Velocity of transverse sound oscillations in the metals

The Bohm–Staver description of sound waves in metals in the jellium model is generalized by taking into account not only the self-consistent electric field but also the second correlation moment of internal electric field that provides shear elasticity. The system of linearized equations that contains the second correlation moment of the field as a new variable is built. The wave equation is worked out and the velocities of longitudinal and transverse sound are found. The estimation of the field correlation value through the sublimation heat and the electronic Fermi-gas energy is offered for the metals. The velocities of transverse sound are found, which matches well the velocity obtained from the shear modules.

A Simplified Analytic Treatment of Shell-Effects in Metal Clusters

A simplified treatment of shell-effects in metal clusters, such as those of Na, is considered. This treatment is carried out by means of an approximate scheme based on the spherical harmonic oscillator jellium model and its advantage is that it suggests the possibility quantities of physical interest to be calculated analytically. As a result, the variation of these quantities with the number of the valence electrons of the atoms in the cluster could be given explicitly in certain cases.

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.

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.