Low-Frequency Bremsstrahlung in Coulomb Scatterings of Nonrelativistic Electrons

A simplified derivation of the low-frequency bremsstrahlung cross section in the classical limit is presented. Also, by expanding Elwert's exact quantum-mechanical expression for the cross section in powers of (Ze2/ħv)2 and in powers of ħv/Ze2, corrections are obtained to the Born-limit and classical formulas, respectively. Averaging over a Maxwellian distribution of incident electrons gives the low-frequency thermal emission and absorption coefficients; corrections to the Born-limit and classical formulas are expressed as power series in Z2 Ry/kT and (kT/Z2 Ry)1/2, respectively. Significantly, the coefficient of the first-order correction term for the classical formulas for the cross section, and thermal coefficients turns out to be zero.