AhKin: A modular and efficient code for the Doppler shift attenuation method

Abstract

We present a set of programs for measuring lifetimes τ of nuclear states by the Doppler shift attenuation method (DSAM). The algorithms are based on the analysis of a probabilistic model of the processes occurring during a DSAM experiment. This analysis allows us to formulate the calculation of the theoretical lineshape as the application of an integral transform that converts the probability density of the cascade time (the time elapsed from nucleus creation to state decay) into the probability density of the (scaled) photon energy in the laboratory reference frame. The kernel of this integral transform, which encapsulates information related to the processes of nuclei stopping and photon detection, is independent of the state decay process, and hence needs not be recalculated on every trial of a candidate τ-value, allowing for fast computation of theoretical lineshapes. Further efficiency is gained by using algorithms that approximate continuous random variables by suitably chosen discrete ones. These codes were used to measure the lifetimes and sidefeeding times of the excited states of the normally deformed bands of 83Y (Rodriguez, et al. 2019) finding for all states good agreement between the experimental lineshape and the best-fitting theoretical one. Program summaryProgram Title: AhKinProgram Files doi:http://dx.doi.org/10.17632/559kb329p2.1Licensing provisions: MITProgramming language: C++Nature of problem: Measurement of lifetimes of excited nuclear states by the Doppler shift attenuation method. This involves simulating the measured energy spectrum (lineshape) of photons emitted in transitions between excited states of a nucleus traveling in a stopping material. The reduction in time of the nucleus velocity relates the state lifetime to the observed Doppler shift of the photon’s energy. The measured lifetime is assumed as the value producing the theoretical lineshape that best approximates the experimental spectrum.Solution method: A probabilistic model allows to formulate the computation of theoretical lineshapes as the evaluation of an integral transform that converts the probability density of cascade times to the Doppler-shifted photon energy spectrum. The kernel of this integral transform is independent of the state decay process, and need not be recalculated for every trial of a candidate lifetime value, permitting swift computation of lineshapes. Additional algorithmic efficiency is obtained by approximating continuous random variables by discrete ones.