# Full Characterization of a Molecular Cooper Minimum Using High-Harmonic Spectroscopy
## 3 Results and Discussion
### Identifying the Cooper Minimum in Methyl Chloride  
In order to compare methane to methyl chloride, the spectra and RABBITT scans were recorded in identical conditions. We firstly discuss the normalized spectra, which are shown in Figure 3a. As was discussed in Section 2.2, we normalized the spectral intensities to remove the contributions from  
Figure 2: Laser intensity scaling in methane. Measured XUV group delays (circles) are shown from harmonic generation in methane, fitted with intensities as shown in the legend. As with the xenon scan of Figure 1, the lowest-intensity curve was fitted according to Equation (9), and scaled by the measured input power ratio for each additional scan (curves). Each intensity was separated by 0.2 fs for visual clarity. \(\Gamma_{target}\) and \(\Gamma_{ref}\), and extracted the CM cross-section from the ratio of the envelopes in \(HHG_{\text{CH}_{3}Cl}\) and \(HHG_{\text{CH}_{4}}\). The envelopes were obtained by finding harmonic peaks and smoothing the result with a second-order Savitzky-Golay filter, and they appear in Figure 3a as solid lines. The yields were not expected to be the same; to keep conditions identical, HHG was optimized for methyl chloride to avoid saturating ionization in either sample. In the range of \(\sim\)35-55 eV, methane generated a considerably larger yield, before the signal for the two species agreed once again in the harmonic cut-off. Because identical focal conditions were used (see the intensity scan discussion above), and because the two targets had similar IPs, we expected nearly the same cut-off energy. The ratio of the normalized envelopes is shown in Figure 3b with the maximum suppression occurring around 42.4 eV. Such suppression was previously seen in chlorinated molecules [14], and was attributed to a CM. Here, we note that, unlike the HHG spectra from di- and tetra-chloromethane, the spectrum of methyl chloride alone does not show an unambiguous minimum in the harmonic intensities. Identifying the methyl chloride structure as a CM required, therefore, further validation from the calibrated spectral intensity ratio and from the methyl chloride GD for a full characterization. Shown in Figure 4 are the GDs of methane and methyl chloride (a) after removal of the atomic and filter delays (\(\tau_{HHG}\)), and (b) after further removal of \(\tau_{SFA}\) (\(\tau_{target}\)). This comparison was necessary due to the ambiguous interpretation of GD as emission time in the SFA model; in the presence of additional features beyond the SFA, the fit was poorly conditioned. Thus, under identical conditions, we fitted to  
Figure 3: Influence of the methyl chloride Cooper minimum (CM) on the spectral intensity relative to methane. (**a**) Normalized spectra were taken in sequence with identical harmonic generation conditions for the intensity comparison of methane (blue) and methyl chloride (green); (**b**) The ratio of normalized spectra from (**a**) shows the relative minimum in amplitude. Because the laser field was held constant and the spectra were normalized, the difference was attributable exclusively to the chlorine substitution. the SFA intensity of methane, applied the same intensity to methyl chloride, and removed the same attochirp from both measurements. While they were not entirely consistent near the cut-off, from 25-60 eV they agreed well but for a \(\sim\)120-as reduction centered near 42 eV; this is similar to the CM measured in argon [12], though shifted in energy, which seems sensible given the analogous electronic similarity between the highest occupied molecular orbital (HOMO) of methyl chloride and the ground state of argon. In fact, the methyl chloride HOMO was calculated [9] as having approximately 80% of its population in the chlorine \(p\) orbital. With only the contribution from the angle-integrated RDME remaining, we integrated the delay-corrected GD to retrieve the phase variation across the interaction up to an arbitrary shift.