The total room-temperature, velocity-averaged, total cross section for atom-atom and atom-molecule collisions can be approximated using a universal function depending only on the magnitude of the leading order dispersion coefficient, C6. This feature of the total cross section together with the universal function for the energy distribution transferred by glancing angle collisions (pQDU6[James L. Booth et al 2019 New J. Phys.
21, 102001]) can be used to empirically determine the total collision cross section and realize a self-calibrating, vacuum pressure standard. This was previously validated for Rb+N2 and Rb+Rb collisions. However, the post-collision energy distribution is expected to deviate from pQDU6 in the limit of small C6 and small reduced mass. Here we observe this deviation experimentally by performing a direct cross-species loss rate comparison between Rb+H2 and Li+H2 collision. We measure a velocity averaged total collision cross section ratio, R=〈σtotv〉Li+H2
:〈σtotv〉Rb+H2
= 0:83(5). Based on an ab initio computation of 〈σtotv〉Li+H2
= 3.104×10-15 m3/s, we deduce〈σtotv〉Rb+H2
= 3.6(2)×10-15 m3/s, in agreement with a Rb+H2 ab initio value of〈σtotv〉Rb+H2
= 3.574×10-15 m3/s. By contrast, fitting the Rb+H2 loss rate as a function of trap depth to the universal function we find 〈σtotv〉Rb+H2
= 5.52(9)×10-15 m3/s. Finally, this work demonstrates how to perform a cross-calibration of sensor atoms to extend and enhance the cold atom based pressure sensors.