Simplified semiclassical theory for the electronic shell structure of metallic clusters

We present a simplified theory for the electronic shell structure of large metallic clusters by extending the semiclassical analysis by Gutzwiller, Balian and Bloch. Thus analytical results are given for the shell effect in the Fermi energy and cohesive energy. In particular, results for the temperature dependence of the shell structure are given. New results are presented for the shell structure in the ionization potential and photoyield and for the existence of electronic- versus atomic shell structure as a function of cluster size and temperature. We obtain good quantitative agreement with previous numerical calculations and with experiments on Na clusters.