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In the track structure model, the inactivation cross section is found by summing an inactivation probability over all impact parameters from the ion to the sensitive sites within the cell nucleus. The inactivation probability is evaluated by using the dose response of the system to gamma rays and the radial dose of the ions and may be equal to unity at small impact parameters. We apply the track structure model to recent data with heavy ion beams irradiating biological samples of E. Coli, Bacillus Subtilis spores, and Chinese hamster (V79) cells. Heavy ions have observed cross sections for inactivation that approach and sometimes exceed the geometric size of the cell nucleus in mammalian cells. We show how the effects of inactivation may be taken into account in the evaluation of the mutation cross sections from heavy ions in the track structure model through correlation of sites for gene mutation and cell inactivation. The model is fit to available data for HPRT (hypoxanthine guanine phosphoribosyl transferase) mutations in Chinese hamster cells, and good agreement is found. The resulting calculations qualitatively show that mutation cross sections for heavy ions display minima at velocities where inactivation cross sections display maxima. Also, calculations show the high probability for mutation by relativistic ions due to the radial extension of the ion track from delta rays in agreement with the microlesion concept. The effects of inactivation on mutation rates make it very unlikely that a single parameter such as LET (linear energy transfer) or Z*2/ β2(where Z*is effective charge number and β is ion velocity) can be used to specify radiation quality for heavy ion bombardment.