  We have examined fine-structure mixing between the rubidium $5^{2}P_{3/2}$
and $5^{2}P_{1/2}$ states along with quenching of these states due to
collisions with methane gas. Measurements are carried out using ultrafast laser
pulse excitation to populate one of the Rb $5^{2}P$ states, with the
fluorescence produced through collisional excitation transfer observed using
time-correlated single-photon counting. Fine-structure mixing rates and
quenching rates are determined by the time dependence of this fluorescence. As
Rb($5^{2}P$) collisional excitation transfer is relatively fast in methane gas,
measurements were performed at methane pressures of $2.5 - 25$ Torr, resulting
in a collisional transfer cross section ($5^{2}P_{3/2} \rightarrow
5^{2}P_{1/2}$) of $(4.23 \pm 0.13) \times 10^{-15}$ cm$^{2}$. Quenching rates
were found to be much slower and were performed over methane pressures of $50 -
4000$ Torr, resulting in a quenching cross section of $(7.52 \pm 0.10) \times
10^{-19}$ cm$^{2}$. These results represent a significant increase in precision
compared to previous work, and also resolve a discrepancy in previous quenching
measurements.
