High-energy direct photoelectron spectroscopy in strong-field ionization

Recently, in a strong Coulomb field regime of tunneling ionization an unexpected large enhancement of photoelectron spectra due to the Coulomb field of the atomic core has been identified by numerical solution of time-dependent Schr\"odinger equation [Phys. Rev. Lett. \textbf{117}, 243003 (2016)] in the upper energy range of the tunnel-ionized direct electrons. We investigate the origin of the enhancement employing a classical theory with Monte Carlo simulations of trajectories, and a quantum theory of Coulomb-corrected strong field approximation based on the generalized eikonal approximation for the continuum electron. Although the quantum effects at recollisions with a small impact parameter yield an overall enhancement of the spectrum relative to the classical prediction, the high energy enhancement itself is shown to have a classical nature and is due to momentum space bunching of photoelectrons released not far from the peak of the laser field. The bunching is caused by a large and nonuniform, with respect to the ionization time, Coulomb momentum transfer at the ionization tunnel exit