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For a particle of mass mx traversing a thickness of
materialδx, the Landau probability distribution may be written in terms of the universal Landau function φ(λ) as[1]: f (, δx) = 1 ξφ(λ) where φ(λ) = 1 2π i Zc−i∞
c+i∞ exp (u ln u + λu) du c ≥ 0
λ = − ¯ ξ −γ 0−β2−ln ξ Emax γ0 = 0.422784 . . . = 1 − γ γ = 0.577215 . . . (Euler’s constant) ¯
= average energy loss = actual energy loss
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