content_image/338864.jpg content_image/338865.jpg content_image/338866.jpg content_image/338867.jpg content_image/338868.jpg content_image/338869.jpg content_image/338870.jpg content_image/338871.jpg content_image/338872.jpg content_image/338873.jpg content_image/338874.jpg content_image/338875.jpg
where we assume a Maxwell-Boltzmann distribution of relative velocities given by 

<img src='content_image/338864.jpg'>

with v 2 r = v 2 x + v 2 $_{y}$. A factor of v 2 z in both the numerator and denominator of Eqn. (7) accounts for the fact that the m$_{L}$ = 0 p -wave inelastic collision rate scales as collision energy ∝ v 2 $_{z}$. Similarly, for m$_{L}$ = ± 1 collisions, the collision rate scales as v 2 r and we find the average relative energy for two colliding particles using 

Adding this to the k$_{B}$T$_{i}$ from the center-of-mass energies, we get 

<img src='content_image/338865.jpg'>

<img src='content_image/338866.jpg'>

<img src='content_image/338867.jpg'>

<img src='content_image/338868.jpg'>

<img src='content_image/338869.jpg'>

<img src='content_image/338870.jpg'>

Putting this into the expression for the heating rate (Eqn. (6)), we find that 

In the main text, we defined the loss rate coefficient as 

<img src='content_image/338871.jpg'>

<img src='content_image/338872.jpg'>

<img src='content_image/338873.jpg'>

where K$_{0}$ and K$_{1}$ depend on the induced dipole moment. The inelastic collision rate per particle is related to β through 

<img src='content_image/338874.jpg'>

<img src='content_image/338875.jpg'>

