We present a fourth-order Green's-function decoupling theory for the description of optical properties in the one-dimensional antiferromagnetically coupled Heisenberg paramagnet TMMC [(CD3)4NMmCl3]. Analysis of the crystal structure shows that Raman scattering in the "two-spin-wave" mode is expected to be weak, so we present detailed predictions only for infrared absorption. A truncation approximation is introduced to solve the Green's-function equations. The relationship of this work to theories of Kawasaki, Elliott, and Thorpe, and Blume and Hubbard is discussed.
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