FITEVT: A FORTRAN program for arrival-time analysis of nuclear-decay events

Abstract

FITEVT is a FORTRAN program designed to analyze recorded arrival times of nuclear-decay events affected by dead-time. The primary goal of the program is precise and accurate determination of half-lives. Its method involves imposition of a known sufficiently long extending dead-time to the recorded event sequence, so that the original dead-time effects are completely obliterated and the remaining live-times of the survived events are known exactly. Upon completion of the analysis, the arrival-time spectrum and the live-time spectrum are predicted and compared to those constructed from the survived events. Program summaryProgram title: FITEVTLicensing provisions: MITCPC Library link to program files:https://doi.org/10.17632/scg6p9jxjk.1Programming language: FORTRAN (using double precision)Nature of problem: Accurate determination of the ideal event rate from the observed event rate in a nuclear decay can be a challenging task due to the inevitable presence of detection system's dead-time, whose nature and extent are typically unknown. Consequently, the results of nuclear half-life measurements may depend on the method used to correct for event losses due to dead-time. Therefore, there is a need for an exact method of data analysis and the means to apply it in order to ensure reproducibility, accuracy and optimized precision of the results.Solution method: FITEVT performs arrival-time analysis of the recorded events, in which a known, sufficiently large extending dead-time is imposed by means of software, so that in the resulting set of survived events the original dead-time effects are completely replaced by the effects of the imposed dead-time. As a result, the dead-time following each survived event and the remaining live-time preceding each surviving event are known exactly. This allows for application of the maximum-likelihood method of estimation, in which the half-lives as well as the other parameters of the ideal-decay-rate function can be accurately determined.Additional comments including restrictions and unusual features: In its original form the program can handle contributions from a constant event rate (i.e., a typical background) plus up to 4 different exponentially-decaying event rates. One of these 4 contributions is allowed to be negative, so that the program can be applied to the general case involving a single two-component decay chain. The employed method of analysis produces accurate results even when the product of the ideal event rate (ρ) and the extending dead-time parameter (τe) is as large as 51.2 [1]. Example used in the present paper involves simulated events having initial rate of 105 s−1, to which extending dead-time of 64 μs is imposed.Data analysis is based on maximum-likelihood principle, in which minimization of the deviance involves calculations in double precision and determination of its derivatives is based on analytical expressions. This is done in order to optimize precision and accuracy of the results as well as the program execution time.With the provided input data and a typical contemporary laptop computer, the program execution typically lasts about 5 minutes. Reducing the imposed dead-time to zero increases the number of survived events approximately by a factor of 6, but the program execution time increases by about a factor of 3.