New cascade analysis techniques for determining spontaneous atomic transition probabilities

Abstract

Several new analysis techniques which account for the effects of cascades in the measurement of atomic transition probabilities have been developed at the University of Toledo, and will be described here. These techniques involve the incorporation of information from the direct measurement of the decay curves of cascading transitions into the analysis of the decay curve of the main level of interest. The traditional curve fitting techniques, as well as the new analysis techniques, are investigated by the use of computer simulated data containing various numbers of known exponentials. A diagrammatic mnemonic which trivially generates the theoretical decay curves for cascade schemes of arbitrary complexity will be described. The traditional curve fitting techniques are extended to include constraints imposed by the coefficients in the theoretical decay curve, which can be measured in terms of relative intensities of the cascading transitions. The population differential equation is converted to an integral equation involving only experimentally measurable quantities and the desired transition probability. Integrals over some arbitrary time interval of the decay curves can be photometrically measured, and given a common normalization through a wavelength relative efficiency calibration of the detection system. Integrated decay curves of all transitions, either directly into or out of the level of interest, can be summed in a manner which determines its transition probability. By varying the choice of time interval it can be verified that all contributing transitions have been correctly included. A variation of this technique allows the construction of the decay curve of an unmeasured cascade, provided the transition probability of the level into which it cascades is known. This variation can be used to investigate radiationless transitions and transitions outside the range of available detectors. Further, if there is additional a priori information concerning the shape of the unseen cascade decay curve, both its litetime and that level into which it cascades can be determined.