Effective lambda-proton and lambda-neutron potentials from subthreshold inverse scattering

Abstract

Potentials are constructed for the lambda-nucleon interaction in the S 1 0 and S 3 1 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 lambdanucleon force in the S 1 0 channel is observed to be stronger than in the S 3 1 channel, as expected. In addition, the potentials bear certain distinctive features whose effects on hypernuclear systems can be explored through Schrödinger calculations.

$ΛNN $ three-body problem within $s$-wave inverse scattering on theoretical data

“…The charge-asymmetric pair of Λp and Λn potentials used in this paper were developed through Gel'fand-Levitan-Marchenko theory [14]. These potentials were restored through the application of this method on sub-threshold theoretical s-wave scattering phases.…”

“…Figure 1 illustrates the features of GLM-YN0 potentials, especially a noticeable charge symmetry breaking. The theoretical scattering phases used for inverse scattering theory in [14] carry in them not only this feature of charge asymmetry, but also Λ − Σ coupling. Therefore, it can be stated that even though GLM-YN0 potentials only explicitly have a central term, the effects of charge symmetry breaking and Λ − Σ coupling are built into this central term, since phase equivalence with NSC1997f was verified in [14].…”

“…The theoretical scattering phases used for inverse scattering theory in [14] carry in them not only this feature of charge asymmetry, but also Λ − Σ coupling. Therefore, it can be stated that even though GLM-YN0 potentials only explicitly have a central term, the effects of charge symmetry breaking and Λ − Σ coupling are built into this central term, since phase equivalence with NSC1997f was verified in [14]. The parameters V i , µ i and σ i in Equation (3) were determined through a nonlinear least squares fit.…”

“…After evidence for a possible bound state was inferred from heavy-ion experiments by the HypHI Collaboration at GSI, a number of recent theoretical studies based on improved ΛN forces from Meson-Exchange theory, Chiral Effective Field theory and quantum chromodynamics have also argued against the existence of such a bound state [7,8,9,10,11,12,13]. In order to provide a new perspective on the ΛN force, inverse scattering theory has recently been applied on theoretical Λp and Λn scattering data [14]. Spin averages of the recovered Λp and Λn potentials (GLM-YN0) were tested in [15] by computing the binding energy and root-mean-square radius of Λnp (J π = 1/2 + ), using Malfliet-Tjon V potential for the NN interaction.…”

Faddeev calculations on lambda hypertriton with potentials from Gel’fand–Levitan–Marchenko theory

“…These differences also suggest that new perspectives from alternative theories may be needed to complement existing theories. In line with the quest for alternative theories for the lambda-nucleon force, new lambda-proton and lambda-neutron potentials were developed in [20], through the application of Gel'fand-Levitan-Marchenko theory. The aim of this paper is to test the accuracy of the potentials developed in [20], by computing the binding energy and root mean square radius of a lambda hypertriton.…”