Fermi distribution deformed

One conceptually simple approach which has been used to represent temperature effects in metallic clusters is the random matrix model, developed by Akulin et al. [700]. The principles of the random matrix model, developed in the context of nuclear physics by Wigner and others, were outlined in chapter 10. The essential idea is to treat the cluster as a disordered piece of a solid. In the first approximation, the cluster is regarded as a Fermi gas of electrons, moving in an effective, spherically symmetric short range well. Without deformations, one-electron states then obey a Fermi distribution. As the temperature is raised, various scattering processes and perturbations arise, all of which lead to a random coupling between the states of the unperturbed system. One can... 

Generalizations of the Fermi model to describe deformed nuclei have been applied e.g. in the study of energies for highly charged uranium [44,45]. The nuclear radius parameter c in the Fermi distribution (1) is then replaced by... 

The charge form factor of the deformed nucleus is accurately known from the muonic x-ray measurements of Zumbro et al. [49] and can be parameterized by the deformed Fermi distribution... 

From the point of symmetry, we can see on both surfaces that the sp-sp transition has a three-fold deformation as compared to the circular distribution expected from a perfect nearly-free electron system. This indicates that the measurement is sensitive to the bulk band structure surrounding the [111] bulk direction, which also depends on the direction of the vector k, not only on its magnitude as for the quasi-free electron dispersion. Because the initial states relevant in the measurement are near the Fermi level near the [111] direction, the observed three-fold deformation reflects the distortion of the Ag Fermi surface near its [111] neck-regions, as has also been seen in Cu(lll). This is a general manifestation of bulk electronic states near the sp-band gap of noble metals. 

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