Relativistic Expressions for the r.m.s. Radii of the λ-Particle Orbits in Hypernuclei and of the Corresponding Potential Energies

Abstract

The root mean square radii of the Λ-particle orbits in hypemuclei are calculated semi-analytically for every bound state, using the Dirac equation with a scalar potential Us{r) and the fourth component of a vector potential Uv{f) in the case of rectangular shapes of these potentials with the same radius R.ln addition an analytic expression of the expectation value of the corresponding potential energy operator is derived. For the above quantities, expressions of the energy eigenvalues in terms of the potential parameters are needed and approximate formulae may be used, in certain cases. The variation of these quantities with the mass number is also investigated and numerical calculations are performed.