Strong field non-Franck–Condon ionization of H$$_2$$: a semi-classical analysis

Electro-Nuclear Dynamics of Single and Double Ionization of H2 in Ultrafast Intense Laser Pulses

“…From eq we can deduce that the variation of the population in H 2 between time t and time t + δ t is equal to normalΔ P normalH 2 ( t + δ t ← t ) = prefix− δ t ∫ W normalH 2 ( R , t ) false| normalΨ H 2 false( R , t false) false| 2 d R where the minus sign indicates a population loss. It is well known that molecular ionization rates can vary significantly with R , since the ionization potential itself is usually a function of the internuclear distance . We can see in eq that this important dependence of the ionization rate on R is well accounted for in this model.…”

“…The evolution over a short time interval (of extension δ t ) of the nuclear wave packet Ψ H2 ( R , t ) representing the H 2 molecule is then performed numerically in two successive steps. In the first step, the population loss due to the ionization of the neutral molecule is taken into account by introducing the instantaneous ionization rate W H2 ( R , t ), according to Ψ̅ normalH 2 ( R , t ) = false[ 1 − W normalH 2 ( R , t ) δ t false] 1 / 2 Ψ normalH 2 ( R , t ) To evaluate the ionization rate of H 2 in an intense laser field, we use the molecular ionization model , derived from the PPT approach, − as described in detail in Vigneau et al for instance. Finally, in a second step, the resulting wave packet Ψ̅ normalH 2 ( R , t ) is propagated numerically according to Ψ normalH 2 ( R , t + δ t ) = Û normalH 2 ( t + δ t ← t ) Ψ̅ normalH 2 ( R , t ) with the evolution operator Û normalH 2 ( t + δ ...…”

“…In the first step, the population gain due to the ionization of the neutral molecule in the H 2 + ground state is calculated using Ψ̅ g ( R , t ) = Ψ g ( R , t ) − i α ( t ) false[ W normalH 2 ( R , t ) δ t false] 1 / 2 Ψ normalH 2 ( R , t ) where α( t ) is a normalization factor calculated numerically to impose a population gain in H 2 + that exactly offsets, during each time step δ t , the loss in H 2 given in eq . The nuclear wave packet associated with the first excited electronic state of H 2 + remains unchanged at this point, with Ψ̅ u ( R , t ) = Ψ u ( R , t ) since the ionization of H 2 in an intense laser field produces H 2 + in its ground electronic state only . In a second step, the two coupled wave packets Ψ̅ g ( R , t ) and Ψ̅ u ( R , t ) are propagated numerically according to true[ .25ex2ex lefttrue Ψ̅ …”

“…To evaluate the ionization rate of H 2 in an intense laser field, we use the molecular ionization model 40,41 derived from the PPT approach, 37−39 as described in detail in Vigneau et al 46 for instance. Finally, in a second step, the resulting wave packet R t ( , )…”

“…It is therefore during this coupled propagation step that the first (2pσ u ) electronic state of H 2 + is populated. Finally, in a third and last step, the population losses due to the ionization of H 2 + are taken into account using the molecular-PPT 46 ionization rates W g (R, t) and W u (R, t) associated with the 1sσ g and 2pσ u states…”