Role of Lambda N and Lambda NN interaction parameters on binding energy of Lambda H4 and Lambda H4*

Abstract: Variational Monte Carlo study has been done for the two hypernuclear systems $\Lambda^4$H and $\Lambda^4$H$^*$ for calculation of binding energies. For the two hypernuclear systems under study, different potential models have been used for the interactions involved in these hypernuclear systems. ArgonneV${18}$ NN, Urbana IX NNN and phenomenological $\Lambda$N and $\Lambda$NN potentials have been used in our study. Our potential models are based on our previous studies on different double lambda hypernuclear systems. From our results, hyperon-nucleon parameters ie. two-body $\Lambda$N parameter and three-body $\Lambda$NN parameters are found to be important for binding the hypernuclear systems under study. With reduction in the values of Lambda NN interaction parameters used in earlier works , there is significant difference in the values of binding energy of $\Lambda^4$H and $_\Lambda^4$H$^*$. Also, $\Lambda$N interaction parameters are also found to play important role in binding.