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Title: $Nuclear matrix elements for double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>decay
Abstract: Background: Direct determination of the neutrino mass through double-$β$ decay is at the present time one of the most important areas of experimental and theoretical research in nuclear and particle physics. Purpose: We calculate nuclear matrix elements for the extraction of the average neutrino mass in neutrinoless double-$β$ decay. Methods: The microscopic interacting boson model (IBM-2) is used. Results: Nuclear matrix elements in the closure approximation are calculated for $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{110}$Pd, $^{116}$Cd, $^{124}$Sn, $^{128}$Te, $^{130}$Te, $^{148}$Nd, $^{150}$Nd, $^{154}$Sm, $^{160}$Gd, and $^{198}$Pt decay. Conclusions: Realistic predictions for the expected half-lives in neutrinoless double-$β$ decay with light and heavy neutrino exchange in terms of neutrino masses are made and limits are set from current experiments.