On the Validity of Collider-Mass Scaling for Molecular Rotational Excitation

TL;DR

This paper critically examines the common practice of using reduced-mass scaling to estimate molecular rotational excitation rates, demonstrating its limitations and proposing the need for explicit calculations or measurements for accuracy.

Contribution

The study shows that standard reduced-mass scaling is invalid for estimating collisional rate coefficients, advocating for explicit calculations or alternative scaling methods.

Findings

Reduced-mass scaling is unreliable for collisional rate estimates.

Explicit calculations are preferred over scaling methods.

Interaction potential strength influences inelastic cross sections.

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$_2$, 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$_2$, $^3$He, and $^4$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$_2$ 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.