  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.
