Nondipole Effects in Photo-Double-Ionization of He by a vuv Photon

We present a dynamical model-independent, ab initio parametrization of the quadrupole transition amplitude for photo-double-ionization of He. An asymmetry of the triple differential cross section induced by the nondipole corrections is discussed and shown to be significant even for an excess energy as low as 80 eV. We provide predictions for two different kinds of experiments in which nondipole effects should be observable with current experimental capabilities.

Figure 1

Experimental geometries suitable for observation of nondipole effects in PDI. Vectors ${\mathbf{p}}_1$, ${\mathbf{p}}_2$, $\widehat{\mathbf{ϵ}}$, $\mathbf{k}$, and ${\mathbf{k}}^{\prime }$ lie in one plane. Two independent measurements of the TDCS should be performed: one for ($\widehat{\mathbf{ϵ}},\mathbf{k}$), and another for ($\widehat{\mathbf{ϵ}},{\mathbf{k}}^{\prime }=-\mathbf{k}$). (a) Case of equal energy sharing; (b) case of unequal energy sharing (for ${\widehat{\mathbf{p}}}_2=-{\widehat{\mathbf{p}}}_1$, i.e., ${\theta }_{12}\equiv \theta =180°$).

Figure 2

Present results for the dipole-quadrupole TDCS [cf. Eqs. (10, 11)] and parameters $\Delta$ and ${\Delta }_{\mathrm{r}\mathrm{e}\mathrm{l}}$ [cf. Eqs. (13, 14)] for the PDI of He by linearly polarized photons for the geometry of Fig. 1a and an excess energy of 80 eV. In (a) and (d), full curves define $\sigma (\widehat{\mathbf{ϵ}},\widehat{\mathbf{k}})$; dashed curves define $\sigma (\widehat{\mathbf{ϵ}},-\widehat{\mathbf{k}})$. In (a)–(c), ${\theta }_1=0°$; in (d)–(f), ${\theta }_1=15°$.

Figure 3

The same as in Fig. 2, but for the back-to-back emission geometry shown in Fig. 1b for two unequal energy sharings [indicated in (a) and (d)]. The parameter $\Delta$ has maxima at ${\theta }_1=35.26°$ and ${\theta }_1=144.7°$, as shown by the dotted lines.