Velocity preservation--A quantitative technique for determining rates of fast inelastic collision processes

Absorption of monochromatic radiation by a low pressure gas will inieet molecules into a state
|U\rangle
, with one component of velocity specified. Collisions then transfer molecules from this state to other states of interest
|s_{i}\rangle
. The scattering kernel
P_{1}(U \rightarrow s_{i}, \upsilon_{z} \rightarrow \upsilon_{z}')
is proportional to the velocity distribution function (VDF) of molecules that have undergone one collisiom Iterates of this kernel give the VDF for those having undergone two or more collisions. We will present numerical results for P
1
and P
2
for hard spheres and the general integral for other interaction potentials. We show that P
2
and higher iterates of P
1
are closely approximated by equilibrium VDF's. Using tuned laser absorption spectroscopy the VDF of each state
|s_{i}\rangle
is measured. This fmmtion is least squares approximated by the weighted sum of the appropriate Gaussian function and the function P
1
. The nonequilibrium contribution is proportional to the cross section for scattering from
|U\rangle
to
|s_{i}\rangle
. If all the important states
|s_{i}\rangle
can be observed and the total deactivation rate of
|U\rangle
is known, these relative cross sections can be converted to absolute terms. We have analyzed the results of a pulsed double resonance experiment in CO
2
at 600 K in terms of these concepts and have found that the rate of rotationally inelastic scattering from
|001, J = 11\rangle
to
|001, J = J'\rangle
can be fit by the phenomenological equation
k(J = 11 \rightarrow J = J')
=\frac{A}{1+(\frac{11-J'}{W})^2} , 3 \leq J' \leq 21
where
A = (1.0 \pm 0.3) \times 10_{6}
s
^-1
.torr
^-1
and
W = 8 \pm 2
. We will discuss other systems to which this technique should be applicable and its limitations.