Time delay in two-electron photodetachment and tests of fundamental threshold laws

The photoelectron group delay, also known as the Wigner time delay (WTD), is examined in photodetachment of the ${\mathrm{H}}^{-}$ and ${\mathrm{Li}}^{-}$ ions near their lowest inelastic and the double detachment thresholds. These threshold processes promoting the remaining bound electron to an excited state or ejecting it to the continuum involve two active electrons and are termed collectively two-electron photodetachment. The opening of an inelastic channel is governed by the Wigner threshold law which affects the WTD very differently in ${\mathrm{H}}^{-}$ and ${\mathrm{Li}}^{-}$ . At the same time, the Wannier threshold behavior of the WTD in double detachment is similar in both targets. Experimental verification of these theoretical predictions will subject the Wigner and Wannier threshold laws to a set of stringent tests in the time domain.

Figure 1

(a) Cross section (2), (b) the phase of the transition amplitude, and (c) the WTD (4) of ${\mathrm{H}}^{-}$ in various photodetachment channels near the $n=2$ threshold. The experiment [32] is displayed in the top panel.

Figure 2

Same as Fig. 1 for the ${\mathrm{Li}}^{-}$ ion near the $2p$ excitation threshold. Experimental cross-section results [38, 39] are displayed in the top panel.

Figure 3

(a) ${\beta }_{2p}$ parameter in ${\mathrm{Li}}^{-}$ and ${\mathrm{H}}^{-}$ above the first excitation threshold plotted versus the excess energy. The ${\mathrm{H}}^{-}$ data from Hyman et al. [45] and Venuti and Decleva [46] are also shown. The partial photoionization cross sections of ${\mathrm{H}}^{-}$ (b) and ${\mathrm{Li}}^{-}$ (c) are plotted on the absolute excess energy scale. Below threshold cross sections for the main ionization channel $1s\to Ep$ for ${\mathrm{H}}^{-}$ and $2s\to Ep$ for ${\mathrm{Li}}^{-}$ are overplotted.

Figure 4

(a) Double ionization cross sections of ${\mathrm{H}}^{-}$ and ${\mathrm{Li}}^{-}$ are plotted against the excess energy. The Wannier threshold law (12) is shown with the straight lines for both targets. The ${\mathrm{Li}}^{-}$ cross section is also shown in the reduced coordinates ${\sigma }^{2+}{Z}^4$ vs $E/Z^2$, where $Z$ is the charge of the core. (b) Phase of the two-electron photodetachment amplitude (13) fitted with the $s$-wave Coulomb ansatz.