Boltzman averages of the free--free Gaunt factor in the screened Coulomb potential
R and D Associates, Santa Monica, Calif. (USA), J Green · 1974
where 00 -E/kT kl / w j g(E,4E)e "'"« (6) is the Boltzman average of the Gaunt factor.The Gaunt factor, g, of course, contains all of the physics involved in the absorption process.Naturally, g will depend on the interaction potential connecting the electron and its scattering center, Here we assume that the absorbing electron is moving about a central charge Z in a screened Coulomb potential which is given by V(r) = ^~-, 'iydbergs (7) wfiere r is measured in units of Bohr radii.Of course, u is the inverse Debye length i_, measured in units of Bohr radii u = a o A D .(8) By referring to the original Schroedinger equation, it can be shown that 2 in a potential of this kind E and &E scale with l/Z , r scales with Z and u scales with l/Z.Consequently, if g(E,AE;u.Z) is a Gaunt factor for a potential parameterized by u,Z, then g(E,AE;,i,Z) MJ^fif.l). *z z -I-Thus if g, the Boltsnan average, la known for Z * 1, it is known for all values of Z.Elsewhere [1-2] ve have described in detail the codes and physics under lying a rigorous calculation of g(E,&E;n,l).tfe have also nentioned [2] that there exists a closed-form approximation to g which is g B£ , the Bonr Elwert result.For fixed M and AE we have Lin g (B) = g(E) .(11) £•+« *THE INTEGER IN PARENTHESES IS THE POWER OF TEN BY WHICH THE NUMBER TO THE LEFT IS MULTIPLIED.