data. An approximate finite temperature calculation near one of the resonances improves the description of the data considerably and shows that finite temperature effects account for about 25% of the discrepancy. The paper is organized as follows: In Sec. \[sec:relaxation\] and Sec. \[sec:STMeq\] we explain our theoretical framework. The numerical results at zero temperature are displayed and compared with the experimental data in Sec. \[sec:results\]. In Sec. \[sec:themal\], we carry out an approximate finite temperature calculation near the resonance at $B=685$ G. We summarize our results and conclude in Sec. \[sec:summary\].

Dimer relaxation {#sec:relaxation}
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In this section we discuss the losses of atoms and dimers through inelastic scattering processes and present expressions for the relaxation rate constants.

Before proceeding with our discussion of atom-dimer scattering, we explain our notation and terminology. We label an atom in one of the three hyperfine states of the $^6$Li atoms with an index $i$ where $i=1,2$ or $3$. The S-wave scattering length between atoms in states $i$ and $j$ is denoted either as $a_{ij}$ or as $a_k$ where $k\neq i\neq j$. Two atoms in the same state can not scatter in an S-wave because of the Pauli principle. If the scattering length $a_{ij}$ 