Circular dichroism at equal energy sharing in photo-double-ionization of He

Interference between dipole and quadrupole transition amplitudes in photo-double-ionization of He by an elliptically polarized vuv photon is shown to induce circular dichroism in the case of equal energy sharing. The magnitude of this retardation-induced dichroic effect is estimated and its impact on the nondipole asymmetries of the triply differential cross section is demonstrated.

Figure 1

Geometries suitable for observation of retardation-induced polarization effects. (a) Geometry at which the equal energy sharing CD effect is maximal. Electrons are detected in the $xz$ plane, at angles of $\pm \theta ∕2$ with respect to the $x$ axis. The photon wave vector $\mathbf{k}$ lies in the $yz$ plane and makes an angle 45° with the $z$ axis. (b) Geometry for observation of the retardation-induced asymmetries in the TDCS. The first electron is ejected along the $x$ axis and the second one (whose angular distribution exhibits the asymmetry) along $({\theta }_2,{\varphi }_2)$. (Concerning the angles ${\phi }_{xz}$ and ${\phi }_{yz}$, see Fig. 3.)

Figure 2

The TDCS (9) and absolute $\left({\Delta }_{\mathrm{CD}}\right)$ and relative $\left({\delta }_{\mathrm{CD}}\right)$ CD parameters for PDI of He using circularly polarized light, plotted vs the mutual ejection angle $\theta$. The geometry is as shown in Fig. 1(a). In (a),(b),(e),(f), full curve: $\sigma (\xi =+1)$; dashed curve: $\sigma (\xi =-1)$. The plots in (b),(f) show the TDCSs in the range of $174°<\theta <186°$, in which the parameter ${\delta }_{\mathrm{CD}}$ is large.

Figure 3

The asymmetry of the TDCS (9) for PDI of He using circularly polarized light $(\xi =+1)$. Full curves: the geometry is as in Fig. 1(b); dashed curves: direction of the photon beam is inverted (i.e., $\mathbf{k}\to -\mathbf{k}$); dotted curves: EDA results. ${\phi }_{xz}$ and ${\phi }_{yz}$ are the polar angles of the vector ${\mathbf{p}}_2$ in the planes $xz$ (a), (b) and $yz$ (c), (d), respectively [cf. Fig. 1(b)].