  In this last of three articles on the optical absorption of electrons in a
half-filled Peierls-distorted chain we address the dimerized extended Hubbard
model in the limit of a large on-site interaction $U$. When the Hubbard
interaction is large both compared to the band width $W$ and the nearest
neighbor interaction $V$ the charge dynamics is properly described by the
Harris-Lange model. This model can be exactly mapped onto a model of free
spinless Fermions in parallel (Hubbard-)bands of width $W$ which are eventually
Peierls-split. To determine the coherent absorption features at low
temperatures we design and employ the ``no-recoil approximation'' in which we
assume that the momentum transfer to the spin degrees of freedom can only be
$\Delta q_S=0$ or $\Delta q_S=\pi/a$ during an optical excitation. We present
explicit analytical results for the optical absorption in the presence of a
lattice dimerization $\delta$ and a nearest-neighbor interaction $V$ for the
N\'{e}el and dimer state. We find that the coherent part of the optical
absorption for $V=0$ is given by a single peak at $\omega=U$ and broad but weak
absorption bands for $W\delta\leq |\omega-U| \leq W$. The central peak at
$\omega=U$ only vanishes for $\delta=0$ in the N\'{e}el state. For an
appreciable nearest neighbor interaction $V>W/2$ almost all spectral weight is
transferred to the $\Delta q_C=0$-exciton and the $\Delta q_C=\pi/a$-exciton
whose relative spectral weights very sensitively depend on both the lattice and
the spin dimerization of the ground state.
