CONSTRAINTS ON UNCERTAINTIES AND THEIR APPLICATION TO THE EMISSION PROBABILITIES OF ALPHA-PARTICLES

It often happens that the mean values of certain quantities are subject to constraints as, for example, when a sum is known exactly although the individual contributions have been measured independently and their corresponding uncertainties assigned. In this paper, the influence of a constraint on the final expression of the results is studied in detail, and is illustrated in the alpha-particle emission probabilities for several nuclides from nuclear data tables. A simple rule emerges: If the mean values must add to 100% and if one of the variances is greater than half the sum of all the variances, then the precision in the expression of the results can be improved.