THE USE OF EFFECTIVE FEYNMAN DIAGRAMS FOR ATOMIC CROSS-SECTION CALCULATIONS

Abstract
In the developing research of plasma diagnostics it is necessary to know tne cross-sections for many atomic processes to determine the temperature and population densities in stationary or time-dependent plasmas. The main difficulty in calculating atomic cross sections is due to the wavefunctions of the atom. We suggest a technique to overcome this difficulty by using "effective Feynman diagrams". This technique is illustrated by obtaining a simple relation between the cross-sections of electron impact excitation (e + X_n → e + X_m ) and resonant photon absorption (hν + X_n → X_m). The relation reads, [MATH] where α = 1/137, mc² is tile electron rest energy, E is the kinetic energy of the incoming electron, I^mn - the excitation energy, Γ^mn - the natural width and, [MATH], Impressive agreement with experiment is found for transitions widely different in nuclear charge, degree of ionization and atomic levels. An explicit expression for the electron Gaunt factor is given. The technique developed in this paper is a breakthrougn in calculating the various electronion and ion-ion scattering cross-sections and the corresponding rate-coefficients.