On the effect of "glancing" collisions in the cold atom vacuum standard

We theoretically investigate the effect of ``glancing" collisions on the ultra-high vacuum (UHV) pressure readings of the cold atom vacuum standard (CAVS), based on either ultracold $^7$Li or $^{87}$Rb atoms. Here, glancing collisions are those collisions between ultracold atoms and room-temperature background atoms or molecules in the vacuum that do not impart enough kinetic energy to eject an ultracold atom from its trap. Our model is wholly probabilistic and shows that the number of the ultracold atoms remaining in the trap as a function of time is non-exponential. We update the recent results of a comparison between a traditional pressure standard -- a combined flowmeter and dynamic expansion system -- to the CAVS [D.S. Barker, et al., arXiv:2302.12143] to reflect the results of our model. We find that the effect of glancing collisions shifts the theoretical predictions of the total loss rate coefficients for $^7$Li colliding with noble gases or N$_2$ by up to $0.6$ %. Likewise, we find that in the limit of zero trap depth the experimentally extracted loss rate coefficients for $^{87}$Rb colliding with noble gases or N$_2$ shift by as much as 2.2 %.