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Efficient Machine Learning Approach for Optimizing the Timing Resolution of a High Purity Germanium Detector
TL;DR: In this article, a machine learning based approach for the optimization of parameters used for extracting the arrival time of waveforms, in particular those generated by the detection of 511 keV annihilation gamma-rays by a 60 cm3 coaxial high purity germanium detector (HPGe), is presented.
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Abstract: We describe here an efficient machine-learning based approach for the optimization of parameters used for extracting the arrival time of waveforms, in particular those generated by the detection of 511 keV annihilation gamma-rays by a 60 cm3 coaxial high purity germanium detector (HPGe). The method utilizes a type of artificial neural network (ANN) called a self-organizing map (SOM) to cluster the HPGe waveforms based on the shape of their rising edges. The optimal timing parameters for HPGe waveforms belonging to a particular cluster are found by minimizing the time difference between the HPGe signal and a signal produced by a BaF2 scintillation detector. Applying these variable timing parameters to the HPGe signals achieved a gamma-coincidence timing resolution of ~ 4.3 ns at the 511 keV photo peak (defined as 511 +- 50 keV) and a timing resolution of ~ 6.5 ns for the entire gamma spectrum--without rejecting any valid pulses. This timing resolution approaches the best obtained by analog nuclear electronics, without the corresponding complexities of analog optimization procedures. We further demonstrate the universality and efficacy of the machine learning approach by applying the method to the generation of secondary electron time-of-flight spectra following the implantation of energetic positrons on a sample.
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Figures
Fig. 5 Examples of pulse clusters corresponding to four different neuron hits (50 pulses in each panel). (a) 511 keV annihilation γ-rays (identified by amplitude) that induced a relatively fastrising pulse. (b) Detector pulses that were produced by the inelastic scattering of incident annihilation γ-rays in the detector. (c) 511 keV annihilation γ-rays that induced a relatively slow-rising pulse. (d) A cluster that corresponds to either false triggers or extremely lowamplitude pulses. 
Fig. 6 HPGe-BaF2 coincidence peaks. For the creation of the γ-γ coincidence peaks all γ energies from 40 keV to 561 keV were utilized unless otherwise specified. The FWHM of the coincidence peaks is provided next to each peak, representing the coincidence timing resolution. (a) The grey peak was obtained by applying the conventional amplitude-based ELET algorithm to the HPGe and BaF2 pulses. The larger FWHM and asymmetric distortion result from the variety of HPGe pulse shapes. In contrast, the violet peak was created with the modified ELET algorithm described in Section 3.2. (b) A comparison of the aforementioned peak constructed with the modified ELET algorithm (violet) and the peak resulting from this same modified ELET algorithm in tandem with the ANN clustering procedure (red). (c) The γ-γ coincidence spectra obtained by applying the modified ELET with ANN clustering (red) compared to the coincidence peak obtained with the same algorithm but considering only those γ-ray energies that lie within the 511 keV photopeak, defined as 511 ± 50 keV (cyan). ![Fig. 7 Time-of-flight spectra of the positron-induced secondary electrons. Both secondary electron spectra were constructed from the same data set (Data set 4) with the application of different timing methods as described in the legend. The histograms were constructed by measuring the time difference (Δt) between the detection of the annihilation γ-ray by the HPGe detector and the detection of the positron-induced electron by the electron detector. Here, a beam of monoenergetic positrons (~ 17 eV) is incident on a sample biased to -500 V (resulting in a positron energy of ~ 517 eV). The spectra generated using both methods are consistent with previously reported positron-induced secondary electron spectra [44]. The secondary electron spectrum generated with the ANN method distinguishes itself with important characteristics— such as a sharper low-energy (higher Δt) edge and a reduced FWHM—indicating improved timing resolution of the HPGe detector.](/figures/figure7-1-2wfi44b3zc9a.png)
Fig. 7 Time-of-flight spectra of the positron-induced secondary electrons. Both secondary electron spectra were constructed from the same data set (Data set 4) with the application of different timing methods as described in the legend. The histograms were constructed by measuring the time difference (Δt) between the detection of the annihilation γ-ray by the HPGe detector and the detection of the positron-induced electron by the electron detector. Here, a beam of monoenergetic positrons (~ 17 eV) is incident on a sample biased to -500 V (resulting in a positron energy of ~ 517 eV). The spectra generated using both methods are consistent with previously reported positron-induced secondary electron spectra [44]. The secondary electron spectrum generated with the ANN method distinguishes itself with important characteristics— such as a sharper low-energy (higher Δt) edge and a reduced FWHM—indicating improved timing resolution of the HPGe detector. 
Fig. 3 A representative portion of the HPGe detector pulses (67 pulses) that comprise the input vectors to the SOM neural network. The wide variation in the rise times of the output of the pre-amplified pulses can be seen here. The SOM network undergoes unsupervised training to cluster similar waveforms according to the specific characteristics of their individual shapes. 
Fig. 2 A series of flow diagrams to elucidate the workings of the clustering and optimizat ion procedure. In panel (a), we begin by collecting four datasets: three γ-γ coincidence sets and one γ-e- coincidence set. (b) The first dataset is used to train the SOM clustering network. The input vectors (as shown in Fig. 3) for training the SOM network are selected portions of the HPGe 
Fig. 4 A “sample hits” plot of the 32x32 self-organizing map neural network. The sample hits represent a type of SOM visualization, in which the number of pulses associated with each neuron in the 32x32 hexagonal topology are given. The group of neurons highlighted in purple consist of pulses with relatively fast rise times, whereas the neurons highlighted in green consist of pulses with slower rise times. The yellow region consists primarily of noise and very lowamplitude pulses, and the rather diffuse, unmarked white region consists of pulses that represent inelastically scattered γ-rays within the detector. The red neurons were randomly selected to be roughly representative of each group of clusters, and their corresponding pulses are provided in Fig. 5.
![Fig. 7 Time-of-flight spectra of the positron-induced secondary electrons. Both secondary electron spectra were constructed from the same data set (Data set 4) with the application of different timing methods as described in the legend. The histograms were constructed by measuring the time difference (Δt) between the detection of the annihilation γ-ray by the HPGe detector and the detection of the positron-induced electron by the electron detector. Here, a beam of monoenergetic positrons (~ 17 eV) is incident on a sample biased to -500 V (resulting in a positron energy of ~ 517 eV). The spectra generated using both methods are consistent with previously reported positron-induced secondary electron spectra [44]. The secondary electron spectrum generated with the ANN method distinguishes itself with important characteristics— such as a sharper low-energy (higher Δt) edge and a reduced FWHM—indicating improved timing resolution of the HPGe detector.](/figures/figure7-1-2wfi44b3zc9a.webp)
Citations
Digital Pulseshape Analysis by Neural Networks for the Heidelberg-Moscow-Double-Beta-Decay-Experiment
TL;DR: In this article, the authors developed a new technique for event recognition based on neural networks, which used all the information contained in a recorded digital pulse, and used it in the Heidelberg-Moscow Experiment.
35
Implementation of a machine learning technique for estimating gamma direction using a coaxial High Purity Germanium detector
R. W. Gladen,T. J. Harvey,Sunil S. Chirayath,A. J. Fairchild,A. R. Koymen,A. Weiss,Varghese Anto Chirayath +6 more
TL;DR: In this article , the authors demonstrate the ability to obtain the direction of the gamma rays using a standard coaxial high purity germanium (HPGe) detector using the direction-sensitive information embedded in the shape of the pre-amplified HPGe signals.
6
Machine Learning in Nuclear Physics
A. Boehnlein,M. Diefenthaler,Nobuo Sato,M. Schram,Veronique Ziegler,Morten Hjorth-Jensen,Michelle Kuchera +6 more
TL;DR: A snapshot of nuclear physics research which has been transformed by machine learning techniques is provided in this paper , where surrogate models for accelerator models have been used to facilitate scientific discoveries and societal applications.
6
Two-dimensional total absorption spectroscopy with conditional generative adversarial networks
TL;DR: This work investigates the use of conditional generative adversarial networks (cGANs) to simultaneously unfold E x and E γ data in TAS detectors, and employs a Pix2Pix cGAN, a generative modeling technique based on recent advances in deep learning, to treat matrix unfolding as an image-to-image translation problem.
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R. W. Gladen,Varghese Anto Chirayath,A. J. Fairchild,Philip A. Sterne,Ali R. Koymen,Alex H. Weiss +5 more
TL;DR: In this article, a method for the analysis of the Doppler broadened spectrum of gamma photons emitted following the annihilation of surface trapped positrons with the electrons of bilayer graphene supported on polycrystalline Cu substrate is presented.
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The timing resolution of scintillation-detector systems: Monte Carlo analysis.
TL;DR: The Monte Carlo analysis developed in this work will allow us to optimize the scintillation detectors for timing and to understand the physical factors limiting their performance.
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