Nonsequential double ionization

Atoms exposed to intense laser fields may be multiply ionized. Along the simplest pathway, this happens step by step. However, already more than twenty years ago, evidence was mounting for the contribution of a different pathway whereby two electrons are freed in one coherent process [1]. Clearly, this requires that the participating two electrons be correlated. Regardless of the detailed mechanism, this process is referred to as nonsequential double ionization (NSDI) for reviews, see [2]. 

Fig. 4.3. Linear-scale density plot of the distribution of the ion momentum P = (P,l, P ) in nonsequential double ionization of neon at 8 x 1014 W/cm2 and Hu> = 1.55 eV. From [26]...

Fig. 4.6. Left-hand panels Momentum correlation function (4.20) of the electron momenta parallel to the laser field for nonsequential double ionization computed with the uniform approximation using the contact interaction (4.14b). The field frequency is u> = 0.0551 a.u. and the ponderomotive energy IJP = 1.2 a.u., which corresponds to an intensity of 5.5 x 1014W/cm2. The first two ionization potentials are Soi = 0.79a.u. and I-E02I = 1.51 a.u. corresponding to neon. Panel (a) shows the yield for the case where the transverse momenta pnj (n = 1,2) are completely integrated over, whereas in the remaining panels they are restricted to certain intervals. In panels (6) and (c), p2 is integrated, while 0 < pi /[Up]1/2 < 0.1 and 0.4 < Pi /[Up]1 2 < 0.5, respectively. In panels (d), (e), and (/), both transverse momenta are confined to the intervals 0 < Pn /[Up]1/2 < 0.5, 0.5 < pjn /[Up]1/2 < 1, and 1 < pjn /[Up]1/2 < 1.5, respectively. Right-hand panels, same as left panels, but for the Coulomb interaction (4.14a). From [17]...

Applicability of the modern TDDFT approaches for the treatment of multiple electron ionization processes is another problem related to the quality of time-dependent xc-energy functionals. Most of approximate xc functionals lack the important property of the exact functional, the discontinuity of its derivative with respect to the number of particles N, when N passes through integer values [78]. Several attempts to apply TDDFT with such approximate functionals for calculations of nonsequential double ionization were unsuccessful [79,80]. Recently it was shown [81] that the derivative discontinuity is crucial for correct description of double ionization. 

Observation of Nonsequential Double Ionization of Helium with Optical Tunnelling. 

Nonsequential double and multiple ionization are to a large part classical phenomena. Indeed, the S-matrix approach suggests a pertinent classical limit. We have summarized evidence that the latter reproduces the fully quantum-mechanical results very well in parameter regions where this can be expected. Finally, we have extended such classical avenues to a statistical description of nonsequential triple and quadruple ionization. For neon, such a classical statistical model yields a fair description of the available data. While a more microscopic description of these extremely involved phenomena lies in the future, we believe that the simple models summarized in this paper will remain valuable as benchmark results. 

Multiphoton ionization (MPI) occurs when an atom or molecule loses more than one electron in an intense electromagnetic field. It was discovered to be a nonsequential process, meaning that the probability of double ionization can be much greater than the product of two independent ionization events, thus leading to a knee in the double ionization probability as a function of intensity.TDDFT calculations have been unable to reproduce this knee accurately, and it has been shown that a correlation-induced derivative discontinuity is needed in the time-dependent KS potential for the method to give proper results. 

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