Search for the best analytical formula in the tunneling and the barrier-suppression ionization regimes

Abstract

In this work we derive an analytical formula for the ionization rate of the hydrogen atom in its ground state in the strong linearly polarized laser field. The derivation utilizes Keldysh-like probability amplitude in the length gauge in the dipole approximation including Coulomb effects in the final state of the ionized electron. We apply a properly chosen pre-exponential factor into the Gordon–Volkov wave function. We compare our theory with many previously known numerical or theoretical results for the field parameters for which (the laser frequency is less than the binding energy of the atom; usually ) and ( is the peak laser field). Thus, we consider both the tunneling and the barrier-suppression ionization regimes. It appears that in most cases ionization rates computed here are very close to those obtained long ago within the Perelomov, Popov and Terent’ev theory or its later modification by Popruzhenko et al. However, including Coulomb effects in the final state of the ionized electron in the present Keldysh-like theory leads to non-trivial changes (in relation to ordinary Keldysh theory without these Coulomb effects) in photoelectron energy spectra or angular distributions.