Nonlinear scaling in photon momentum transfer caused by two-electron effects

The photon momentum transfer in the two-photon double ionization of helium is theoretically studied based on the $abinitio$ calculations. A nonlinear dependence of the transferred momentum on the photon energy is identified at relatively small photon energies. As expected, the linear dependence is recovered with the slope approaching 1.60 when the photon energy becomes sufficiently large. With a semianalytical model including the Coulomb screen effect in the two-electron ground state, we can qualitatively reproduce the nonlinear dependence and find that it is mainly contributed by the fast electron. However, compared with the results from the $abinitio$ calculations, the quantitative discrepancies at relatively small photon energies can be accounted for only by the electron correlation in the intermediate state. The present study reveals the vital roles played by the two-electron effects for the complicated photon momentum transfer process in the few-photon and few-electron systems.

Figure 1

Illustration of the four steps of TPDI of helium. The electron correlation in TPDI can be divided into three types, i.e., in the initial state (a, I), in the intermediate state (b, II, III), and in the final state (c, IV).

Figure 2

(a) The sum of the momenta transferred to the two photoelectrons for laser pulses with $\omega \in (42,150)$ eV. Insets I and II show a linear fitting in different ranges with the slope being 1.31 and 1.49, respectively. (b) $F$ (see text for definition) as a function of the photon energy. The horizontal gray dashed line represents the asymptotic value of 1.60, corresponding to that for PSI of the ground state of hydrogen-like atom. The vertical gray dashed line marks the boundary of the sequential and the nonsequential regimes.

Figure 3

The sum of the momenta transferred to the two photoelectrons and the respective momentum of each electron at different photon energy range marked in each panel. The lines in each panel represent a linear fitting of the results from either the TDSE or the TDPT model, and their slopes are indicated in the legend.

Figure 4

The total and respective photon momentum transferred at relatively lower photon energies of $\omega \in (42,70)$ eV. The gray dashed line in (a) marks the boundary of the nonsequential and the sequential regimes. In (b), (c), and (d), the photon momentum transferred for the fast or the slow electron is linearly fitted in different ranges of its average energy divided by $c$, with the slope indicated in the legend.

Figure 5

The parameter $F^{\mathrm{SAE}}$ as a function of the photon energy.

Figure 6

The momentum transferred to the electron with SAE approximation at different photon energy regimes. The lines in each panel represent the linear fitting, and their slopes are indicated in the legends.