Field ionization rate for PIC codes

An improved formula is proposed for field ionization rate covering tunnel and barrier suppression regime. In contrast to the previous formula obtained recently in [I. Yu. Kostyukov and A. A. Golovanov, Phys. Rev. A 98, 043407 (2018)], it more accurately describes the transitional regime (between the tunnel regime and the barrier suppression regime). In the proposed approximation, the rate is mainly governed by two parameters: by the atom ionization potentials and by the external electric field, which makes it perfectly suitable for particle-in-cell (PIC) codes dedicated to modeling of intense laser-matter interactions.