Gerade System*

We present a flexible numerically solvable two-dimensional (with one nuclear and one electronic degree of freedom) model describing the collision of an electron with the H₂⁺ molecule (and its isotopologues) in the gerade symmetry [arXiv:2112.10820 (2021)]. Constructed in a way reminiscent of the previous quantum defect work of Jungen and Ross [Phys. Rev. A 49, 4353 (1994)], the model is comprised of three coupled two-dimensional channels in the space of s, p, d partial waves of the incoming electron. We show how this model reproduces the Born-Oppenheimer properties of the H₂ molecule in the relevant range of internuclear distances and how it can be applied to describe processes such as (ro-)vibrational excitation and dissociative recombination. Previous theoretical studies of H₂⁺ and HD⁺ dissociative recombination employ the frame transformation theory and the MQDT quasidiabatic theory and include various physically motivated approximations. The numerical solution of our model is suitable as an alternative theoretical tool to study these processes without said approximations. We use it to compute rovibrationally inelastic cross sections and dissociative recombination cross sections and compare with the data of previous studies.