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On the possibility to measure nuclear matrix elements of neutrinoless double beta decay in charge-exchange reactions  [PDF]
Vadim Rodin,Amand Faessler
Physics , 2010, DOI: 10.1016/j.ppnp.2011.01.048
Abstract: As shown in Ref.\cite{Rod09}, the Fermi nuclear matrix element $M^{0\nu}_F$ of neutrinoless double beta ($0\nu\beta\beta$) decay can be reconstructed if one is able to measure the isospin-forbidden single Fermi transition matrix element from the ground state of the final nucleus to the isobaric analog state (IAS) of the initial nucleus, for instance by means of charge-exchange reactions of the $(n,p)$-type. Here, simple estimates for $^{82}$Se are made which show that indeed the tiny cross section $\sigma_{np}(0_f^+\to IAS)$ is dominated by the admixture of the double IAS in the ground state of the final nucleus provided that the isospin mixing is weak and can be treated perturbatively. A measurement of such a cross section would definitely be a very difficult task, but it can advance a lot our knowledge of the $0\nu\beta\beta$ nuclear matrix element.
Empirical Survey of Neutrinoless Double Beta Decay Matrix Elements
Robertson, R. G. H.
High Energy Physics - Phenomenology , 2013, DOI: 10.1142/S0217732313500211
Abstract: Neutrinoless double beta decay has been the subject of intensive theoretical work as it represents the only practical approach to discovering whether neutrinos are Majorana particles or not, and whether lepton number is a conserved quantum number. Available calculations of matrix elements and phase-space factors are reviewed from the perspective of a future large-scale experimental search for neutrinoless double beta decay. Somewhat unexpectedly, a uniform inverse correlation between phase space and the square of the nuclear matrix element emerges. As a consequence, no isotope is either favored or disfavored; all have qualitatively the same decay rate per unit mass for any given value of the Majorana mass.
Empirical Survey of Neutrinoless Double Beta Decay Matrix Elements  [PDF]
R. G. H. Robertson
Physics , 2013, DOI: 10.1142/S0217732313500211
Abstract: Neutrinoless double beta decay has been the subject of intensive theoretical work as it represents the only practical approach to discovering whether neutrinos are Majorana particles or not, and whether lepton number is a conserved quantum number. Available calculations of matrix elements and phase-space factors are reviewed from the perspective of a future large-scale experimental search for neutrinoless double beta decay. Somewhat unexpectedly, a uniform inverse correlation between phase space and the square of the nuclear matrix element emerges. As a consequence, no isotope is either favored or disfavored; all have qualitatively the same decay rate per unit mass for any given value of the Majorana mass.
Consensus Report of a Workshop on "Matrix elements for Neutrinoless Double Beta Decay"  [PDF]
K. Zuber
Physics , 2005,
Abstract: This is the consensus of a Workshop on "Matrix elements for Neutrinoless Double Beta Decay" held at the IPPP Durham (UK). The aim of this workshop has been to define a well planned, coherent strategy to reduce the errors on nuclear matrix element calculations for double beta decay to a level of 30% by performing the necessary measurements with currently existing and planned facilities. These measurements should provide reliable input for the theoretical calculations. The outcome of the workshop has been organised in working packages. The consensus might act as a starting point for an international coherent effort to achieve this goal.
Nuclear matrix elements for double beta decay  [PDF]
Vadim Rodin
Physics , 2009,
Abstract: The present status of calculations of the nuclear matrix elements for neutrinoless double beta decay is reviewed. A proposal which allows in principle to measure the neutrinoless double beta decay Fermi matrix element is briefly described.
Neutrinoless double beta decay  [PDF]
K. Zuber
Physics , 2012, DOI: 10.1007/s12043-012-0387-1
Abstract: The physics potential of neutrinoless double beta decay is discussed. Furthermore, experimental considerations are presented as well as the current status of experiments. Finally an outlook towards the future, work on nuclear matrix elements and alternative processes is given.
Nuclear matrix elements for neutrinoless double-beta decay and double-electron capture  [PDF]
Amand Faessler,Vadim Rodin,Fedor Simkovic
Physics , 2012, DOI: 10.1088/0954-3899/39/12/124006
Abstract: A new generation of neutrinoless double beta decay experiments with improved sensitivity is currently under design and construction. They will probe inverted hierarchy region of the neutrino mass pattern. There is also a revived interest to the resonant neutrinoless double-electron capture, which has also a potential to probe lepton number conservation and to investigate the neutrino nature and mass scale. The primary concern are the nuclear matrix elements. Clearly, the accuracy of the determination of the effective Majorana neutrino mass from the measured 0\nu\beta\beta-decay half-life is mainly determined by our knowledge of the nuclear matrix elements. We review recent progress achieved in the calculation of 0\nu\beta\beta and 0\nu ECEC nuclear matrix elements within the quasiparticle random phase approximation. A considered self-consistent approach allow to derive the pairing, residual interactions and the two-nucleon short-range correlations from the same modern realistic nucleon-nucleon potentials. The effect of nuclear deformation is taken into account. A possibility to evaluate 0\nu\beta\beta-decay matrix elements phenomenologically is discussed.
Accurate shell-model nuclear matrix elements for neutrinoless double-beta decay  [PDF]
R. A. Sen'kov,M. Horoi
Physics , 2014, DOI: 10.1103/PhysRevC.90.051301
Abstract: We investigate a novel method of accurate calculation of the neutrinoless double-$\beta$ decay shell-model nuclear matrix elements for the experimentally relevant case of $^{76}$Ge. We demonstrate that with the new method the nuclear matrix elements have perfect convergence properties and, using only the first 100 intermediate states of each spin, the matrix elements can be calculated with better than 1% accuracy. Based on the analysis of neutrinoless double-beta decays of $^{48}$Ca, $^{82}$Se, and $^{76}$Ge isotopes, we propose a new method to estimate the optimal values of the average closure energies at which the closure approximation gives the most accurate nuclear matrix elements. We also analyze the nuclear matrix elements for the heavy-neutrino-exchange mechanism, and we show that our method can be used to quench contributions from different intermediate spin states.
Light-neutrino mass hierarchies, nuclear matrix elements, and the observability of neutrinoless double-beta decay  [PDF]
O. Civitarese,J. Suhonen
Physics , 2002, DOI: 10.1016/j.nuclphysa.2003.10.004
Abstract: Results for neutrino flavor oscillations and neutrino mixing mechanisms, obtained from the analysis of the Sudbury Neutrino Observatory (SNO), the SuperKamiokande (SK), CHOOZ, KamLAND and WMAP data, are used to calculate the effective neutrino mass relevant for the neutrinoless double-beta decay. The observability of the decay of 76Ge is discussed within different light-neutrino mass hierarchies and by presenting a systematics on the available nuclear matrix elements.
Neutrinoless Double Beta Decay and Neutrino Masses  [PDF]
Michael Duerr
Physics , 2012, DOI: 10.1063/1.4742106
Abstract: Neutrinoless double beta decay is a promising test for lepton number violating physics beyond the standard model of particle physics. There is a deep connection between this decay and the phenomenon of neutrino masses. In particular, we will discuss the relation between neutrinoless double beta decay and Majorana neutrino masses provided by the so-called Schechter--Valle theorem in a quantitative way. Furthermore, we will present an experimental cross check to discriminate neutrinoless double beta decay from unknown nuclear background using only one isotope, i.e., within one experiment.
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