The Efficiency of the Tube Counter

The efficiency of counting ionizing particles by the tube counter is investigated, taking account of the electrical behavior of the counter and the random nature of the arrival of the particles. Expressions are obtained for the efficiency of counting, average recovery time, average voltage impulse delivered to the amplifier, and the average number of particles counted per unit time, $N$, in terms of the number of particles arriving per unit time, $N_0$, the time constant of the counter, and one other parameter, $d$, which is constant for a given counter. Methods for measuring $d$ (which for most counters will lie between 1.3 and five) are indicated. The efficiency of counting decreases with an increase of $N_0$, rapidly at first, then more slowly, so as to have the asymptotic value $\frac{1}{d}$. The determination of $N_0$ from $N$, and the general question of counter efficiency are discussed.