C-430

Computer Physics Communications 13 (1977) 281-287 © North-Holland Publishing Company

COUNTING A SMALL NUMBER OF RADIOACTIVE ATOMS

A.M. A U R E L A

Wihuri Physical Laboratory, University of Turku, $F-20500 Turku 50, Finland

Received 14 March 1977

PR OGR AM SUMMARY

2~tle of program: Counting few radioactive atoms

Catalogue number: AAUS

Computer: UNIVAC 1108 Installation: State Computer Centre, Helsinki.

Operating system: EXEC-8

Programming language used: ASA FORTRAN

High speed storage required: 25067 words.

No. of bits in a word: 36.

Overlay structure: none.

No. of magnetic tapes required: none.

Other peripherals used: Card reader and line printer

No. of cards in combined program and test deck: 123.

Keywords: Nuclear physics, radioactive decay, radioactive atoms, small sample, decays, statistical analysis, Bayesian analysis.

Nature of physical problem The problem is to determine the frequency function P(n) of the posterior probability that a small sample of a radioactive isotope R contains n atoms at the end of the production of R, when the counts in the subsequent counting periods are known.

Method of solution First, P(n) is computed for the beginning of the last counting period by a Bayesian method. Then P(n) is used for computing a new P(n) for the beginning of the preceding interval, if there was an interval. Then P(n) is computed in the same way for the beginning of the preceding counting period, and so on. Mixed probability distributions are used for taking into ac- count uncertainty in the efficiency and background rate of the detector.

Restriction on the complexity of the problem n < 129 .

Typical running time 32 s (20 s CPU) on UNIVAC 1108.

Unusual features of the program The repetitive application of Bayes's method to the multiple branches of possibilities, and the built-in a priori constraint n ~ 0, which reduces the error estimates.