Low-frequency Bremsstrahlung for the Critical Geometry

The discrepancy between the experimental [1] and theoretical [2,3] results for the critical geometry, i.e., when $({\bf e} \cdot\Delta{\bf p})=0$ (where ${\bf e}$ and $\Delta{\bf p}$ are the polarization vector and the transferred electron momentum), is analyzed for examples of one-photon and two-photon low- frequency Bremsstrahlung (BrS) in a Coulomb field. For this geometry, the well-known Kroll-Watson approximation yields a zero BrS cross section while no significant decrease of the BrS radiation intensity is observed in experiments [1]. We present an analytical expression for the low-frequency cross sections for one- and two-photon stimulated BrS for the $({\bf e} \cdot\Delta{\bf p})\approx 0$ - region and find them to be small (of the order of $x^2\ln^2{x}$, where $ x=m\hbar\omega/p^2$ for the one-photon case) as compared to the cross section outside the critical geometry region. Thus our results are in accordance with those in Refs. [2,3] and disagree with Ref. [1]. [1] B. Walbank and J.K. Holmes, Phys. Rev. A {\bf 48}, R2515 (1993); [2] K.M. Dunseath and M. Terao-Dunseath, J. Phys. B {\bf 37}, 1305 (2004); [3] S. Hokland and L.B. Madsen, Eur. Phys. J. D {\bf 29}, 209 (2004).