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.

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 approximation and the jellium model, are parametrized by means of the (symmetrized) Woods-Saxon and "Wine-Bottle" symmetrized Woods-Saxon potentials with the aim of investigating the dependence of size and energy quantities on the cluster particle number. The potential parameters are determined by vari­ous least-squares fitting procedures. It is found that for the radius R of the above potentials, complex expressions are more appropriate than the stan­dard one R = r0N^{1/3} for relatively small values of N. Furthermore, N-power expansions are derived for those complex expressions of R, as well as for the r.m.s. radius of the potential. It is also found that improved results in these cases are obtained with an expression of the form R = r0N^{1/3}+b, which is still very simple. There is also investigated the variation of energy quan­tities, such as the single particle energies of the 1s and 1p states, the level spacing |E1p-E1s| and the average energy level spacing, with respect to the particle number N. Expressions for the first three of these quantities with N-dependent terms of the form aN^{2/3} + βΝ^{-1} give good results.

The variation of the Ηωwith the particle number and the appearance of "kinks" for atomic clusters

The dependence of the harmonic oscillator (HO) energy level spacing Ηω on the particle number Ν is studied analytically for atomic clusters on the basis of their electronic densities, parametrizing Ekardt's results (for sodium clusters) by means of a Fermi distribution. An interesting feature of such an approach is that it leads, under the assumptions made, to "kinks", that is to "marked discontinuities in the slope" of Ηω at the closed shells. These discontinuities diminish as Ν increases.

Determination of the Harmonic Oscillator Energy Level Spacing for Atomic Clusters

The harmonic oscillator energy level spacing Κω for atomic clusters as a function of the particle number Ν is expressed analytically in terms of the parameters of a Woods-Saxon (or Symmetrized Woods-Saxon) potential which approximates the effective spherical self-consistent jellium model potential. The expressions derived depend an the particular scheme adopted to approximate the potential by the harmonic oscillator one and on the assumed dependence of the potential radius R on N. It is also observed, considering the case of sodium clusters,that for large Ν the expressions of Ηω are in good agreement with the well known expression of Ηω in terms of the Wigner-Seitz radius.

Experimental Study on Construction of a Newly Supersonic Oven With Liquid Lithium

The seeded supersonic oven originally used to produce sodium clusters was incapable for lithium clusters that should be produced at higher temperatures. Ultimately, we designed a new compact stainless steel (SS) oven with thicker walls and constructed two molybdenum alloy (TZM) heaters for this new oven. The newly designed SS oven and heaters have been tested with liquid lithium, and the tested results demonstrated they can successfully work at ∼1000 °C, and a deposition layer of lithium was observed.