The mean free path is the average distance between 2 collisions. We simply copy the things in Bohr and Mottelson, Bertulani and Banielewicz, and John Lilley in here.

Since a nucleus has finite size, the mean free path can be view as **transparency** of nucleon scattering. Since the total cross section is smaller for higher energy, the mean free path is proportional to energy.

The wave number under a complex optical potential is

.

There are two solutions, one has imaginary ,

where is the nucleon mass, is the incident energy, is the velocity inside the nucleus, and is the mean free path,

Since the imaginary potential , from 150 MeV to 400 MeV. The calculated mean free path for proton is shown in here. (Take , proton mass , the is in fm.)

The blue line on the plot is exact calculation, the purple line is approximation .

This plot is taken from S.S.M. Wong, showing the radial shapes of the volume term (simialr to central term) of proton-nucleus optical potential.

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in J. Killey, the is taken as,

,

which is the wave number without . The result only for weak .

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