Resonances and levels¶

Quasi-bound states: the Born–Oppenheimer approximation to them, the exact two-dimensional poles, and how to tell a resonance from an artefact.

BO/LCP resonance levels — quasi-bound vibrational states of the anion — Born–Oppenheimer quasi-bound levels in the complex curve.
Exact (non-Born-Oppenheimer) resonance states of the 2-D model — the same levels without the approximation: poles of the full 2-D S-matrix, and what the Born–Oppenheimer error actually measures on N₂.
Exact resonance states of H₂⁺, against the Born–Oppenheimer picture — the same comparison on H₂⁺, against a σ_DR sweep: the Born–Oppenheimer error sorted by regime, and the four “resonances” that turned out not to be.
Potential factory — fitting model surfaces to target curves — fitting a richer model surface to a tiered target curve: round-tripped against N₂/NO/F₂’s own published parameters, then O₂ from Alt & Houfek’s published curves to its spin–orbit-resolved VE cross section on the paper’s own nonlocal-model comb (O₂ — the first fitted target).
Coupled partial waves in the NO shape resonance: does the fixed-l reduction hold? — the parked angular-coupled-channels direction, delivered: does NO’s single-partial-wave shape resonance stay a single pole and a good approximation once it is allowed to couple to neighbouring partial waves? Yes to both. Only l = 1 hosts a resonance at all — O⁻ has one bound orbital, 2p — which explains the single pole rather than merely observing it, and the truncation costs 2–7 % on the angle-integrated VE cross section against a reference converged to 0.3–0.5 %. That observable is the wrong one for the question anyway, since it sums over the exit partial waves the anisotropy produces; the differential cross section has not been computed.