Parametrization of the effective potential in sodium clusters

The effective radial electronic potentials for neutral sodium clus­ters determined by the local density approximation and the jellium model are parametrized by means οf (symmetrized) Woods-Saxon and "Wine-Bottle" symmetrized Woods-Saxon potentials. The potential parameters are deter­ mined by various least-squares fitting procedures. Particular attention is paid to the dependence of the radius parameter R on the particle number Ν and it is realized that for relatively smaller values of N, complex expressions of R as a function of N, are more appropriate than the standard one R = r_0N^{1/3}. It is also found that improved results in these cases are obtained with an expression, of the form R = r_0N^{1/3} + 6, which is still very simple.