Fig. 5: Comparison of thermally averaged HDRCE rate coefficients from experiment and theory.
From: Quantum suppression of cold reactions far from the s-wave energy limit
a The measured rate coefficient as a function of temperature (black point) is compared to theoretical predictions based on multichannel quantum defect theory (MQDT) scattering calculations and semiclassical approximations. Solid lines show full MQDT results including angular momentum (l)-dependent short-range parameters; dashed lines omit this dependence. Dotted and dash-dotted lines represent semiclassical models [Eqs.(23) and(2)], with and without l-dependence, respectively. Each color denotes a different pair of short-range quantum defects \({\mu }_{g}^{(0)}\), \({\mu }_{u}^{(0)}\), which parameterize the unknown relative scattering phase shifts between the gerade and ungerade potentials shown in Fig. 1b. The black dash-dotted line marks the classical high-temperature prediction, kHDRCE = (3/16) × kL, corresponding to incoherent partial-wave contributions. We note that while the Langevin rate coefficient kL sets the absolute scale, its theoretical value only uniformly rescales both the computed and experimental results. Vertical error bars represent one-standard-deviation (1σ) binomial uncertainties, and the horizontal bar indicates the systematic range bounded by our model fit. b Contour map of the ratio kHDRCE/kL as a function of temperature and quantum defect difference \({\mu }_{g}^{(0)}-{\mu }_{u}^{(0)}\), computed using the semiclassical model in Eq. (23) with phase shifts derived from Eq. (24). The solid black contour shows the locus of theory points consistent with the central experimental value while the dashed gray and dotted white contours indicate the corresponding ± 1σ bounds. Suppression below the classical limit (blue dashed line on the color scale) occurs only within a narrow region of near-equal short-range phases, consistent with partial-wave phase locking, extending a large temperature range relative to the s-wave limit ( ~ 0.08μK). At higher temperatures (T ≳ 0.05K), the model predicts that suppression weakens as partial-wave phase locking breaks down.
