# Virial expansion: Potential that depends on velocities

1. Feb 12, 2016

### Korbid

I'm studying this potential that depends on positions and velocities. http://motion.cs.umn.edu/PowerLaw/
$$E(\tau)=\frac{k}{\tau^2}e^{-\tau/\tau_0}$$
where τ is the time to collision.
By extrapolation $$\tau=\frac{b-\sqrt{d}}{a}$$
$$a=||\vec{v}_{ij}||^2$$
$$b=-\vec{r}_{ij}\cdot\vec{v}_{ij}$$
$$c=||\vec{r}_{ij}||^2 - (R_i+R_j)^2$$
$$d=b-ac$$
Where Ri is the radius of the particles and κ,τ0 characteristic parameters.

I need to find the second virial coefficient for a certain temperature, even numerically. Is it possible?

2. Feb 17, 2016

### Staff: Admin

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

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