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.

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

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• Possible studies at the first stage of the NICA collider operation with polarized and unpolarized proton and deuteron beams
• Full-Coupled Channel Approach to Doubly Strange $s$-Shell Hypernuclei
• The lightest neutral hypernuclei with strangeness -1 and -2
• The onset of $\Lambda \Lambda$ hypernuclear binding
• Hyperonic mixing in five-baryon double-strangeness hypernuclei in a two-channel treatment
• Three-body resonances Lambda-n-n and Lambda-Lambda-n
• Strangeness -2 hypertriton
• ${}_{\Lambda \Lambda }^4$H in halo effective field theory
• Lambda-Lambda hypernuclei and stranger systems
• Light $\Xi$ hypernuclei
• Full-coupled channel approach to S=-2 s-shell hypernuclear systems
• Resonant State in Helium-4 Lambda
• The ${}_{\Lambda \Lambda }^{4}n$ system
• Consistency of Lambda-Lambda hypernuclear events
• Hypernuclei in Halo/Cluster Effective Field Theory
• Possibility of a new neutral hypernucleus (n,n,Lambda,Lambda)
• ${\Xi }^{-}t$ quasibound state instead of $\Lambda \Lambda nn$ bound state
• Variational Monte-carlo study of ${}_{\Lambda \Lambda }^{4}H$
• Neutral baryonic systems with strangeness
• ${}_{\Lambda \Lambda }^5$H and ${}_{\Lambda \Lambda }^5$He Hypernuclei reexamined in Halo/Cluster Effective Theory
• Behaviour of the potentials due to strangeness degree of freedom in ${}_{\Lambda \Lambda }^6$He hypernucleus