Article pubs.acs.org/JPCA
Laser-Induced Low Energy Electron Diffraction in Aligned Molecules Suk Kyoung Lee, Yun Fei Lin, Lu Yan, and Wen Li* Department of Chemistry, Wayne State University, Detroit, Michigan 48202, United States ABSTRACT: We measured the photoelectron spectra and angular distributions of partially aligned N2, O2, and CO2 in the rescattering plateau of above threshold ionization (ATI). The measured ATI electrons have relatively low collision energies ( 0.86 a.u.), the features appear drastically different among the three molecules. A noticeable feature for N2 is the strong signals in the momentum region pf = ∼1.6 a.u. (∼34 eV) along the polarization axis of the laser beam (φ = 0°, where φ is the angle between the polarization axis and the direction of the detected electron; at this angle, the signal is mainly from backscattered electrons with a scattering angle of 180°), while O2 and CO2 have very weak or no signal around that region. For all three systems, there are four distinct lobes with the ratio higher than 1. These lobes show some subtle differences of peak angles and distances from the center. For O2, the signal along the laser polarization at pf = ∼1.15 a.u. (∼18 eV) is much stronger for aligned molecules. Can the origin of these differences be structural? It has been well established that strong field ionization is strongly dependent on the symmetry of the ionizing orbital.23 This appears fitting in the case of O2 and N2, which have very similar bond lengths but different ionizing orbital symmetry (σg vs πu). Corkum and co-workers17 have reported such symmetry dependence of the ATI of directly ionized electrons ( 13 eV). However, whether these differences are the main reasons for different conclusions is unclear. Another previous experiment by Okunishi et al. reported a suppression of ATI yield along the laser polarization at electron energy around 23 eV in unaligned O2 sample.11 This was interpreted as a result of a novel fourpath destructive interference and the ungerade character of the O2 HOMO orbital. The energy of this suppression is close to the enhancement maxima observed in current experiment. The opposite sign suggests that the suppression is more significant in the antialigned geometry than that in the random aligned system. Because of the strong angular dependence of ionization, the ions are partially aligned,15 even though the neutral sample is randomly aligned. The absence of such enhancement maximum in CO2, which has the same HOMO orbital symmetry, calls into question previous interpretation, which was based on MSFA. At present, while the QRS appears successful in treating highenergy electrons of ATI, complete modeling of low energy electron ATI experiments has not been accomplished. Limited theoretical work provides important clues to our observation: the strong energy dependence in the ratio image is a direct consequence of the energy dependence of σ(θ,φ,Er). In a recent R-matrix calculation,25,26 the origin of this dependence was attributed to a scattering resonance and/or energy dependent Coulomb phases. The involvement of lower lying orbitals in strong field ionization further complicates this picture. Even though the HOMO−1 orbital does not contribute significantly to the total ionization rate, the interference between electrons ionized from different orbitals might affect the PAD. A more complete theoretical approach, which takes into account all these factors, is needed to interpret our experimental observation. On the one hand, the dynamical character of the scattering process precludes any simple retrieval of structural properties of molecules. On the other hand, it suggests that laser-induced electron diffraction could be a sensitive and practical tool for studying low energy electron−ion scattering dynamics. These dynamics has been the subject of numerous previous efforts30 due to its important role in high temperature plasma33 and solar/stellar atmosphere.34 Compared with conventional low energy electron−ion scattering experiments, laser-induced electron diffraction with a velocity mapping imaging setup
ically. We take the value from the most recent theoretical result calculated for the HOMO orbital of N2, O2, and CO2 by Petretti et al.27 The angular distribution A(θ,t) is obtained by fitting the time-dependent ionization rate (B(t)), which is directly related to the time-resolved rotational revival structure by B(t) = ∫ I(θ)A(θ,t)dθ. B(t) could be measured in the experiment by monitoring the time-dependent total ion (or electron) counts (Figure 4a). Many A(θ,t) are first calculated with the experiment laser intensity and different initial rotational temperatures. The one with the B(t) best fitting the experiment is selected as the angular distribution and used in eqs 2 and 3 (Figure 4b,c). We usually fit the experimental trace with a length of more than one-half of the rotational period (with 30 fs step size), which includes at least two revival features. This approach works well and has been employed previously to obtain the angular dependent ionization rate.28 We note that when adding the HOMO−1 orbital contribution, the fitting to the measured B(t) generally becomes poor. This shows that the lower lying orbital does not contribute significantly to the ionization at the laser intensity used in our study. Strong field ionization from multiple orbitals has been reported in N2,29 CO24, and N2O45. To test the validity of the two-center interference model, we will look at the data along the laser polarization direction (φ = 0°), where the electrons are backscattered. These backscattered electrons have the highest probability of scattering off the shortrange potential and thus seeing the ionic core. For those electrons scattered at other angles, the interaction with Coulomb potential usually dominates, which tends to obscure the structural information26,30 (see also references in ref 30). We show the calculated results of ratio vs R/λ in Figure 5. For N2, there is a maximum in the ratio image around R/λ = 0.65 (Figure 5a). From our experiment data, the peak corresponds to recollision energies around ∼10 eV (long trajectory) and ∼14 eV (short trajectory). If we add the ionization potential of the HOMO orbital, the total electron energy is 25.6 and 29.6 eV, respectively. We obtain bond lengths RN2 of about 1.65 Å and 1.45 Å, which are both larger than the established 1.1 Å. For O2, the first maximum appears at a much smaller R/λ = 0.29 with an ungerade ionizing orbital (Figure 5b). The experimental recollision energies for the maximum is about 5 eV (long) and 9 eV (short). We obtain RO2 = 0.86 Å and 0.77 Å, which severely underestimate the O2 bond length (1.2 Å). For CO2, there is no obvious maximum with φ = 0° to compare with our calculated results. Instead, there is a broader suppression of signal for electron energies >2Up. In the calculated result, which is the same as that in Figure 5b, we see a similar flat feature between R/λ = 0.7 and R/λ = 1.56 with ratio
