  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.
