Timing Boundary Depth Scans

Dead-Time Count Boundary Three-Row Scan

Dead time is the part of the clock that the detector spends unable to accept another event after a count. In this 12-second clock ledger, 4 counts at 1 second each leave 8 live seconds, 6 counts leave 6 live seconds, and 8 counts leave 4 live seconds. Real dead-time corrections depend on detector recovery, pulse pileup, rate changes, clock calibration, finite counts, and uncertainty.

Detected count changes dead time, live time, and observed rate together. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Four counts leave most of the clock live

Detected count 4 with one second per count uses dead time 4 seconds and leaves live time 8 seconds.

L=12−4×1=8,Ro=1/3L=12\mathbin{-}4\times1=8,\quad R_o=1/3
Dead-time budgetDetected counts reserve dead-time intervals.clock=12 slive=8 srate=1/2 HzclockTime=12 sdeadTimeEach=1 sdetectedCount=4 countdeadTimeTotal=4 sliveTime=8 sobservedRate=1/3 Hz

Six counts split the clock evenly

Detected count 6 with one second per count uses dead time 6 seconds and leaves live time 6 seconds.

L=12−6×1=6,Ro=1/2L=12\mathbin{-}6\times1=6,\quad R_o=1/2
Dead-time budgetDetected counts reserve dead-time intervals.clock=12 slive=6 srate=1 HzclockTime=12 sdeadTimeEach=1 sdetectedCount=6 countdeadTimeTotal=6 sliveTime=6 sobservedRate=1/2 Hz

Eight counts leave four seconds live

Detected count 8 with one second per count uses dead time 8 seconds and leaves live time 4 seconds.

L=12−8×1=4,Ro=2/3L=12\mathbin{-}8\times1=4,\quad R_o=2/3
Dead-time budgetDetected counts reserve dead-time intervals.clock=12 slive=4 srate=2 HzclockTime=12 sdeadTimeEach=1 sdetectedCount=8 countdeadTimeTotal=8 sliveTime=4 sobservedRate=2/3 Hz