Analytical evaluation of the plasma dispersion function for a Fermi Dirac distribution

Abstract

An efficient method for the analytic evaluation of the plasma dispersion function for the Fermi-Dirac distribution is proposed. The new method has been developed using the binomial expansion theorem and the Gamma functions. The general formulas obtained for the plasma dispersion function are utilized for the evaluation of the response function. The resulting series present better convergence rates. Several acceleration techniques are combined to further improve the efficiency. The obtained results for the plasma dispersion function are in good agreement with the known numerical data.

Analytical solution of the Coulomb potential for spherical nuclei

“…As known, the solution of problems in many areas of physics (solid state physics, atomic and molecular physics, nuclear physics, astrophysics, statistical physics) depends on the calculation of the exponential type integrals such as ∫ ( − ± 1) ⁄ ∞ 0 [1][2][3][4][5]. For example, the calculation of the Fermi-Dirac function, which is one of the exponential type integrals and changing in [0, ∞] range, reveals the solution of many physical problems [4,5].…”

“…⁄ 𝑑𝑑𝑡𝑡 ∞ 0 [1][2][3][4][5]. For example, the calculation of the Fermi-Dirac function, which is one of the exponential type integrals and changing in [0, ∞] range, reveals the solution of many physical problems [4,5].…”