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Counting a small number of radioactive atoms
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 PROGRAM SUMMARY
2~tle of program: Counting few radioactive atoms
Keywords: Nuclear physics, radioactive decay, radioactive
Catalogue number: AAUS
atoms, small sample, decays, statistical analysis, Bayesian analysis.
Computer: UNIVAC 1108 Installation: State Computer Centre,
Nature of physical problem
Helsinki.
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.
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.
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 account uncertainty in the efficiency and background rate of the detector.
Other peripherals used: Card reader and line printer Restriction on the complexity of the problem No. of cards in combined program and test deck: 123.
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.
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 PROGRAM SUMMARY
2~tle of program: Counting few radioactive atoms
Keywords: Nuclear physics, radioactive decay, radioactive
Catalogue number: AAUS
atoms, small sample, decays, statistical analysis, Bayesian analysis.
Computer: UNIVAC 1108 Installation: State Computer Centre,
Nature of physical problem
Helsinki.
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.
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.
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 account uncertainty in the efficiency and background rate of the detector.
Other peripherals used: Card reader and line printer Restriction on the complexity of the problem No. of cards in combined program and test deck: 123.
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.