  We study nuclear stopping in central collisions for heavy-ion induced
reactions in the Fermi energy domain, between $15$ and $100$ A\,\textrm{MeV}.
Using the large dataset of exclusive measurements provided by the $4\pi$ array
\emph{INDRA}, we determine the relative degree of stopping as a function of
system mass and bombarding energy. We show that the stopping can be directly
related to the transport properties in the nuclear medium. By looking
specifically at free nucleons (here protons), we present for the first time a
comprehensive body of experimental results concerning the mean free path, the
nucleon-nucleon cross-section and in-medium effects in nuclear matter. It is
shown that the mean free path exhibits a maximum at $\lambda_{NN}=9.5 \pm 2$
\textrm{fm}, around $E_{inc}=35-40$ A\,\textrm{MeV} incident energy and
decreases toward an asymptotic value $\lambda_{NN}= 4.5 \pm 1$ \textrm{fm} at
$E_{inc} = 100$ A\,\textrm{MeV}. After accounting for Pauli blocking of elastic
nucleon-nucleon collisions, it is shown that the effective in-medium \emph{NN}
cross section is further reduced compared to the free value in this energy
range. Therefore, in-medium effects cannot be neglected in the Fermi energy
range. These results bring new fundamental inputs for microscopic descriptions
of nuclear reactions in the Fermi energy domain.
