THE INFLUENCE OF SHELLS, ELECTRON THERMODYNAMICS, AND EVAPORATION ON THE ABUNDANCE SPECTRA OF LARGE SODIUM METAL-CLUSTERS

Measurements of the mass abundance spectra of sodium clusters containing up to 600 atoms are presented. The clusters are produced in a seeded supersonic expansion of Ar or Kr gas, and the spectra are obtained by a time-of-flight technique. The sawtooth features in the spectra are interpreted as evidence of a regular spherical shell structure with magic numbers, N0, scaling approximately with the cube root of the number of sodium atoms. Altogether twelve shell closings are observed, N0 = 2, 8, 20, 40, 58, 92, 138, 196, 260, 344, 440 and 558. There is also a pronounced odd-even staggering all the way up to N = 70. The experimentally observed intensity changes for the clusters around the magic numbers are discussed in terms of the electronic free energy, F(N), calculated at finite temperature, and the second differences of the free energy DELTA-2F(N) = F(N - 1) - 2F(N) + F(N + 1). The processes behind the non-uniform abundance distributions, and the thermodynamics of finite electron systems with non-uniform level spacings are discussed on this basis.