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Title: On the validity of collider-mass scaling for molecular rotational excitation

Abstract

Rate coefficients for collisional processes such as rotational and vibrational excitation are essential inputs in many astrophysical models. When rate coefficients are unknown, they are often estimated using known values from other systems. The most common example is to use He-collider rate coefficients to estimate values for other colliders, typically H{sub 2}, using scaling arguments based on the reduced mass of the collision system. This procedure is often justified by the assumption that the inelastic cross section is independent of the collider. Here we explore the validity of this approach focusing on rotational inelastic transitions for collisions of H, para-H{sub 2}, {sup 3}He, and {sup 4}He with CO in its vibrational ground state. We compare rate coefficients obtained via explicit calculations to those deduced by standard reduced-mass scaling. Not surprisingly, inelastic cross sections and rate coefficients are found to depend sensitively on both the reduced mass and the interaction potential energy surface. We demonstrate that standard reduced-mass scaling is not valid on physical and mathematical grounds, and as a consequence, the common approach of multiplying a rate coefficient for a molecule-He collision system by the constant factor of ∼1.4 to estimate the rate coefficient for para-H{sub 2} collisions is deemedmore » unreliable. Furthermore, we test an alternative analytic scaling approach based on the strength of the interaction potential and the reduced mass of the collision systems. Any scaling approach, however, may be problematic when low-energy resonances are present; explicit calculations or measurements of rate coefficients are to be preferred.« less

Authors:
; ;  [1];  [2];  [3]
  1. Department of Physics and Astronomy and Center for Simulational Physics, The University of Georgia, Athens, GA 30602 (United States)
  2. Department of Chemistry, University of Nevada, Las Vegas, NV 89154 (United States)
  3. Department of Physics, Pennsylvania State University, Berks Campus, Reading, PA 19610 (United States)
Publication Date:
OSTI Identifier:
22365526
Resource Type:
Journal Article
Resource Relation:
Journal Name: Astrophysical Journal; Journal Volume: 790; Journal Issue: 2; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; ASTROPHYSICS; CARBON MONOXIDE; COLLISIONS; COMPARATIVE EVALUATIONS; CROSS SECTIONS; ELECTRIC GROUNDS; EXCITATION; GROUND STATES; HELIUM 3; HELIUM 4; HYDROGEN; INTERACTIONS; MASS; MOLECULES; SCALING; SCATTERING

Citation Formats

Walker, Kyle M., Yang, B. H., Stancil, P. C., Balakrishnan, N., and Forrey, R. C. On the validity of collider-mass scaling for molecular rotational excitation. United States: N. p., 2014. Web. doi:10.1088/0004-637X/790/2/96.
Walker, Kyle M., Yang, B. H., Stancil, P. C., Balakrishnan, N., & Forrey, R. C. On the validity of collider-mass scaling for molecular rotational excitation. United States. doi:10.1088/0004-637X/790/2/96.
Walker, Kyle M., Yang, B. H., Stancil, P. C., Balakrishnan, N., and Forrey, R. C. Fri . "On the validity of collider-mass scaling for molecular rotational excitation". United States. doi:10.1088/0004-637X/790/2/96.
@article{osti_22365526,
title = {On the validity of collider-mass scaling for molecular rotational excitation},
author = {Walker, Kyle M. and Yang, B. H. and Stancil, P. C. and Balakrishnan, N. and Forrey, R. C.},
abstractNote = {Rate coefficients for collisional processes such as rotational and vibrational excitation are essential inputs in many astrophysical models. When rate coefficients are unknown, they are often estimated using known values from other systems. The most common example is to use He-collider rate coefficients to estimate values for other colliders, typically H{sub 2}, using scaling arguments based on the reduced mass of the collision system. This procedure is often justified by the assumption that the inelastic cross section is independent of the collider. Here we explore the validity of this approach focusing on rotational inelastic transitions for collisions of H, para-H{sub 2}, {sup 3}He, and {sup 4}He with CO in its vibrational ground state. We compare rate coefficients obtained via explicit calculations to those deduced by standard reduced-mass scaling. Not surprisingly, inelastic cross sections and rate coefficients are found to depend sensitively on both the reduced mass and the interaction potential energy surface. We demonstrate that standard reduced-mass scaling is not valid on physical and mathematical grounds, and as a consequence, the common approach of multiplying a rate coefficient for a molecule-He collision system by the constant factor of ∼1.4 to estimate the rate coefficient for para-H{sub 2} collisions is deemed unreliable. Furthermore, we test an alternative analytic scaling approach based on the strength of the interaction potential and the reduced mass of the collision systems. Any scaling approach, however, may be problematic when low-energy resonances are present; explicit calculations or measurements of rate coefficients are to be preferred.},
doi = {10.1088/0004-637X/790/2/96},
journal = {Astrophysical Journal},
number = 2,
volume = 790,
place = {United States},
year = {Fri Aug 01 00:00:00 EDT 2014},
month = {Fri Aug 01 00:00:00 EDT 2014}
}
  • The relative populations of rotational states in the v=0 and v=1 vibrational states of OH produced in the reaction of H+NO/sub 2/..-->..OH+NO in crossed molecular beams were measured by laser-induced fluorescence. The excited vibrational state v=1 was found to be produced at 1.3 +- 0.3 times the rate of v=0. High degrees of rotational excitation were also observed. The rotational-state distributions were analyzed in information theoretic terms. A linear surprisal was found, which yielded a rotational surprisal parameter lambda/sub ROT/=-2.69 +- 0.57 for v=0. (AIP)
  • Integral cross sections for rotational transitions out of the lowest rotational level of NH(/sup 3/summation/sup -/)v = 0, namely N = 0, J = 1 F/sub 1/, induced by collisions with argon have been measured in a crossed beam experiment. A pulsed beam of rotationally cold NH(/sup 3/summation/sup -/) was produced by 193 nm photolysis of a dilute mixture of ammonia in nitrogen seed gas at the tip of a nozzle, the argon beam was also prepared in a pulsed source. The final rotational and spin--state populations were interrogated in the collision zone by laser fluorescence excitation in the Amore » /sup 3/Pileft-arrowX /sup 3/summation/sup -/(1,0) band of NH. Within a given N' manifold, the F/sub 1/ spin level had the largest values for the cross sections out of N = 0. The spin--state distributions are, in fact, well described by the general formulas for inelastic collisions of a case (b) /sup 3/summation molecule. The derived spin--free tensor opacities show a rapid decrease as a function of increasing N'.« less
  • The ability to calculate rotational excitation cross sections {sigma}{sub j{sub o}{r_arrow}j}({sup r}) for a large number of initial rotational levels (and a few {Delta}j = j {minus} j{sub o}) is important because molecular targets are usually gases in a Boltzmann distribution of initial rotational states. This research focuses on scaling approximations based on the fixed-nuclear-orientation (FNO) approximation. The authors examine such scaling methods for several small molecules (H{sub 2}, N{sub 2}, and CO{sub 2}) for {Delta}j = 2 excitations and show that they work quite well over energy ranges that include both resonant and nonresonant scattering. The authors evaluate themore » accuracy of simple algebraic expressions and their high j{sub o} limits. Finally, they present a very simple way to generate these cross sections directly from just a few elements of the body-frame FNO T-matrix. These obviate the need (in certain cases) for carrying out complicated frame-transformations.« less
  • We examine the question, given a set of state-to-state rate constants k( j = 0 ..-->.. j'Vertical BarT) for collision-induced rotational transitions in a diatomic molecule, where j and j' are initial and final rotational quantum numbers and T is the translational temperature, can one use scaling analyses to predict a full set of j ..-->.. j' rate constants. To answer this we consider a rigid rotator model of CO in a bath of Ar at 500 K, and we calculate accurate quasiclassical k( j ..-->.. j'Vertical BarT) for j = 0, 10, and 20 and j' = 0--29. Thesemore » are used to test the energy sudden (ES) and energy-corrected sudden (ECS) scaling procedures. Both procedures are used to predict the j = 10 and j = 20 rate constants from the j = 0 values. The ES procedure, which has no adjustable parameters, overestimates the rates out of excited states by a factor of about 1.5 with a rms error of about 60%. The ECS procedure, in contrast, when the one parameter b/sub c/ (a critical impact parameter) is about 1.75--2.0 A, yields excellent excited-state rates on the average and has a rms error of less than 20%. The value of b/sub c/ can be estimated by a weighted average impact parameter leading to inelastic collisions from a j = 0 initial state.« less