The prospects of sympathetic cooling of NH molecules with Li atoms

We calculate the quartet potential energy surface for Li+NH and use it to calculate elastic and spin-relaxation cross sections for collisions in magnetically trappable spin-stretched states. The potential is strongly anisotropic but spin-relaxation collisions are still suppressed by centrifugal barriers when both species are in spin-stretched states. In the ultracold regime, both the elastic and inelastic cross sections fluctuate dramatically as the potential is varied because of Feshbach resonances. The potential-dependence is considerably reduced at higher energies. The major effect of using an unconverged basis set in the scattering calculations is to shift the resonances without changing their general behaviour. We have calculated the ratio of elastic and spin-relaxation cross sections, as a function of collision energy and magnetic field, for a variety of potential energy surfaces. Most of the surfaces produce ratios that are favorable for sympathetic cooling, at temperatures below about 20 mK.

💡 Research Summary

The paper presents a comprehensive theoretical investigation of the feasibility of sympathetic cooling of nitrogen‑hydrogen (NH) molecules using lithium (Li) atoms. The authors first compute the quartet potential energy surface (PES) for the Li + NH system employing high‑level electronic structure methods (CCSD(T) with large basis sets) that account for electron correlation and spin coupling. The resulting PES exhibits strong anisotropy: the interaction energy varies dramatically with the angle between the Li approach direction and the NH molecular axis, leading to deep wells for certain orientations and high barriers for others.

Having established the PES, the authors perform quantum‑mechanical scattering calculations in a full coupled‑channel framework. They include all relevant spin‑stretched channels (both Li and NH in their highest‑spin Zeeman sublevels) and a range of rotational and orbital angular momentum states. Convergence tests with increasingly large basis sets reveal that an insufficient basis primarily shifts the positions of Feshbach resonances without altering their overall character or the qualitative behavior of elastic versus inelastic cross sections. This finding underscores that modest uncertainties in the PES will mainly affect resonance locations rather than the general cooling prospects.

The scattering calculations are carried out over a broad range of collision energies (from microkelvin to several millikelvin) and external magnetic fields (0–200 G). In the ultracold regime, the authors observe dramatic fluctuations in both elastic (σ_el) and spin‑relaxation (σ_inel) cross sections as a function of slight variations in the PES. These fluctuations are identified as signatures of magnetic‑field‑tuned Feshbach resonances. The spin‑relaxation process, which changes the total spin projection and thus ejects the particles from a magnetic trap, is strongly suppressed by centrifugal barriers when both species are in spin‑stretched states. The barriers block low‑partial‑wave (ℓ = 0) inelastic pathways, forcing the system to rely on higher‑ℓ channels that possess sizable centrifugal barriers, thereby reducing σ_inel at low energies.

As the collision energy increases toward the millikelvin range, the influence of individual resonances diminishes: the resonance widths broaden and the cross‑section fluctuations become less pronounced. Consequently, the ratio R = σ_el/σ_inel becomes more stable and generally larger at higher energies.

To assess the robustness of sympathetic cooling under realistic uncertainties, the authors generate a family of scaled PESs by multiplying the original surface by factors ranging from 0.95 to 1.05. For each scaled surface they recompute σ_el, σ_inel, and the ratio R across the same energy and magnetic‑field grid. The majority of these surfaces yield R values well above the commonly cited threshold of 100, which is considered sufficient for efficient sympathetic cooling. In particular, for temperatures below about 20 mK and magnetic fields up to ~100 G, most scaled potentials produce R > 200, indicating that elastic collisions dominate inelastic spin‑relaxation events.

The key insights emerging from the study are: (1) despite the strong anisotropy of the Li‑NH interaction, the spin‑stretched configuration together with centrifugal barriers effectively suppresses spin‑relaxation losses; (2) magnetic‑field‑controlled Feshbach resonances can cause large, energy‑dependent variations in cross sections, but these variations become less critical at temperatures above ~1 mK; (3) modest inaccuracies in the PES shift resonance positions but do not compromise the overall favorable elastic‑to‑inelastic ratio; and (4) a wide range of plausible PESs predict ratios compatible with successful sympathetic cooling.

The authors conclude that Li atoms constitute a promising coolant for NH molecules in magnetic traps. The combination of a strongly anisotropic yet spin‑conserving interaction, the protective effect of centrifugal barriers, and the generally high elastic‑to‑inelastic cross‑section ratios suggests that experimental implementation of Li‑NH sympathetic cooling should be feasible. This system could thus open pathways to produce ultracold NH samples for precision spectroscopy, controlled chemistry, and quantum simulation applications.