A one-parameter formula for estimating the Λ well depth

Abstract

A one parameter, semi-empirical formula for Λ-binding energy of heavy hypernuclei in the inverse powers of core mass number (A _c) has been developed in the framework of the folding model. Unlike similar calculations reported by other authors (Deloff 1971; Daskaloyanniset al 1985), we are able to take into account the effect arising from the difference in the number of protons and neutrons of the core nuclei having same mass number. The radius and diffuseness are parametrized using the experimentally known charge density data of a fairly large number of medium and heavy nuclei. The well depth parameter (i.e. Λ-binding energy in infinite nuclear matter) in the formula is obtained from a fit to theB _Λ data of ²⁸_Λ Si, ⁴⁰_Λ Ca, ⁵¹_Λ V and ³⁹_Λ Y. Using the original Λ-nucleus potential, theB _Λ of ground and the experimentally known excited states of these hypernuclei have also been calculated by solving numerically the two-body Schrödinger equation. The agreement with the experimental data is satisfactory.