M. M. Nagels

A potential model for hyperon--nucleon scattering

Abstract Low energy ΛN- and ΣN-scattering has been calculated in a potential model by solving the multichannel Schrodinger equation. Meson theoretic potentials are used which describe the exchange of nonets of pseudoscalar and vector mesons and uncorrelated two pion exchange. At short distances hard cores are employed. Coupling constants are taken from SU(3), SU(6), and the conserved current theory for vector mesons. Coulomb effects are included and different baryon masses within isomultiplets are considered. Charge symmetry breaking between the Λp- and Λn-channel due to one pion and one rho exchange has been taken into account. The model is checked in nucleon-nucleon scattering where it gives a good qualitative description of the NN-phaseshifts below the pion production threshold. A least-squares fit to the low energy Λp, Σ+p, and Σ−p data yields a very satisfactory result. The model leads then to the low energy parameters of Σ+p: a 8 c = −2.42 ± 0.30 fm , r 8 c = 3.41 ± 0.30 fm a t c = + 0.71 fm , r t c = −0.78 fm . The scattering lengths a and effective ranges r for Λp are a 8 p = −2.16 ± 0.26 fm , r 8 p = 2.03 ± 0.10 fm a t p = − 1.32 ± 0.07 fm , r t p = 2.31 ± 0.08 fm . and for Λn a 8 n = −2.67 ± 0.35 fm , r 8 n = 2.04 ± 0.10 fm a t n = − 1.02 ± 0.05 fm , r t p = 2.55 ± 0.10 fm . The possible existence of 2S1 resonances in the neighborhood of the ΣN thresholds is discussed. Coupled channel effective range expansions are given around the ΣN-thresholds.

COMBINED NN AND YN ANALYSES WITH POTENTIAL MODELS

Publisher Summary A good meson theoretical model together with SU(3) should he able to fit simultaneously all low energy baryon–baryon data (NN, ΛΝ, and ΣΝ). The very accurate NN data are used in one model, called A, only to check this model and in another model, called B, to determine the meson–nucleon coupling constants. The model A contains the Brueckner and Watson two pion exchange potential (TPEP), whereas model B contains the scalar meson ɛ (720) that is considered to be a unitary singlet. The TPEP neglects contributions to the spin-orbit potentials. Model A is essentially an s-wave model. The low energy YN data shows dominant s-wave character. In model B, the NN coupling constants and cores are determined by fitting to the X2 surface data of the energy independent NN phase shift analysis. The obtained X2/data are reasonably low despite the strong constraint from the low energy parameters and introduce a low mass fictitious σ-meson.