The ground-state (cis) binding energies of the Ehyperon in the few known Zhypernuclei have been analysed by adopting a simple Z --nucleus potential for which the Schrddinger equation can be solved analytically and in addition simple formulae for the nuclear part of the E GS binding energy, kinetic and potential energy as functions of the mass number of the core nucleus A,=A may be derived. For the Coulomb part of the interaction the diffuseness of the surface has been taken into account in the framework of an approximate procedure. A comparison has been made of the volume integrals of the E--nucleon and A-nucleon potentials lvz-Nl and lVANl by using estimates of the parameters involved by means of least-squares fittings. The value of the ratio y = vz-NIVAN is found to be c 0 . 8 . It is also found that similar conclusions are reached by using in the same way other potential models, such as the Woods-Saxon one.

An investigation is made of the effect of the (central) A-nucleon potential V~and of the density distribution p of the a particle on the central part of the V~interaction, in the framework of the rigid-core model, adopted originally in this context by Dalitz and Downs.Single and double Gaussian shapes for V~and p are considered, the latter having the advantage that the charge form factor fits rather well the experimental results deduced from the electron scattering experiments including those at high momentum transfers. The differences observed in the values of Vz depend mainly on the central A-nucleon potential assumed and they are very strong for small values of r. Differences also exist in this region because of the various densities used. The double Gaussian density has the effect of lowering the values of VA near the center of the a particle in almost all the cases of double Gaussian A-nucleon potentials. NUCLEAR STRUCTURE Hypernuclei; qHe; A-a interaction; A-N interaction, density of. He.

The so-called 'cosh' or symmetrized Woods-Saxon potential which has been used in nuclear physics is discussed and certain comments are made regarding its form factor, depth and radius. A rough estimate of its parameters is also attempted by using various possibilities. This is done either by considering a number of individual nuclei or by least-squares fitting. The potential depth parameter V0, apart from being state dependent, varies also with the mass number of the nucleus. Comments on relevant limitations and inaccuracies are made and the state dependence of V0 is also discussed in relation with the concept of an effective nucleon mass.

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