ROOT MEAN-SQUARE RADII OF THE LAMBDA-PARTICLE ORBITS IN HYPERNUCLEI USING RECTANGULAR SHAPE POTENTIALS IN A RELATIVISTIC TREATMENT

The root mean square radii of the fl-particle orbits in hypernuclei ar e calculated in the ground and first excited states using the Dirac eq uation with scalar and vector potentials of rectangular shape and of t he same radius. An exact analytic and also approximate expressions are derived for the root mean square radius of the ii-particle orbit in i ts ground state. It is shown analytically that in the ground state the r.m.s. radius varies, as in the non-relativistic case, to a good appr oximation, linearly with A(core)(1/3) namely: <gamma(Lambda)(2)>(1/2)( s 1/2) = cA(core)(1/3) + b for the higher mass hypernuclei, where the constants c and b are related to the potential parameters. On the basi s of this treatment and the assumptions made, the upbending of the cur ve <gamma(Lambda)(2)>(1/2)(s 1/2) versus A(core)(1/3) observed in the region of the lower mass hypernuclei is also understood.