Abstract
Potentials are constructed for the lambda-nucleon interaction in the and channels. These potentials are recovered from scattering phases below the inelastic threshold through Gel’fand-Levitan-Marchenko theory. Experimental data with good statistics is not available for lambda-nucleon scattering. This leaves theoretical scattering phases as the only option through which the rigorous theory of quantum inverse scattering can be used in probing the lambda-nucleon force. Using rational-function interpolations on the theoretical scattering data, the kernels of the Gel’fand-Levitan-Marchenko integral equation become degenerate, resulting in a closed-form solution. The new potentials restored, which are shown to be unique through the Levinson theorem, bear the expected features of short-range repulsion and intermediate-range attraction. Charge symmetry breaking, which is perceptible in the scattering phases, is preserved in the new potentials. The lambda-nucleon force in the channel is observed to be stronger than in the channel, as expected. In addition, the potentials bear certain distinctive features whose effects on hypernuclear systems can be explored through Schrödinger calculations.
Highlights
The development of accurate potentials for hyperon-nucleon and hyperon-hyperon interactions is of prime importance in hypernuclear physics
Observation of the results reveals that these new potentials bear the features of shortrange repulsion and intermediate-range attraction, as expected for a baryon-baryon interaction
Charge symmetry breaking that is discernible in the lambda-nucleon scattering data is preserved in the new potentials: the lambda-proton force is slightly more attractive than the lambda-neutron force
Summary
The development of accurate potentials for hyperon-nucleon and hyperon-hyperon interactions is of prime importance in hypernuclear physics. The nonzero strangeness quantum number of hyperons allows hypernuclei to occupy states that would be Pauli-forbidden if they contained only nucleons These hyperons can be seen as probes for such genuine hypernuclear states. Some important phenomena within hypernuclei require accurate hyperon-nucleon and hyperon-hyperon potentials for a clearer understanding Examples of such phenomena include the nonmesonic decay of hyperons in light hypernuclei and the reduction of nuclear size arising from the glue effect of hyperons. These potentials are required in simulations of astrophysical objects with multistrangeness, for example the highdensity core of a neutron star
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