Scaling of the Low-Energy Structure in Above-Threshold Ionization in the Tunneling Regime: Theory and Experiment

A calculation of the second-order (rescattering) term in the $S$-matrix expansion of above-threshold ionization is presented for the case when the binding potential is the unscreened Coulomb potential. Technical problems related to the divergence of the Coulomb scattering amplitude are avoided in the theory by considering the depletion of the atomic ground state due to the applied laser field, which is well defined and does not require the introduction of a screening constant. We focus on the low-energy structure, which was observed in recent experiments with a midinfrared wavelength laser field. Both the spectra and, in particular, the observed scaling versus the Keldysh parameter and the ponderomotive energy are reproduced. The theory provides evidence that the origin of the structure lies in the long-range Coulomb interaction.

Figure 1

Low-energy photoelectron energy spectra of Ar [(a),(b)] and Xe [(c)–(f)] in a midinfrared laser field. (a),(c),(e) Calculated from Eqs. (1b) (solid line) and (1a) (dashed line); (b),(d),(f) experimental results.

Figure 2

The dependence of the LES high-energy boundary $E_H$ on the Keldysh parameter $\gamma$ and the ponderomotive energy $U_p$ for various atoms and wavelengths. Left-hand column: Theoretical results; right-hand column: experimental results.