Description

The ionization of highly charged ions in an intense laser field can be studied by solving the time-dependent Dirac equation, but this is very demanding. However, when the highly charged ion is exposed to a low frequency, high intensity laser field, the ionization process can be approximately described by the quasi-static approximation. This regime is characterized by γ≪1, where γ is the Keldysh parameter (γ=ω√(2m_e E_B )/|e|F, where ω,m_e E_B,e,F, are the laser frequency, the electron mass, the binding energy, the elementary charge, and the external field strength respectively). In this case, the external laser field corresponds to a slow time varying electric field. The Coulomb potential experienced by the electrons is distorted by being electric-field component of the laser field. Thus the electron can tunnel through the distorted barrier, or even escape over it for sufficiently intense fields. The tunneling ionization rate of a ground-state hydrogen atom in a static electric field was analytically given by Landau [1]. In addition, several authors have discussed the ionization rate of an atom in an alternating electromagnetic field [2,3]. We present a theoretical study of the time averaging of the quasi-static ionization rate in a time-dependent linearly polarized laser field. The integration over one period of the field leads to a complicated integral. It can be solved analytically by using a Taylor expansion. Alternatively, the entire function is numerically integrated. While in previous works, e.g. [2,3], only the first-order term of the Taylor expansion has been considered, in this work the importance of the higher-order terms derived for the first time is discussed. [1] L.D. Landau and E.M. Lifshitz, Quantum Mechanics, 3rd. Ed. Pergamon, 1978. [2] A.M. Perelemov, V.S. Popov and M.V. Terent'ev, Sov. Phys. JETP. 23, 924 (1964). [3] M.V. Asommosov, N.B. Delone, and V.P. Krainov, Sov. Phys. JETP. 20, 1191-1194 (1986).