^{3}H+\Lambda$ threshold, even for a weak $\Lambda \Lambda$ interaction strength deduced from a recent experimental $B_{\Lambda \Lambda }{(}_{\Lambda \Lambda }^{6}He)$ value. The binding energies obtained are close to, and slightly larger than, the values obtained from the three-body $d\Lambda \Lambda$ model in the Letter.

Comments: Corrected typos, added addtional calculations regarding a truncated to l=0 interaction model, 4 pages, 3 figures