# Scattering cross-section of a nano-particle with background gas in high vacuum

Let's say I have a Silica nano-particle trapped with an optical tweezer in high vacuum (pressure ~ $$10^{-6} \mathrm{mbar}$$). I know the molar mass of the background gas and its temperature.

How would you calculate the scattering cross-section with the background gas? Or equally, the number of gas collisions per second?

$$\sigma = 4 \pi R^2$$ with $$R$$ being the radius of the sphere. The scattering rate would then be
$$\gamma = \sigma n \bar{v}$$ with n the particle density and $$\bar{v}$$ the mean velocity of the gas particles.