Parameters (assumed): independent Poisson arrivals, square pulse width w = 50 μs, count rate per tube 6 counts / min.
Formula
For short pulses the accidental-coincidence rate is approximated by
R_c ≈ 2 · w · R²
where R is the rate in counts per second and w is the pulse width in seconds.
Computed values
| Quantity | Value |
|---|---|
| Single-tube rate R | 6 counts / min = 0.1 s⁻¹ |
| Pulse width w | 50 μs = 50×10⁻⁶ s |
| Accidental-coincidence rate Rc | 1.0×10⁻⁶ s⁻¹ |
| Per minute | 6.0×10⁻⁵ per minute |
| Per hour | 0.0036 coincidences / hour |
| Per day | 0.0864 coincidences / day |
| Per year (365 days) | 31.536 coincidences / year |
Probability of ≥1 accidental coincidence
Using a Poisson model with mean μ = expected coincidences in the interval:
- Probability of at least one in a day: 1 − exp(−0.0864) ≈ 0.08277 (≈ 8.28%).
- Probability of at least one in a year: 1 − exp(−31.536) ≈ 0.99999999999998 (effectively 100%).
Short summary
Accidental coincidence rate ≈ 1.0×10⁻⁶ s⁻¹ (≡ 6.0×10⁻⁵ /min). That gives ≈ 0.0864 per day (≈ one every 11.6 days) and ≈ 31.54 per year. The chance of seeing at least one accidental coincidence in a given day ≈ 8.28%.
Note: result assumes independent Poisson processes and square pulses. Real detectors may have dead-time, non-zero resolving time, or correlated background which change the numbers.