Abstract
No published \LambdaΛn scattering data exist. A relativistic heavy-ion experiment has suggested that a \LambdaΛnn bound state was seen. However, several theoretical analyses have cast serious doubt on the bound-state assertion. Nevertheless, there could exist a three-body \LambdaΛnn resonance. Such a resonance could be used to constrain the \LambdaΛn interaction. We discuss \LambdaΛnn calculations using nn and \LambdaΛn pairwise interactions of rank-one, separable form that fit effective range parameters of the nn system and those hypothesized for the as yet unobserved \LambdaΛn system based upon four different \LambdaΛN potentials. The use of rank-one separable potentials allows one to analytically continue the \LambdaΛnn Faddeev equations onto the second complex energy plane in search of resonance poles, by examining the eigenvalue spectrum of the kernel of the Faddeev equations. Although each of the potential models predicts a \LambdaΛnn sub-threshold resonance pole, scaling of the \LambdaΛn interaction by as little as \sim∼5% does produce a physical resonance. This suggests that one may use photo-(electro-)production of the \LambdaΛnn system from tritium as a tool to examine the strength of the \LambdaΛn interaction.
Highlights
For hypernuclear physics there exist no published Λn scattering data
We have investigated extracting an experimental constraint upon the Λn interaction from data that may be obtained in an experimental measurement of a Λnn resonance
Our analysis is based on the assumption that states of the ΛNN system, which are close to the three-body threshold, are dominated by the effective range parameters of the pairwise interactions governing the Λnn system
Summary
For hypernuclear physics there exist no published Λn scattering data. This reflects the absence of neutron and Λ targets or beams. We explore the possible existence of a Λnn resonance even though the underlying nn and Λn interactions are predominantly s-wave and support no two-body bound state To accomplish this we consider a model in which the pairwise interactions are represented by rank-one separable potentials that reproduce the effective range parameters (scattering length and effective range) of 1) the nn system and 2) those predicted for the yet to be observed Λn system by five different Nijmegen one-boson-exchange potentials [11,12,13,14,15] and the Juelich one-boson-exchange potential [16], and a chiral ΛN potential [17]. We would like to suggest the thesis that if one observes a Λnn resonance, the energy and width of such a resonance might be used to place some constraint on the Λn scattering lengths, to complement the experimental Λp scattering data
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