PhenomenologicalΛ-Nucleon Potentials fromS-Shell Hypernuclei. I. Dependence on Hard-Core Size

Abstract

The binding-energy data of the $s$-shell hypernuclei and the total cross sections of the $\Lambda$-proton scattering are examined with two-body, spin-dependent, charge-independent, central $\Lambda$-nucleon potentials which have an intrinsic range of 1.5 F and a hard core with a radius of 0, 0.3, 0.45, or 0.6 F. The main purpose is to see whether there exists a hard core in the $\Lambda$-nucleon interaction. The results show that a hard core very likely does exist and has a radius greater than about 0.3 F. Also, it is found that even when the hard-core radius is as large as 0.6 F, the $\Lambda$-nucleon interaction is not strong enough to bind together a two-body $\Lambda$-hypernuclear system. However, it does seem to be strong enough to allow the formation of a particle-stable excited state in the hypernucleus ${}_{\Lambda }{}^{}{}_{}{}^{}\mathrm{H}_{}^4{}_{}{}^{}$ with a small binding energy.