Do you want to measure or to calculate the mean free path?

Also, which mean free path do you need? - for ionisation, for elastic/ineleastic collisions (without ionisation), between electrons and electrons or electrons and neutrals? - That you have to be clear of before you start.

Usually you can simply calculate the mean free path \lambda for an ideal gas with the particle density n and the collision cross section \sigma via:

\lambda = 1/ (\alpha * \sigma * n)

where \alpha is a facte which takes into account the mass ratio of the colliding particles:

\alpha = sqrt{µ/m_1}

where m_1 is the electron mass and µ is the reduced mass of both collision partners:

µ = m_1 * m_2/(m_1 + m_2)

if both masses are equal (so electron - electron collisions), \alpha = sqrt{2} and \alpha = 1 if m_1

I mean to calculate the mean free path of electrons for ionization, elastic and inelastic collision between electron and neutrals.

Then my answer is the information you need.

There is something missing in the Johannes answer. \sigma is not constant. For example for inelastic processes it is zero before the threshold E* and therefore for energies lower than E* the mean free path is infinite, and the formula by Johannes can be applied only for E>E* and, supposing a step function for \sigma, you should also add the Boltzmann factor to introduce the dependence on the temperature.

The best expression is to calculate the ration of collision frequency

freq=integral(f(E)*v(E)*sigma(E)*n*dE)

and mean velocity

vm=integral(v(E)*f(E)dE)

giving

lambda=vm/freq.

f(E) is the energy distribution function of the electrons

v(E) is the electron velocity at

E is the electron energy

For a Boltzmann distribution and approximating the cross section with a step function the integral is straightforward, giving Johannes formula for elastic collisions (E*=0) but not for inelastic collisions and ionization, introducing terms depending on the temperature.

The electron-neutral collision mean free path, lambda (for in-elastic collision and ionization) can be calculated as

lambda = 1 / (n*sigma),

where n is the neutral density,

sigma is the cross-section of neutral.

n can be calculated according to workng pressure. The neutral density of atmosphere is 2.69e25 /m3.

The electron-neutral collision frequency can be calculated as f = n*sigma*v, where v is the velocity.

@Gianpiero: true, that I should have mentioned, of course - sigma is not constant. Thanks for the remark.

Arun, we have compared the theoretical values with experimental data in a He GD at low pressure in the presence of supra thermal electrons, if you are interested in this kind of works check A.B. Martín-Rojo et al, Plasma Sources Sci. Technol. 22 (2013) 035001

Good luck!