Based on the Schwinger source theory, an alternative derivation of the scattering cross section of non-relativistic bremsstrahlung is provided. In this approach, the vacuum persistence amplitude of the source theory is replaced by the wave function * vacuum persistence amplitude. It is then shown that the imaginary part of this amplitude automatically yields the scattering cross-section and the intensity of radiation. The Bethe–Heitler cross section is recovered in the Born approximation.