Breaking a tetrahedral molecular ion with electrons: Study of NH$_4^+$

We apply a general theoretical model to study the dissociative recombination of the polyatomic ion NH$_4^+$. The high symmetry of the molecule, represented by the tetrahedral group, leads to complex vibronic couplings responsible for dissociative recombination. By applying multi-channel quantum defect theory and using symmetry considerations, we treat the doubly and triply degenerate modes and electronic states of NH$_4^+$ to calculate a theoretical cross section which agrees well with existing experimental data. This represents, to our knowledge, the first DR study for a molecular ion with triply degenerate electronic states and normal modes.