Nucleon orbit radii in tin isotopes

The RMS radii of valence orbits in the tin isotopes are calculated using the single-particle potential model. Comparison with experimental data yields conclusions concerning the distribution of spectroscopic strength in these nuclei. Several recent analyses of the cross sections of nucleon transfer reactions (Chapman et al 1979, Warwick et al 1979a, b) have given values of the RMS radii of the probability distributions of the nucleons in particular quantum states. These RMS radii can also be calculated from a single-particle model, so it is interesting to see how well such values agree with those obtained experimentally and what conclusions can be drawn from the comparison. To do this, we use the global single-particle potential BH of Bear and Hodgson (1978), whose parameters were chosen to give a good overall fit to the centroid binding energies of many single-particle states in nuclei from 40Ca to zOsPb. This potential has the standard form V(r)= Vc(r) + Vf(r) + ( $ e ) * V S f $ L d where Vc(r) is the Coulomb potential (for protons only) and the form factor f(r)= (1 +exp[(r-R)/a])-' with R=r0A1I3. The potential depth for surface states is V= V t " for -15 <E < O (2) and for deep states V= V t " -p(E + 15) for E < 15 MeV (3) where the superscripts indicate neutron or proton potentials. These depend on the asymmetry potential Vl and can be expressed in the forms V; = V, + [ (NZ)/A I V, vo" = V, [ ( N Z)/AI V, . (4) The form factor parameters were fixed to the values ro = 1.236 fm, a=0.62 fm for the central potential and V, = 7 MeV, rs = 1.1 fm, a, =0.65 fm for the spin-orbit potential. The fit to a range of nuclei gave VO =55.7 MeV, V I =39.3 MeV and P=O.Sl. The Perey non-locality correction was applied to all states with range parameter 0.87 fm and the wavefunctions were orthogonalised as described by Malaguti et a1 (1978). 0305-46 16/8 U081057 + 05 $01.50