  Measurements of the 0--0 hyperfine resonant frequencies of ground-state
$^{85}$Rb atoms show a nonlinear dependence on the pressure of the buffer gases
Ar, Kr, and Xe. The nonlinearities are similar to those previously observed
with $^{87}$Rb and $^{133}$Cs and presumed to come from alkali-metal--noble-gas
van der Waals molecules. However, the shape of the nonlinearity observed for Xe
conflicts with previous theory, and the nonlinearities for Ar and Kr disagree
with the expected isotopic scaling of previous $^{87}$Rb results. Improving the
modeling alleviates most of these discrepancies by treating rotation quantum
mechanically and considering additional spin interactions in the molecules.
Including the dipolar-hyperfine interaction allows simultaneous fitting of the
linear and nonlinear shifts of both $^{85}$Rb and $^{87}$Rb in either Ar, Kr,
or Xe buffer gases with a minimal set of shared, isotope-independent
parameters. To the limit of experimental accuracy, the shifts in He and N$_2$
were linear with pressure. The results are of practical interest to vapor-cell
atomic clocks and related devices.
