The variation of the Ηωwith the particle number and the appearance of "kinks" for atomic clusters

The dependence of the harmonic oscillator (HO) energy level spacing Ηω on the particle number Ν is studied analytically for atomic clusters on the basis of their electronic densities, parametrizing Ekardt's results (for sodium clusters) by means of a Fermi distribution. An interesting feature of such an approach is that it leads, under the assumptions made, to "kinks", that is to "marked discontinuities in the slope" of Ηω at the closed shells. These discontinuities diminish as Ν increases.

Wilson Loops in Antisymmetric Representations from Localization in Supersymmetric Gauge Theories

Large-[Formula: see text] phase transitions occurring in massive [Formula: see text] theories can be probed by Wilson loops in large antisymmetric representations. The logarithm of the Wilson loop is effectively described by the free energy of a Fermi distribution and exhibits second-order phase transitions (discontinuities in the second derivatives) as the size of representation varies. We illustrate the general features of antisymmetric Wilson loops on a number of examples where the phase transitions are known to occur: [Formula: see text] SQCD with various mass arrangements and [Formula: see text] theory. As a byproduct, we solve planar [Formula: see text] SQCD with three independent mass parameters. This model has two effective mass scales and undergoes two phase transitions. In memory of Ludvig Dmitrievich Faddeev

Moments of the three-parameter Fermi distribution

The moments [Formula: see text] of the spherical three-parameter Fermi distribution (3pF) are presented for [Formula: see text] to 8 as a function of the parameter [Formula: see text], the half-density radius [Formula: see text] and the diffuseness parameter [Formula: see text] through the introduced parameter [Formula: see text], which can be applied to study the neutron skin in neutron rich nuclei. The general expression of the moment can be written as the combination of integrals [Formula: see text] with [Formula: see text]. The errors of the analytic moments [Formula: see text] are estimated with the typical values of the parameters in 3pF compared with the numerical results.

NEUTRON DENSITY DISTRIBUTIONS IN SPHERICALLY SYMMETRIC LEAD ISOTOPES

Based on a relativistic Thomas–Fermi model, it is shown that a two-parameter Fermi distribution can be used for describing the neutron density distribution in the 208 Pb nucleus.