Live fraction is the part of the clock that remains available for real counting after dead time is removed. With a 12-second clock, live times of 8, 6, and 4 seconds give live fractions 2/3, 1/2, and 1/3 before the effective rate is reported. Real effective rates also depend on source stability, pileup model, trigger thresholds, clock accuracy, finite counting statistics, and uncertainty.
Live fraction and source rate combine into an effective rate. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
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Long live time on a slow source gives one third hertz
Live time 8 seconds over clock 12 seconds gives live fraction 2/3.
Reff=1/2×2/3=1/3
Half-live clock gives one half hertz
Live time 6 seconds over clock 12 seconds gives live fraction 1/2.
Reff=1×1/2=1/2
Short live time on a fast source gives two thirds hertz
Live time 4 seconds over clock 12 seconds gives live fraction 1/3.