Study of the Resonance Structures of the Preionizing Spectrum of Molecular Hydrogen by Phase-shifted Multichannel Quantum Defect Theory

The resonance structure of the preionization spectrum of $H_2$ in the region immediately above its ionization threshold, ($^2{\sum}_{g}^{+}$, $\nu^+=0$, $N^+=0$) converging toward its rotationally excited ($\nu^+=0$, $N^+=2$) limit, is complicated due to perturbation by the vibrationally excited levels $7_{p\pi}\;v=1$ and $57_{p\pi}\;v=2$. The spectra of interlopers are separated from the rotationally preionizing Rydberg series to allow analysis of this complex resonance structure. Although only two vibrationally excited levels perturb the rotational preionization spectrum, at least 6 interloper Rydberg series participate in the complex spectrum over most of its energy range and more interloper series participate at a narrow range around $124500cm^{-1}$ in the spectrum. To allow handling of an arbitrary number of interloper series, MATLAB$^{(R)}$'s symbolic operation is used to perform on-the-fly formulation.