Soft Bremsstrahlung
  Simple analytic formulas are considered for the energy radiated in low
frequency bremsstrahlung from fully ionized gases. A formula that has been
frequently cited over many years turns out to have only a limited range of
validity, more narrow than for a formula derived using the Born approximation.
In an attempt to find a more widely valid simple formula, a soft photon theorem
is employed, which in this context implies that the differential rate of photon
emission in an electron-ion collision with definite initial and final electron
momenta is correctly given for sufficiently soft photons by the Born
approximation, to all orders in the Coulomb potential. Corrections to the Born
approximation arise because the upper limit on photon energy for this theorem
to apply to a given collision becomes increasingly stringent as the scattering
approaches the forward direction. A general formula is suggested that takes
this into account.
