  In the framework of the nuclear spectral function approach for incoherent
primary proton--nucleon and secondary pion--nucleon production processes we
study the inclusive $\phi$ meson production in the interaction of 2.83 GeV
protons with nuclei. In particular, the A-dependences of the absolute and
relative $\phi$ meson yields are investigated within the different scenarios
for its in-medium width as well as for the cross section ratio $\sigma_{pn \to
pn{\phi}}/{\sigma_{pp \to pp{\phi}}}$. Our model calculations take into account
the acceptance window of the ANKE facility used in a recent experiment
performed at COSY. They show that the pion--nucleon production channel
contributes distinctly to the $\phi$ creation in heavy nuclei in the chosen
kinematics and, hence, has to be taken into consideration on close examination
of the dependences of the phi meson yields on the target mass number with the
aim to get information on its width in the medium. They also demonstrate that
the experimentally unknown ratio $\sigma_{pn \to pn{\phi}}/{\sigma_{pp \to
pp{\phi}}}$ has a weak effect on the A-dependence of the relative $\phi$ meson
production cross section at incident energy of present interest, whereas it is
found to be appreciably sensitive to the phi in-medium width, which means that
this relative observable can indeed be useful to help determine the above width
from the direct comparison the results of our calculations with the future data
from the respective ANKE-at-COSY experiment.
