  We propose a possible way to simulate a hump structure in the optical
scattering rate. The optical scattering rate of correlated charge carriers can
be defined within an extended Drude model formalism. When some electron and
hole doped copper oxide systems are in the spin density or charge density wave
phases they show hump structures in their optical scattering rates. The hump
structures have not yet been simulated and understood clearly. We are able to
simulate the hump structure by using a peak followed by a dip feature in the
normalized density of states within a generalized Allen formalism. We observe
that reversing the order of the dip and peak gives completely different
features in the optical scattering rate; a peak-dip (dip peak) results in a
hump (a valley) in the scattering rate. We also obtain the real part of the
optical conductivity and reflectance spectra from the simulated optical
scattering rate and compare them with published experimental spectra. From
these comparisons we conclude that the peak-dip order can give the hump
structure, which is observed experimentally in copper oxide systems. Finally we
fit two published optical spectra with our new model and discuss our results
and the possible origin of the dip or peak features in the normalized density
of states.
