Next-to-leading order correction to the factorization limit of the radiation spectrum

A next-to-leading order correction to the high-energy factorization limit of radiation spectrum from an ultrarelativistic electron scattering in an external field is evaluated. Generally, it does not express through scattering characteristics, and accounts for smoothness of the crossover between the initial and final electron asymptotes. A few examples of application of this formula are given, including bremsstrahlung in amorphous matter and undulator radiation.