  The Coulomb dissociation method to obtain the astrophysical S-factor,
$S_{17}(0)$, for the $^7$Be($p,\gamma)^8$B reaction at solar energies is
investigated by analysing the recently measured data on the breakup reaction
$^{208}$Pb$(^8$B,$^7$Be$~p)^{208}$Pb at 46.5 MeV/A beam energy. Breakup cross
sections corresponding to E1, $E2$ and $M1$ transitions are calculated with a
theory of Coulomb excitation that includes the effects of the Coulomb recoil as
well as relativistic retardation. The interplay of nuclear and Coulomb
contributions to the breakup process is studied by performing a full quantum
mechanical calculation within the framework of the distorted-wave Born
Approximation. In the kinematical regime of the present experiment, both
nuclear as well as Coulomb-nuclear interference processes affect the pure
Coulomb breakup cross sections very marginally. The $E2$ cross sections are
strongly dependent on the model used to describe the structure of $^8$B. The
value of $S_{17}(0)$ is deduced with and without $E2$ and $M1$ contributions
added to the $E1$ cross sections and the results are discussed.
