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Manuscript Title: Counting a small number of radioactive atoms.
Authors: A.M. Aurela
Program title: COUNTING FEW RADIOACTIVE ATOMS
Catalogue identifier: AAUS_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 13(1977)281
Programming language: Fortran.
Computer: UNIVAC 1108.
Operating system: EXEC - 8.
RAM: 25K words
Word size: 36
Keywords: Nuclear physics, General experiment, Radioactive decay, Radioactive atoms, Small sample, Decays, Statistical analysis, Bayesian analysis.
Classification: 17.4.

Nature of 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.

Solution method:
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.

Restrictions:
n<= 129.

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

Running time:
32 s (20s CPU) on UNIVAC 1108.