Ground state systematics and collective dipole excitations of spheroidally deformed sodium clusters in a diffuse jellium model

We solve the Kohn-Sham equations self-consistently in the local density approximation for spheroidal sodium clusters in the particle range 8 ≤ Z ≤ 40. We use a smooth fermi-like jellium density to simulate the influence of the ions in the surface region and obtain similar results as Ekardt and Penzar, but slightly different regions of prolate-to-oblate transitions. We present the systematics of potential energy curves with respect to transitions between oblate, prolate and spherical shapes. Shape transitions occur at particle numbers 12/14 (prolate/oblate), 18/20/22 (oblate/spherical/prolate) and 30/32 (prolate/oblate), which are in good agreement with experimental results. The quadrupole and hexadecupole overlap of the electron density with the jellium is investigated, showing a strong hexadecupole dependence for selected clusters. Collective dipole resonances are described in a simple sum rule approach, which reveals a double splitting according to the different resonance frequencies along the principal axes of the spheroid. The systematics of the resonance peaks for the larger clusters with Z ≥ 20 is in good agreement with experimental results.