Counting Errors, Statistics, and Proportional Counting Systems

Vocabulary flashcards covering Minimum Detectable Activity (MDA), pulse-height discrimination, crosstalk mechanisms, calibration criteria, voltage plateaus, and analysis counting modes.

Minimum Detectable Activity (MDA)

The smallest concentration of radioactivity in a sample that can be detected with a $5\%$ probability of erroneously detecting radioactivity when none is present (Type I error) and a $5\%$ probability of not detecting radioactivity when it is present (Type II error).

MDA Equation (Equation 20)

The mathematical expression used to determine minimum detectable activity: $\text{MDA (dpm)} = \frac{\frac{3}{T_s} + 3.3\sqrt{\frac{R_b}{T_s} + \frac{R_b}{T_b}}}{E(\text{eq.6})}$, where $R_b$ is background count rate, $T_b$ is background count time, and $T_s$ is sample count time.

Type I Error

The error committed by erroneously detecting radioactivity in a sample when, in fact, none is present (set at a $5\%$ probability for MDA calculations).

Type II Error

The error committed by failing to detect radioactivity in a sample when, in fact, radioactivity is present (set at a $5\%$ probability for MDA calculations).

Pulse-Height Discrimination

An electronic method used in proportional counters (such as a Tennelec) that establishes lower and upper voltage thresholds (windows) to simultaneously analyze alpha and beta-gamma activity based on the differences in generated pulse sizes.

Lower Discriminator

The threshold setting in pulse-height discrimination adjusted to filter out electronic noise and ultra-low-energy photon events, ensuring any pulse exceeding this setting is registered as an event or count.

Upper Discriminator

The threshold setting in pulse-height discrimination set such that any pulse surpassing its level is categorized and tallied as an alpha count.

Counting Channels (A, B, and C)

The routing pathways in a counting system where Channel A registers alpha counts, Channel C registers total valid counts exceeding the lower discriminator, and Channel B registers beta-gamma counts determined by $B = C - A$.

Crosstalk (Spillover)

A phenomenon in proportional counting systems where pulses from one type of radiation are misclassified as another due to discriminator settings, such as two beta pulses summing to surpass the upper discriminator or an alpha pulse failing to exceed it.

Beta-to-Alpha Crosstalk Criterion

The calibration criterion specifying that spillover from beta to alpha must be less than $1\%$, established using a strontium-90 ($^{90}\text{Sr}$) beta source to set the upper discriminator.

Alpha-to-Beta Crosstalk Criterion

The calibration criterion specifying that spillover from alpha to beta must be less than $3\%$, established using a polonium-210 ($^{210}\text{Po}$) alpha source to set the discriminator.

Voltage Plateau

A graph plotting a detector's response (counts on the y-axis) against high voltage variations (on the x-axis), used to determine detector quality and identify the optimum operating high voltage.

ALPHA ONLY Mode

An analysis mode where a sample is counted once at the lower alpha voltage, adding counts from both channels together into Channel A to report as alpha counts while clearing Channel B to zero.

ALPHA THEN BETA Mode

An analysis mode where the sample is counted twice—first at the alpha voltage to measure alpha counts and second at the higher beta voltage—with gross alpha ($\alpha$) and beta ($\beta$) counts resolved using an alpha correction factor ($CF_\alpha$).

Alpha Correction Factor ($CF_\alpha$)

The ratio of alpha efficiency at alpha voltage to efficiency at beta voltage, used in the formula $\alpha = \frac{A_1 + B_1}{CF_\alpha}$ to resolve true alpha counts in ALPHA THEN BETA mode.

ALPHA AND BETA (SIMULTANEOUS) Mode

The most commonly used analysis mode where a sample is counted once at the beta voltage, routing alpha events to Channel A and beta-gamma events to Channel B simultaneously.