  A potential model is applied for the analysis of the astrophysical direct
nuclear capture process $^{16}$O(p,$\gamma)^{17}$F. The phase-equivalent
potentials of the Woods-Saxon form for the p$-^{16}$O interaction are examined
which reproduce the binding energies and the empirical values of ANC for the
$^{17}$F(5/2$^+$) ground and $^{17}$F(1/2$^+$) ($E^*$=0.495 MeV) excited bound
states from different sources. The best description of the experimental data
for the astrophysical $S$ factor is obtained within the potential model which
yields the ANC values of 1.043 fm$^{-1/2}$ and 75.484 fm$^{-1/2}$ for the
$^{17}$F($5/2^{+}$) ground and $^{17}$F($1/2^{+}$) excited bound states,
respectively. The zero-energy astrophysical factor $S(0)=9.321$ KeV b is
obtained by using the asymptotic expansion method of D. Baye. The calculated
reaction rates within the region up to 10$^{10}$ K are in good agreement with
those from the R-matrix approach and the Bayesian model in both absolute values
and temperature dependence.
