Journal of Russian Laser Research, Volume 36, Number 4, July, 2015 LASER FIELD IONIZATION RATES IN THE BARRIER-SUPPRESSION REGIME Tatjana B. Miladinovi´ c and Violeta M. Petrovi´ c * Department of Physics, Faculty of Science, Kragujevac University Radoja Domanovi´ ca Street 12, Kragujevac 34000, Serbia * Corresponding author e-mail: violeta.petrovickg @ gmail.com Abstract We analyze the influence of ponderomotive and Stark shifts on the barrier suppression transition rate for noble and alkali atoms for a low-frequency linearly-polarized laser field. We consider three approaches to the barrier suppression ionization (BSI) rate: through a critical field, an ion charge, and the Airy function. We show that ponderomotive and Stark shifts affect the rate differently in these three approaches. Generally, the rate curve of K is more strongly lowered than the one of Ar. Keywords: transition rate, barrier suppression ionization (BSI), Stark shift, ponderomotive potential. 1. Introduction There is no a single method for modeling all potential routes to ionization for any given atom. Within the atom itself, ionization depends upon the level of excitation for the electron to be released. Externally incident radiation may be absorbed so that an electron may simply be excited rather than ionized, or it may undergo stimulated emission from an incident photon and relax to a lower energy state [1]. In a time-varying electric field, such as that imposed by a laser, we find that the product of excitation and relaxation processes leading up to ionization can result in even ionization by direct photon absorption being a nonlinear process [2]. The mechanisms by which an electromagnetic field directly causes ionization are described as field ionization. In 1965, Keldysh derived a formula describing field ionization for a hydrogen atom in the low-frequency regime, where photon energy is beneath the binding energy or ionization energy of the electron [3]. It was shown that, when γ ≫ 1, scaling of the ionization rate with incident laser-field intensity I went as I K , where K is the number of photons absorbed and γ is the Keldysh parameter. This scaling is characteristic of multiphoton ionization. In the multiphoton case, it is also suitable for modeling the tunneling ionization rate in hydrogen atoms as it includes no corrections for different electron orbitals or excited states at the Keldysh parameter γ ≪ 1. Excited states were considered by Perelomov et al. [4] and this work was extended to produce the Amosov–Delone–Krainov (ADK) equation for the ionization rate suitable for complex ions of arbitrary principle, angular, and magnetic quantum numbers [5]. The ADK theory has shown good agreement with experiments [6]. The ADK equation makes use of an effective principle quantum number for an electron orbital n * = Z/  2I p = n − δ n , where δ n is the quantum defect, I p is unperturbed ionization potential, and Z is the ion charge. The quantum defect is a correction arising from the fact that outer shell electrons are not perfectly shielded from the nucleus as even outer orbitals will occasionally pass close enough to feel it. 312 Manuscript submitted by the authors in English first on April 24, 2015 and in final form on June 4, 2015. 1071-2836/15/3604-0312 c  2015 Springer Science+Business Media New York DOI 10.1007/s10946-015-9505-0