  We demonstrate the effect of bandstructure on the superconducting properties
of Pb by calculating the strong-coupling features in the optical conductivity,
$\sigma(\omega)$, due to the electron-phonon interaction. The importance of
momentum dependence in the calculation of the properties of superconductors has
previously been raised for MgB$_2$. Pb resembles MgB$_2$ in that it is a two
band superconductor in which the bands' contributions to the Fermi surface have
very different topologies. We calculate $\sigma(\omega)$ by calculating a
memory function which has been recently used to analyze $\sigma(\omega)$ of
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. In our calculations the two components of
the Fermi surface are described by parameterizations of de Haas--van Alphen
data. We use a phonon spectrum which is a fit to neutron scattering data. By
including the momentum dependence of the Fermi surface good agreement is found
with the experimentally determined strong-coupling features which can be
described by a broad peak at around 4.5 meV and a narrower higher peak around 8
meV of equal height. The calculated features are found to be dominated by
scattering between states within the third band. By contrast scattering between
states in the second band leads to strong-coupling features in which the height
of the high energy peak is reduced by $\sim 50%$ compared to that of the low
energy peak. This result is similar to that in the conventional isotropic
(momentum independent) treatment of superconductivity. Our results show that it
is important to use realistic models of the bandstructure and phonons, and to
avoid using momentum averaged quantities, in calculations in order to get
quantitatively accurate results.
