Breit interaction, level spacing statistics and far-infrared absorption in small metal clusters

By considering Coulomb and Breit interactions between the electrons, we derive, for the first time, the variational Breit–Hartree–Fock (BHF) equation. The Breit interaction has an energy scale which corresponds to the weak magnetic spin–spin and spin–orbit interactions. For small randomly shaped jellium clusters with up to 276 electrons, we solved numerically the BHF equation. The calculated level spacing statistics is found to differ qualitatively from the Wigner distribution and correspond better to a Poisson distribution. In particular, the prediction of significantly enhanced far-infrared absorption is in excellent accord with experimental observations. The Breit interaction is identified as key to the semi-metallic behavior persistent in small metal clusters at energy scales much lower than the average level spacing.