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A new Raman process can be used to realize efficient Raman frequency conversion by coherent feedback at low light intensity [Chen B, Zhang K, Bian C L, Qiu C, Yuan C H, Chen L Q, Ou Z Y, and Zhang W P 2013 Opt. Express 21, 10490]. We present a theoretical model to describe this enhanced Raman process, termed as cascade correlation-enhanced Raman scattering, which is a Raman process injected by a seeded light field. It is correlated with the initially prepared atomic spin excitation and driven by the quasi-standing-wave pump fields, and the processes are repeated until the Stokes intensities are saturated. Such an enhanced Raman scattering may find applications in quantum information, nonlinear optics, and optical metrology due to its simplicity.