Show description

9) where m is the magnetic quantum number and n∗ is the effective principal quantum number. s. 9) (divided by ). 9) tells us that the maximal rate is reached at the peak hight of the optical field. 2 Trajectory Description of Ionization Processes in Strong Optical Fields 39 In terms of a tunneling time through the potential barrier, ttun ≡ 2mqtun / |ptun |, the adiabaticity parameter can be represented by γ = ωttun . Hence the condition γ 1 means the adiabatic temporal variation of the optical field with respect to the tunnel frequency of the electron.

The Volkov solution is an exact solution of the quantum equations of motion for a free electron, so when Up EB it is a good approximation to simply replace Ψf (t) by the Volkov solution ΨfV (t) . 8): ∞ (S − SFA 1)f i = −i dt ΨfV (t) , HI Φi (t) . 46) −∞ The only requirement that needs to be stated is that z1 1, with no mention of frequency. The SFA agrees [36] with other analytical approximations at both high and low frequencies. Even the requirement on z1 can be relaxed if the physical problem depends only on high-lying parts of the spectrum, where a photoelectron has enough kinetic energy that residual Coulomb effects are unimportant.

We write the Schr¨ odinger equation simply as i∂t Φ = H0 Φ . 32) form a complete set {Φn }. The atoms or molecules (or the electrons thereof) subjected to the laser field experience the additional interaction arising from the field, so their description is in terms of the more extensive Schr¨odinger equation i∂t Ψ = (H0 + HI (t)) Ψ . 33) form a complete set {Ψn }. R. 34) is satisfied. The conventional adiabatic-decoupling demand that an exponential fall-off in HI occurs, is not needed here. We organize the {Φn } states by the statement that one element of this set, Φi , defines the initial state before an experiment is performed.