Spheroidally deformed sodium clusters in the selfconsistent jellium model

We present the first systematic study of potential energy curves and prolate‐oblate shape transitions of sodium clusters with 8 < N < 40 atoms. The Kohn‐Sham equations are solved in the local density approximation for the jellium model with spheroidal deformations. The ionic background density is taken to have a diffuse surface of Woods‐Saxon type. The quadrupole and hexadecupole moments of the electron and jellium densities are investigated, revealing a strong hexadecupole dependence for selected clusters. Collective dipole resonances are described in the simple surface plasmon model. Shape transitions are found to 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; triaxiality is predicted for Na‐36. Comparing our results with those of molecular dynamics calculations, we confirm the scheme of Kohn‐Sham levels and the gross behaviour of potentials and densities.