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