  We present the first detailed measurement of incoherent photoproduction of
neutral pions to a discrete state of a residual nucleus. The
$^{12}$C$(\gamma,\pi^{0})^{12}$C$^{*}_{4.4MeV}$ reaction has been studied with
the Glasgow photon tagger at MAMI employing a new technique which uses the
large solid angle Crystal Ball detector both as a $\pi^{0}$ spectrometer and to
detect decay photons from the excited residual nucleus. The technique has
potential applications to a broad range of future nuclear measurements with the
Crystal Ball and similar detector systems elsewhere. The data are sensitive to
the propagation of the $\Delta$ in the nuclear medium and will give the first
information on matter transition form factors from measurements with an
electromagnetic probe. The incoherent cross sections are compared to two
theoretical predictions including a $\Delta$-hole model.
