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We present a calculation of the weak localisation correction to thescattering and to the transport mean free path, for waves propagating in a$delta$-correlated random potential, going beyond the usual diffusionapproximation for the loops in the interfering path amplitudes. We find thatnot only the transport mean free path, but also the scattering mean free pathis affected by the interference contributions. We also find the dependence ofthe leading order contribution to both, the scattering and the transport meanfree path, on the disorder parameter $1/kl$ to be linear. This is in contrastto the result obtained from the diffusion approximation according to which thescattering mean free path remains unaffected when changing the disorderparameter, whereas the correction of the transport mean free path scales like$1/(kl)^2$.

Weak disorder corrections of the scattering and transport mean free path