Mean free path ( $ℓ$ )

The mean free path is the average distance travelled between collisions. For dilute targets with number density

n

and effective collision cross-section

σ_{c}

,

ℓ \sim 1/ (n σ_{c})

; identical-particle conventions introduce factors such as

2

.

Table of contents
- Transport mean free path Mean free path
- Mean free path through randomly oriented disc absorbers Mean free path

Transport mean free path ( $ℓ_{tr} = v_{F} τ_{tr} = μ ℏ k_{F} / e$ )

The length associated with relaxation of carrier momentum. In a parabolic band, electron mobility measures the momentum relaxation time, giving the displayed expression. Frequent weak small-angle scattering can make the single-particle scattering time shorter than the transport time, and electron phase coherence has its own lifetime.

Mean free path through randomly oriented disc absorbers ( $ℓ^{- 1} = n_{com} (1 + z)^{3} π R_{d}^{2} /2$ )

For an unclustered population of fully covering circular disc absorbers, the inverse mean free path is proper number density times mean projected area. A comoving number density must first be multiplied by

(1 + z)^{3}

. The incidence then constrains the proper radius; covering factor and multiplicity of detectable lines can change the inference.

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Mean free path by

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The mean free path is a concept from kinetic theory that measures the average distance a particle travels between successive collisions with other particles. This concept is commonly used in fields such as physics, chemistry, and engineering, particularly in the study of gases.

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