Model-Independent Quantum Approach for Intense Laser Detachment of a Weakly Bound Electron

Simple soluble molecular ionization model

“…This agrees precisely with the imaginary part (50) found directly from the properties of the Airy functions, as well as with a simple WKB estimate.…”

“…This helps develop a body of intuition for the behavior of the quasi-bound states as they are Stark shifted and broadened, and also for the resonance structures in the "continuum", which reflect a competition between Ramsauer-Townsend resonant scattering between the two atomic wells and between one or both atomic well(s) and the linear field potential. The most important extension of this model would be to consider the effect of time-dependence in the background electric field, which introduces yet another physical scale into the problem [46,47,48,49,50].…”

Cutoffs of high-energy plateaux for atomic processes in an intense elliptically polarized laser field

“…Substituting in (9) x → z(τ) and expanding z(τ) up to second-order terms near the point τ = τ 1 , we obtain the following approximation for the Bessel function in (5): (10) where Using (10) to evaluate the integral in (5) for k΄ = 0, the resulting approximate value for |M k0 | is (11) where α = k -|z 1 | -ω -1 . The approximation represented by (11) and (6) provides numerical results for | f 2k | that are in excellent agreement with those calculated using the exact equation (4) for k values around the cut-off and beyond the plateau region. An analytical estimate for k c corresponding to the cut-off in the spectrum of | f 2k | may be deduced by estimating the maximum of |M k0 | in (11) as a function of k (cf [4]).…”

“…without a Coulomb tail). As shown in [11,12], the position of plateau cutoffs in ATI/ATD and HHG is essentially independent of the spatial symmetry of an initial bound state and the shape of U(r). Thus in this study we use the most tractable model for U(r), the zero-range potential supporting a single bound state of energy E 0 = - 2 κ 2 (2m) -1 .…”

“…An analytical estimate for k c corresponding to the cut-off in the spectrum of | f 2k | may be deduced by estimating the maximum of |M k0 | in (11) as a function of k (cf [4]). The position of this maximum may be estimated as the average of k b and k e , k max ≡ k c = (k b + k e )/2, where k b ≈ |z 1 | corresponds to the maximum of the Bessel function in (11) and k e ≈ |z 1 | + ω -1 corresponds to the maximum of the exponential in (11). Thus we obtain the following result for k c : (12) which agrees well with the exact numerical results for the cut-off positions in fi gure 1(a) for ≥ 0.6 (or, equivalently, for |η| ≤ 0.5).…”