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تسجيل مستخدم جديدEstimation of nuclear matrix elements of double-$beta$ decay from shell model and quasiparticle random-phase approximation
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The nuclear matrix element (NME) of the neutrinoless double-$beta$ ($0 ubetabeta$) decay is an essential input for determining the neutrino effective mass, if the half-life of this decay is measured. The reliable calculation of this NME has been a long-standing problem because of the diversity of the predicted values of the NME depending on the calculation method. In this paper, we focus on the shell model and the QRPA. The shell model have a rich amount of the many-particle many-hole correlations, and the QRPA can obtain the convergence of the result of calculation with respect to the extension of the single-particle space. It is difficult for the shell model to obtain the convergence of the $0 ubetabeta$ NME with respect to the valence single-particle space. The many-body correlations of the QRPA are insufficient depending on nuclei. We propose a new method to modify phenomenologically the results of the shell model and the QRPA compensating the insufficient point of each method by using the information of other method complementarily. Extrapolations of the components of the $0 ubetabeta$ NME of the shell model are made toward a very large valence single-particle space. We introduce a modification factor to the components of the $0 ubetabeta$ NME of the QRPA. Our modification method gives similar values of the $0 ubetabeta$ NME of the two methods for $^{48}$Ca. The NME of the two-neutrino double-$beta$ decay is also modified in a similar but simpler manner, and the consistency of the two methods is improved.
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Neutrinoless double beta decay searches are currently among the major foci of experimental physics. The observation of such a decay will have important implications in our understanding of the intrinsic nature of neutrinos and shed light on the limit
ations of the Standard Model. The rate of this process depends on both the unknown neutrino effective mass and the nuclear matrix element associated with the given neutrinoless double-beta decay transition. The latter can only be provided by theoretical calculations, hence the need of accurate theoretical predictions of the nuclear matrix element for the success of the experimental programs. This need drives the theoretical nuclear physics community to provide the most reliable calculations of the nuclear matrix elements. Among the various computational models adopted to solve the many-body nuclear problem, the shell model is widely considered as the basic framework of the microscopic description of the nucleus. Here, we review the most recent and advanced shell-model calculations of the nuclear matrix elements considering the light-neutrino-exchange channel for nuclei of experimental interest. We report the sensitivity of the theoretical calculations with respect to variations in the model spaces and the shell-model nuclear Hamiltonians.
The nuclear matrix elements of neutrinoless double-$beta$ decay for nuclei $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd are studied within the triaxial projected shell model, which incorporates simultaneously the triaxial deformation
and quasiparticle configuration mixing. The low-lying spectra and the $B(E2:0^+rightarrow2^+)$ values are reproduced well. The effects of the quasiparticles configuration mixing, the triaxial deformation, and the closure approximation on the nuclear matrix elements are studied in detail. For nuclei $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd, the nuclear matrix elements are respectively reduced by the quasiparticle configuration mixing by 6%, 7%, 2%, 3%, and 4%, and enhanced by the odd-odd intermediate states by 7%, 4%, 11%, 20%, and 14%. Varying the triaxial deformation $gamma$ from $0^circ$ to $60^circ$ for the mother and daughter nuclei, the nuclear matrix elements change by 41%, 17%, 68%, 14%, and 511% respectively for $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te, and $^{150}$Nd, which indicates the importance of treating the triaxial deformation consistently in calculating the nuclear matrix elements.
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Accurate nuclear matrix elements (NMEs) for neutrinoless double beta decays of candidate nuclei are important for the design and interpretation of future experiments. Significant progress has been made in the modeling of these NMEs from first princip
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