The yields of over 200 projectile-like fragments (PLFs) and target-like fragments (TLFs) from the interaction of (E$_{c.m.}$=450 MeV) $^{136}$Xe with a thick target of $^{208}$Pb were measured using Gammasphere and off-line $gamma$-ray spectroscopy, giving a comprehensive picture of the production cross sections in this reaction.The measured yields were compared to predictions of the GRAZING model and the predictions of Zagrebaev and Greiner using a quantitative metric, the theory evaluation factor, {bf tef}. The GRAZING model predictions are adequate for describing the yields of nuclei near the target or projectile but grossly underestimate the yields of all other products. The predictions of Zagrebaev and Greiner correctly describe the magnitude and maxima of the observed TLF transfer cross sections for a wide range of transfers ($Delta$Z = -8 to $Delta$Z = +2). However for $Delta$Z =+4, the observed position of the maximum in the distribution is four neutrons richer than the predicted maximum. The predicted yields of the neutron-rich N=126 nuclei exceed the measured values by two orders of magnitude. Correlations between TLF and PLF yields are discussed.
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