  The cross sections of the ($e,e'N$) and ($\gamma,p$) reactions on $^{16}$O
are calculated, for the transitions to the $1/2^{-}$ ground state and the first
$3/2^{-}$ excited state of the residual nucleus, using single-particle overlap
functions obtained on the basis of one-body density matrices within different
correlation methods. The electron-induced one-nucleon knockout reaction is
treated within a nonrelativistic DWIA framework. The theoretical treatment of
the ($\gamma,p$) reaction includes both contributions of the direct knockout
mechanism and of meson-exchange currents. The results are sensitive to details
of the different overlap functions. The consistent analysis of the reaction
cross sections and the comparison with the experimental data make it possible
to study the nucleon--nucleon correlation effects.
