Energy of partial A-body problem for 9ΛBe and 10ΛΛBe

Abstract

The energy of the degenerate doublet (3+/2, 5+/2) of 9ΛBe, treating it as a partial nine-body system in the Λαα cluster model, has been calculated in the variational Monte Carlo framework. A simplified treatment, with the central two-body Urbana type ΛN and the three-body dispersive and two-pion exchange ΛNN forces along with the central two- and three-body correlations, is found to be adequate in explaining the energy of observed γ-ray transition from the excited degenerate doublet to the ground state. This partial nine-body model of 9ΛBe has been extended for the case of partial ten-body problem 10ΛΛBe in the ΛΛ + αα model where nucleonic degrees of freedom of as are taken into consideration ignoring antisymmetrization between two αs. The central two-body ΛN and ΛΛ and the three-body dispersive and two-pion exchange ΛNN forces, constrained by the Λp scattering data and the observed ground state energies of 5ΛHe and 6ΛΛ, are employed. The product type trial wavefunction predicts binding energy for the ground state considerably less than for the event reported by Danysz et al but however, consistent with the value deduced assuming a γ-ray of 3.04 MeV must have escaped undetected in the decay of the product 9ΛBe* → 9ΛBe + γ of the emulsion event 10ΛΛBe → π− + p + 9ΛBe* and for the excited 2+ state closer to the value measured in the Demachi-Yanagi event. The results of the present work are consistent with the earlier three- and four-body cluster model approaches where as are assumed to be structureless entities.