  Atomic sensors have shown great promise for density and pressure metrology in
the high, ultra-high, and extremely-high vacuum regimes. Specifically, the
density of background gas particles in vacuum can be determined by measuring
the collision rate between the particles and an ensemble of sensor atoms. This
requires preparing the sensor atoms in a particular quantum state, observing
the rate of changes of that state, and using the cross section coefficient for
state-changing collisions to convert the rate into a corresponding density. The
cross section can be known by various methods including by quantum scattering
calculations using an ansatz for the interaction potential between the
collision pair, by measurements of the post-collision sensor-atom momentum
recoil distribution, or by empirical calibration of the sensor atom at a known
density. Identifying systematic errors in the results of these methods can be
aided by direct comparisons between them. Alternatively, measurements of
different sensor atoms exposed to the same background gas offers another point
of comparison free of the systematic errors inherent in creating a background
gas at a known density. Here, we present such measurements for two sensor
atoms, $^{87}$Rb and $^6$Li, and a variety of atomic and molecular background
gases including H$_2$, N$_2$, Ar, Ne, Kr, and Xe. We find results consistent
with, yet statistically different at the level of 3.5(5)%, from recent
theoretical and experiment measurements. This work demonstrates a model-free
method for transferring the primacy of one atomic standard to another sensor
atom and highlights the utility of sensor-atom cross-calibration experiments to
check the validity of direct measurements and theoretical predictions.
