Non-Franck-Condon vibrational distribution in the (1+1’)-photon resonance-enhanced multiphoton ionization of H₂

We have studied the (1+1’)-photon resonance-enhanced multiphoton ionization (REMPI) of H₂ via B¹Σ_u (ν=4, j=1,2) levels considering (i) the effect of interference of different ionizing channels via nearby vibrational levels of B¹Σ_u (ν=0 to 3 and 5 to 14) and C¹Π_u (ν=0 to 2) states, and (ii) the effect of coupling between these vibrational levels via the continuum. We have shown that for this REMPI process, these two effects can lead to a non-Franck-Condon vibrational distribution of H₂⁺ ions in the ν⁺=0 and ν⁺=1 levels of the ground X ²Σ_g state. The nature of the deviation from the Franck-Condon vibrational distribution has been found to depend on the relative strength of different ionizing transitions and hence on the relative magnitude of dipole transition moments as well as the intensity of the laser connecting the intermediate levels to the continuum. As a result, the vibrational branching for transition via different rotational levels (j=1 and j=2) of the B ¹Σ_u (ν=4) state considering R(0) [i.e., X ¹Σ_g(ν=0, j=0) to B ¹Σ_u (ν=4, j=1)] and R(1) [i.e., X ¹Σ_g (ν=0, j=1) to B ¹Σ_u (ν=4, j=2)] transitions, respectively, for the lower step excitation, has been found to exhibit a different nature of non-Franck-Condon distribution in the range of laser intensity 5×10⁹ to 9×10¹⁰ W/cm².

However, for the (1+1’)-photon REMPI via the ν=8, j=2 level of the B¹Σ_u state considering R(1) [i.e., X ¹Σ_g (ν=0, j=1) to B¹Σ_u (ν=8, j=2)] for lower step excitation, this effect of interference has been found to be insignificant on the vibrational branching in ν⁺=1 and ν⁺=2 levels of the H₂⁺ ion in the ground state.