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Track theory has been applied to an earlier suggestion, that the supralinearity of TLDs at high gamma-ray doses is due to pre-existing 1-hit and 2-hit trap structures, to calculate high-LET response. Measured 60Co dose responses for peaks 5 and 6 in LiF (TLD- 700) were decomposed to yield parameters characterizing each peak as a two-component c-hit mixture. One value of “trap radius” was assigned to each two-component representation, different for peak 5 and for peak 6, to calculate their responses for H, He, C, O, and Ne bombardments. Calculations reproduce experimental features of the heavy ion response of TLD-700, and provide a means of connecting the gamma- and high-LET responses, in TLDs.