Connecting Collisional and Photofragmentation Resonances in the H$_2$ Ungerade Symmetry

TL;DR

This work extends an energy-dependent frame transformation framework to ungerade H$_2$ by including rovibrational couplings and dissociation channels, enabling a unified MQDT-based description of dissociative recombination, photoionization, and photodissociation near threshold. The method is benchmarked against an exactly solvable 2D model and experimental photoabsorption data, with the rotational FT bridging body-frame $\Lambda$ channels to laboratory-frame $N^+$ channels via $\ell=1$ p-waves. The EDFT approach reproduces the resonance energies and general cross-section patterns with high accuracy ($\sim$0.1 cm$^{-1}$) across PI, PD, and DR, and reveals how the same resonances manifest with different line shapes in distinct observables. The results underscore the power of combining spectroscopic benchmark data with multichannel quantum defect theory to extract reliable collision information for molecular hydrogen, and point to targeted improvements in delicate resonance regions and potential extensions to more complex molecular targets.

Abstract

A recently developed energy-dependent frame transformation theory that incorporates both ionization and dissociation channels of the H$_2$ molecule, is extended to treat the ungerade states that occur both in dissociative recombination and as the final state in ground state photoabsorption. The theoretical treatment includes the rotational degrees of freedom and is benchmarked against a two-dimensional model that can be solved with high accuracy and also compared with photoabsorption experiments. Analysis of the resulting spectra shows how the same resonances appear in very different observables, often with quite different line shapes.

Figures (6)

• Figure 1: Computed fixed-nuclei zero-energy $p$-wave quantum defects for $^1\Sigma_u^+$ (full curve) and $^1\Pi_u$ (broken curve) symmetry compared with the data extracted from Jungen_Atabek_JCP_1977 shown as crosses ($^1\Sigma_u^+$) and circles ($^1\Pi_u$).
• Figure 2: Energy-normalized transition dipole moments between the ground state X$^1\Sigma_g^+$ and the three lowest states in the $^1\Sigma_u^+$ and $^1\Pi_u$ symmetries. The horizontal dotted line displays the constant value of 1.86 a.u. used in the Ref. Jungen_Dill_JCP_1980 for both symmetries.
• Figure 3: Cross section comparison between DR $^1\Pi_u$ output channel (green curve), DR $^1\Sigma_u^+$ output channel (purple curve), photoionization (black curve) and photodissociation (green curve). The 2D R matrix benchmark for DR is present as the background thick grey curve.
• Figure 4: Cross section cube root comparison close to ground-vibrational-state threshold (which is at approximately 803.746 Å). The cross sections shown are total DR (purple curve), photoionization (black curve), photodissociation (green curve) and experimental photoionization data of Dehmer and Chupka (red data points). As Ref.Dehmer_Chupka points out, their photoionization spectrum observes signal even at energies slightly below the lowest ionization threshold, and they attribute this to the likely presence of weak electric fields. The dashed curve in the PI middle panel of the figure shows our mock photoionization cross section obtained by artificially opening that lowest ionization channel, which simulates the signal expected if very high photon-excited Rydberg states are field ionized in the experiment. In the DR spectrum, an infinite spike marks the lowest ionization threshold, an expected divergence because of the $1/k^2$ factor in the DR cross section formula. The two broad PD resonances below threshold were previously observed by Ref.HerzbergJungen, and their classifications are discussed in the text.
• Figure 5: Photoionization (black curve) and photodissociation (multiplied by -1, green curve) cross sections near 125875 cm$^{-1}$ produced by our model compared with the PI and PD cross sections calculated in Ref.Sommavilla_Merkt_Zsolt_Jungen_2016jcp and shown with dashed curves. The cross sections are all showed on a cube root scale in order to assess the differences and similarities more clearly. The experimental spectrum from Ref.Sommavilla_Merkt_Zsolt_Jungen_2016jcp in this region is not shown here because it is mixed with an obscuring R(1) transition at nearly the same energy. While the R(0) resonance position from our model EDFT calculation is within 1 cm$^{-1}$ of the Ref.Sommavilla_Merkt_Zsolt_Jungen_2016jcp computed position, the resonance width and branching ratio disagree strongly with that 2016 study, presumably indicating a limitation of our model.