New ways for simple and fast derivation/estimate of nuclear lifetimes in RDDS measurements

What is it about?

The Recoil-Distance Doppler-Shift (RDDS) or plunger method for lifetime measurements was originally based on recoil-into-vacuum of the residual nucleus after a nuclear reaction. The gamma-rays deexciting a particular nuclear state at different target-to-stopper distances are emitted during the flight, giving rise to a Doppler-shifted (S) peak in the detected spectrum, or after coming at rest in a stopper, yielding an unshifted (U) component in the detector spectrum. The relative intensities of these two components change when varying the target-to-stopper distance i.e. the flight-time which depends on the (mean) recoil velocity). By investigating the evolution of this splitting of the total intensity into S- and U-components with distance it is possible to determine the lifetime of the nuclear state studied. The feeding time from higher lying levels has to be also taken into account in the procedure, indeed. From the lifetimes, using additional spectroscopic information, absolute transition probabilities can be determined which give information on matrix elements of electromagnetic operators and thus on Nuclear structure. The new approaches for lifetime determination presented in our work are based on fundamental properties of the functions describing the time evolution of the population of excited nuclear states. Partly, one of them represents a contraction of the well known Differential decay-curve method (DDCM) by using the most reliable data point (the maximum of the function describing the population of a level in time) and a purely numerical procedure avoiding any fitting of decay curves. The combination with the standard DDCM analysis is promising for improving the reliability and the precision of the results for the lifetimes obtained. The really novel part of the approach consists of using a chain of equations at the consecutive maxima of the population functions which allow to precisely determine the ratio of the lifetimes of two consecutive levels and in the case where one of these lifetimes is known, to determine the unknown one. In addition, a simple integral derivation of the lifetime is presented involving the peak areas measured at different distances as well as an application of the first moments (expectation values, centroids in time) of the population functions for determining lifetimes. Both are demonstrated to be useful.

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Photo by Thomas Park on Unsplash

Photo by Thomas Park on Unsplash

Why is it important?

Ensuring additional, independent ways for analyzing data is always welcome. Our new procedures may reach only in special, limiting cases the precision achieved by well established methods as the DDCM. However, the independently determined lifetimes values strongly increase the possibility for reliability checks i.e. the elimination of systematic errors. Many state-of-the-art contemporary experiments aimed to study exotic nuclei, e.g. by using radioactive ion beams (RIB), have as inherent features a quite low statistics ans severe limitations on affordable beam-time lengths. In such case, our new approaches may be substantial for obtaining lifetime results. In additions, though biased by mathematical difficulties, the novel chain of equations approach may be used in other methods for lifetime determination apart from the RDDS.

Perspectives