Virtual segmentation of a small contact HPGe detector: inference of hit positions of single-site events via pulse shape analysis

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Exploring hit positions of recorded events can help to understand and suppress backgrounds in rare event searches. We propose a pulse shape analysis method to discriminate single-site events (SSEs) in the inner and outer layer of a small contact P-type germanium detector (HPGe). SSEs in the inner and outer layer have different pulse shape features, of which the rise time of the (TQ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(T_{Q})$$\\end{document} and current pulse (TI)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(T_{I})$$\\end{document} are selected for discrimination. A 500 Bq Thorium-228 (Th-228) source is used to determine the boundaries between the two layers. The double escape peak events from 2614.5 keV 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 are selected as typical SSEs, their numbers in the two layers are used to calculate the volumes and shapes of those layers. Considering the statistical and systematic uncertainties, the inner layer volume is evaluated to be 47.2% ± 0.26%(stat.) ± 0.18%(sys.) ± 0.22%(sys.) of the total sensitive volume. Selecting the inner layer as the analysis volume can reduce the external background in the signal region of Ge-76 neutrinoless double beta (0νββ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u \\beta \\beta )$$\\end{document} decay. We use the Th-228 data to validate the inner layer model and evaluate the background suppression power in the 0νββ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u \\beta \\beta $$\\end{document} signal region (Qββ=2039\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(Q_{\\beta \\beta }=2039$$\\end{document} keV). The virtual segmentation further reduces the background from the external Th-228 source by about 10%. The virtual segmentation could be used to efficiently suppress surface background like electrons from Ar-42 decay in 0νββ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ u \\beta \\beta $$\\end{document} experiments using germanium detectors immersed in liquid argon.