Influence of Background on Apparent Counting Efficiency in Radioactivity Analysis

Abstract

In radioactivity analysis, counting efficiency(E) and background(to be precise, it should be deterministic background) are usually discussed, but apparent counting efficiency(E') and random background are rarely mentioned. However, the influence of background(including both deterministic background and random background) on apparent counting efficiency must be considered, especially for samples with low radioactivity. The relation between E and E' can be described as the equation E' = E + ΔB/A, where A is the sample radioactivity, and ΔB is the residue background, including two parts: the counting rate of residual deterministic background caused by inaccurate deduction of background and the counting rate of random background that cannot be deducted. In this paper, E' was studied on the following assumptions: E was fixed at 90%; A was changing from 0.1 to 100, with a step of 0.1(relative unit, similarly hereinafter); and ΔB was set to be fixed, or to follow a specific distribution. The simplest continuous distribution(uniform distribution) and the most commonly used continuous distribution(normal distribution) were chosen for this research, and the function “random number generator ” of the software Excel was used to simulate the random variable ΔB. Specifically speaking, the random variable ΔB was assumed to follow ±0.1·U(0,1), ±0.1·U(−0.5,0.5), ±0.1·N(0.5,1), or ±0.1·N(0,1), where U stands for uniform distribution and N for normal distribution. The influence of background on apparent counting efficiencies is divided into two aspects: one is the systematic error introduced by inaccurate background deduction, which makes all apparent counting efficiencies deviate from the counting efficiency in the same direction; the other is the accidental error caused by background fluctuations, which makes apparent counting efficiency fluctuate within a certain range. Regardless of the error type, the influence of background on apparent counting efficiency will increase as the radioactivity of the sample decreases. For samples with high radioactivity, the difference between apparent counting efficiency and counting efficiency is so small that it can be ignored, therefore it is not necessary to distinguish between the two concepts of apparent counting efficiency and counting efficiency; but for samples with low radioactivity, they must be used differently. Unless there is no standard sample with high radioactivity, it is not recommended to use the inefficient method, which is reported in Lin’s paper(ACS Earth Space Chem, 2022, 6(7): 1868-1875), to obtain counting efficiency by measuring a large number of samples with low radioactivity. It is advisable to obtain counting efficiency by measuring standard samples with sufficiently high radioactivity, in which the influence of background can be negligible.

Keywords

• radioactivity analysis
• background
• random background
• counting efficiency
• apparent counting efficiency