We compare the results of the semi-classical (SC) and quantum-mechanical (QM) formalisms for angular-momentum changing transitions in Rydberg atom collisions given in a series of papers by Vrinceanu et al, most recently Vrinceanu et al (2012 Astrophys. J. 747 56), with those of the SC formalism using a modified Monte Carlo realization. We find that this revised SC formalism agrees well with the QM results. This provides further evidence that the rates derived from the QM treatment are appropriate to be used when modeling recombination through Rydberg cascades, an important process in understanding the state of material in the early universe. The rates for Δℓ = ±1 derived from the QM formalism diverge when integrated to sufficiently large impact parameter, b. Further to the empirical limits to the b integration suggested by Pengelly and Seaton (1964 Mon. Not. R. Astron. Soc. 127 165), we suggest that the fundamental issue causing this divergence in the theory is that it does not fully cater for the finite time taken for such distant collisions to complete.
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Parts of this work have been supported by the NSF (1108928, 1109061, and 1412155), NASA (10-ATP10-0053, 10-ADAP10-0073, NNX12AH73G, and ATP13-0153), and STScI (HST-AR-13245, GO- 12560, HST-GO-12309, GO-13310.002-A, and HST-AR-13914). MC has been supported by STScI (HST-AR-14286.001-A). PvH was funded by the Belgian Science Policy Office under contract no. BR/154/PI/MOLPLAN.
Williams, R. J. R.; Guzmán, Francisco; Badnell, N. R.; van Hoof, P. A. M.; Chatzikos, Marios; and Ferland, Gary J., "Thermodynamically-Consistent Semi-Classical ℓ-Changing Rates" (2017). Physics and Astronomy Faculty Publications. 651.