Soft Bremsstrahlung

Understand

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.