CLOSED-FORM SOLUTION FOR INVERSE PROBLEMS OF FERMI SYSTEMS

A series of applications of a theorem relating the Dirac delta functio n to the Fermi distribution [Chen, Phys. Rev. A 46, 3538 (1992)] are p resented in this paper. In particular, the inverse problem for determi ning the density of states of Fermi systems, the determination of rela xation-time distribution from dielectric function spectra, and the inv erse isotherm problem for the adsorption energy distribution function are treated with closed-form general solutions. The present method is not only simplified significantly relative to all the previous work, b ut also has the merit of not making a priori assumptions about the sol ution of the integral equation; hence it is a direct way of evaluating the density of states.