PhenomenologicalΛ-Nucleon Potentials froms-Shell Hypernuclei. II. Dependence on Intrinsic Range

Abstract

By examining the binding-energy data of the $s$-shell hypernuclei and the $\ensuremath{\Lambda}$-proton scattering data with a number of effective central $\ensuremath{\Lambda}$-nucleon potentials of various hard-core radii (0-0.6 F) and intrinsic ranges (1.5-2.5 F), a $\ensuremath{\Lambda}$-nucleon potential has been found which yields a very good fit to these experimental data. This potential has an intrinsic range of 2.1 F, a hard-core radius of 0.6 F, and an odd-parity-state strength which is equal to 60% of the even-parity-state strength. Also, it has a rather small degree of spin dependence in the $\ensuremath{\Lambda}$-proton case, with the consequence that the predicted $J=1$ excited state in $_{\ensuremath{\Lambda}}\mathrm{H}^{4}$ has a small excitation energy of only about 0.1 MeV. The $\ensuremath{\Lambda}$-proton effective-range parameters have the following values: ${{a}_{t}}^{p}=\ensuremath{-}2.08$ F, ${{r}_{0t}}^{p}=3.40$ F, ${{a}_{s}}^{p}=\ensuremath{-}2.25$ F, and ${{r}_{0s}}^{p}=3.29$ F. The case of $\ensuremath{\Lambda}$-neutron scattering has also been considered. Here it is found that the total cross sections differ appreciably from those of the corresponding $\ensuremath{\Lambda}$-proton case only when the c.m. energy is less than about 4 MeV.