Moments of the three-parameter Fermi distribution

The moments 〈rm〉 of the spherical three-parameter Fermi distribution (3pF) are presented for m = 1 to 8 as a function of the parameter w, the half-density radius c and the diffuseness parameter a through the introduced parameter β = πa/c, 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 In(k,w) with k = c/a. The errors of the analytic moments 〈rm〉 are estimated with the typical values of the parameters in 3pF compared with the numerical results.