Analytical fitting of γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document}–ray photopeaks in germanium cross strip detectors

Abstract

In an ideal germanium detector, fully-absorbed monoenergetic γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document}–rays will appear in the measured spectrum as a narrow peak, broadened into a Gaussian of width determined only by the statistical properties of charge cloud generation and the electronic noise of the readout electronics. Multielectrode detectors complicate this picture. Broadening of the charge clouds as they drift through the detector will lead to charge sharing between neighboring electrodes and, inevitably, low-energy tails on the photopeak spectra. We simulate charge sharing in our germanium cross strip detectors in order to reproduce the low-energy tails due to charge sharing. Our goal is to utilize these simulated spectra to develop an analytical fit (shape function) for the spectral lines that provides a robust and high-quality fit to the spectral profile, reliably reproduces the interaction energy, noise width, and the number of counts in both the true photopeak and the low-energy tail, and minimizes the number of additional parameters. Accurate modeling of the detailed line profiles is crucial for both calibration of the detectors as well as scientific interpretation of measured spectra.