Circular dichroism in classical Coulomb scattering involving bremsstrahlung

Classical orbit derivations of the triply differential cross section for electron bremsstrahlung (BrS) in a Coulomb field are presented; the classical origin of the circular dichroism effect in the electron scattering angular distributions is established for both spontaneous and laser-stimulated BrS.

Figure 1

Geometry of an angularly resolved BrS process.

Figure 2

Comparison of classical and quantum triply differential cross sections ${\sigma }_{\mathit{cl}}^{\left(3\right)}$ (solid curves) and ${\sigma }^{\left(3\right)}$ (dashed curves) as functions of the electron scattering angle $\theta$ for left- (top curves) and right- (bottom curves) circular polarizations, $\xi =\mp 1$ of the emitted BrS radiation. For all curves, $Z∕p=10\mathrm{a.u.}$, $\nu =1$ (i.e., $\hslash \omega ={10}^{-3}{Z}^2\mathrm{a.u.}$), and $\phi =\pi ∕2$.

Figure 3

Dependence of the ratio ${\sigma }_{\mathit{cl}}^{\left(3\right)}∕{\sigma }^{\left(3\right)}$ (for $\xi =+1$) and, in the inset, ${\sigma }_{\mathit{cl}}^{\left(3\right)}$ (for $\xi =\pm 1$) on $a=Z∕p$, for $\theta =\pi ∕2$, $\phi =\pi ∕2$, and $\nu =0.5$ [i.e., $\hslash \omega =p^3∕\left(2Z\right)$ a.u.].