  Astrophysical models studying the origin of the p-nuclei require knowledge of
the reaction rates of photodisintegrations and capture reactions. Since
experimental data at astrophysically relevant energies are limited, reaction
rate calculations rely on Hauser-Feshbach (HF) theory predictions. The HF
theory requires nuclear physics input such as masses, level densities,
$\gamma$-ray strength functions and proton-nucleus optical potentials (pOMP).
The scope of this work is to improve a global semi-microscopic pOMP at energies
relevant to the p-process. This is achieved by adjusting the normalization
parameters of the OMP to all available proton-capture cross sections measured
at low energies. By establishing the systematic behaviour of these parameters,
one expects to enhance the predictive power of the pOMP when expanding to mass
regions where no data exists. The HF calculations were obtained using TALYS
code. The normalization parameters for the real and imaginary central
potentials ($\lambda_V$ and $\lambda_W$) were adjusted to fit the proton data
in the energy range where the cross-section are independent of the other
nuclear inputs. Results show that the $\lambda_V$ parameter has a strong mass
dependence that can be described by a second-degree polynomial function for A
$\leq$ 100 and an exponential increase for 100 < A < 162. Though variations of
the $\lambda_W$ have a smaller effect on the calculations, a global increase by
50$\%$ improves the results for certain nuclei without affecting the rest of
the cases. The resulting adjustment functions were obtained by fitting all
suitable proton data and can be used with reasonable confidence to generate the
global semi-microscopic pOMP for nuclei in the medium to heavy mass region. For
better statistics, more low-energy (p,$\gamma$) cross section data are needed
for heavier nuclei with mass A $>$ 100.
