  We study two-photon scattering in a mixed cavity optomechanical system, which
is composed of a single-mode cavity field coupled to a single-mode mechanical
oscillation via both the first-order and quadratic optomechanical interactions.
By solving the scattering problem within the Wigner-Weisskopf framework, we
obtain the analytical scattering state and find four physical processes
associated with the two-photon scattering in this system. We calculate the
two-photon scattering spectrum and find that two-photon frequency
anticorrelation can be induced in the scattering process. We also establish the
relationship between the parameters of the mixed cavity optomechanical system
and the characteristics of the two-photon scattering spectrum. This work not
only provides a scattering means to create correlated photon pairs, but also
presents a spectrometric method to characterize the optomechanical systems.
