## Appendix A: how to average Gaunt factors for free-free emissionThe free-free emissivity is the density of electrons and ions multiplied by the differential cross section integrated over the initial velocity distribution . We use the mean energy of the electrons to obtain the scale-free kinetic energy of the final electrons The averaged Gaunt factor can be expressed in terms of a modified distribution function and gives where the velocity is a function of The standard form for the thermally averaged Gaunt factor is divided by the average obtained from the semi-classical expression of Kramers and Wentzel. This leads to The Gaunt factor does not contain the exponential of Eq. A.4 which arises as the integral over initial electron velocities is limited to . © European Southern Observatory (ESO) 2000 Online publication: April 17, 2000 |