PARTICLE NUMBER DEPENDENCE OF SIZE AND ENERGY QUANTITIES IN SODIUM CLUSTERS

The effective radial electronic potentials for neutral sodium clusters , which were determined by Ekardt on the basis of the local density ap proximation and the jellium model, are parametrized by means of the (s ymmetrized) Woods-Saxon and ''wine-bottle''-symmetrized Woods-Saxon po tentials with the aim of investigating the dependence of size and ener gy quantities on the cluster particle number. The potential parameters are determined by various least-squares fitting procedures. It is fou nd that for the radius R of the above potentials, complex expressions are more appropriate than the standard one R = r(0)N(1/3) for relative ly small values of N. Furthermore, N-power expansions are derived for those complex expressions of R, as well as for the rms radius of the p otential. It is also found that improved results in these cases are ob tained with an expression of the form R = r(0)N(1/3) + b, which is sti ll very simple. There is also investigated the variation of energy qua ntities, such as the single-particle energies of the 1s and 1p states, the level spacing \E(1p) - E(1s)\ and the average energy-level spacin g, with respect to the particle number N. Expressions for the first th ree of these quantities with N-dependent terms of the form aN(-2/3) beta N-1 give good results. Finally, the total energy per particle is considered with the aim of deriving its asymptotic expression for larg e values of the particle number.