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The tracks formed in nuclear emulsion by energetic heavy ions are made up of grains sensitized by the passage of a single ion. Cells may also be inactivated by the passage of a single ion, in a mode called ion-kill. Emulsion tracks pass from the grain-count regime, where the tracks is a sequence of isolated grains, to the track-width regime, where the track is fully closed and has a cross-sectional area larger than that of an emulsion grain, with increasing values of z²/β ² for the charged particle causing the track. The measured value of the inactivation cross section for human kidney cells increases in a similar way. The response of cells is not the same as emulsion grains, because cells may also be inactivated by a gamma-kill mode, involving the cumulative effect of overlapping delta rays from several ions, in addition to the ion-kill mode present in both emulsion and cells. These considerations lead to the equations $P=σ /σ ₀=[1-e^{-z²/κ ...
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Katz et al. (1971) studied this question.
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