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 $\Lambda$-proton scattering data with a number of effective central $\Lambda$-nucleon potentials of various hard-core radii (0-0.6 F) and intrinsic ranges (1.5-2.5 F), a $\Lambda$-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 $\Lambda$-proton case, with the consequence that the predicted $J=1\mathrm{}$ excited state in ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^4{}_{}{}^{}$ has a small excitation energy of only about 0.1 MeV. The $\Lambda$-proton effective-range parameters have the following values: ${a_t}^p=-2.08\mathrm{}$ F, ${r_{0t}}^p=3.40\mathrm{}$ F, ${a_s}^p=-2.25\mathrm{}$ F, and ${r_{0s}}^p=3.29\mathrm{}$ F. The case of $\Lambda$-neutron scattering has also been considered. Here it is found that the total cross sections differ appreciably from those of the corresponding $\Lambda$-proton case only when the c.m. energy is less than about 4 MeV.