Centroid Time Research Articles

Method of measuring time delay

The propagation time of a linear system, defined as the group delay at zero frequency, is given by the time centroid of its response to unit impulse. Based on this, a method of measurement is described which is independent of the shape of either the input or output time functions.

Method of evaluating delayed coincidence experiments

Frequently in delayed coincidence work a resolution curve is measured with good accuracy, but no exactly comparable prompt resolution curve is available. The centroid-shift method of evaluating the lifetime τ cannot be applied because the zero of time (centroid of the prompt curve) is not known. If τ is close to the instrumental limit, it cannot be measured from the logarithmic slope of the measured resolution curve. We then require an objective measure of the asymmetry of the measured curve, calculable without reference to any other curve. Such a quantity is the third moment of the measured curve about its own centroid. We show that the normalized third moment is equal to (2 τ 3+ ε), where ε is the normalized third moment of the prompt curve, usually small and frequently negligible. Thus τ can be evaluated with at most only rough knowledge of the prompt curve. The McGill IBM 650 computer has been programmed to perform the arithmetical work, which is otherwise laborious. An application to an actual example is shown. Estimates are given of the accuracy to be expected from the method.