BETHES BREMSSTRAHLUNG SPECTRUM REVISITED

We derive an expression for the Born approximation cross section for b remsstrahlung integrated over final particle directions without making any high energy approximations. Using the momentum distribution which is the integrand of this ''exact'' cross section, we derive a high en ergy approximation for the momentum distribution that is uniformly val id in the region which contributes significantly to the cross section, viz., delta less than or equal to q less than or similar to O(m), i.e . the errors in this high energy distribution are of order (m(2)/epsil on(2)) ln(epsilon/m) for all momentum transfers, q, in this region. (H ere, epsilon refers to either the initial or final electron energy, ep silon(1) or epsilon(2), m is the electron mass, and delta is the minim um kinematically allowed momentum transfer.) We make no assumptions wi th regard to the photon energy, k, which can take on any kinematically allowed value. Using our high energy momentum distribution, we analyz e the errors in Bethe's bremsstrahlung spectrum, which we find to be l ess than indicated by his analysis. Our high energy expression for the integrated cross section, derived solely by neglecting terms of relat ive orders (m(2)/epsilon(2)) ln(2)(epsilon/m) and (beta(2)/m(2)) ln(m( 2)/beta(2)), differs from that given by Bethe by only a single term of O(delta/m), which does not affect the integral over momentum transfer Thus, Bethe's spectrum is valid as well in the limit k --> 0. Our exp ression for the bremsstrahlung spectrum has much smaller errors and is valid over a large range of photon energies. Thus, for example, even for initial electron energies as low as 50 MeV, the error is always le ss than 1% for 0 less than or equal to k/epsilon(1) less than or equal to 0.9; for higher initial electron energies, the errors are even sma ller.