  The cross-section measurement of $^{144}$Sm(p, $\gamma$)$^{145}$Eu
(T$_{1/2}=$5.93(4) days) reaction has been performed at proton energies around
2.6, 3.1, 3.7, 4.1, 4.2, 4.7, 5.1, 5.5, 5.9, 6.4, 6.8 MeV using the activation
technique. These energies correspond to the Gamow window for 3, 4 GK and a
partial portion for 2 GK. $^{144}$Sm has been chosen for the present study
because of its significantly higher abundance compared to the other neighboring
$p$-nuclides (Z $>$ 50). The astrophysical $S-$factor of this reaction has been
measured for the first time at E$^{cm}_p=$ 2.57$\pm$0.13 MeV, $S-$
factor$=$2.542$\pm$1.152($\times$10$^{10}$) MeV-b. Cross-section data were
compared with the previously measured experimental data from literature and the
theoretical predictions obtained using Hauser-Feshbach statistical model codes
TALYS 1.96 and NON-SMOKER. A satisfactory agreement between experimental data
and theoretical results was observed. Molecular deposition technique was used
to prepare the $^{144}$Sm targets having thickness between 100$-$350
$\mu$g/cm$^2$ on Al backing. Obtained results were utilized to predict the
reaction rates for $^{144}$Sm (p, $\gamma$) and $^{145}$Eu ($\gamma$, p)
reactions using TALYS 1.96 and the reciprocity theorem.
