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ABSTRACT: Within QRPA we achieve partial restoration of the isospin symmetry and hence
fulfillment of the requirement that the $2\nu\beta\beta$ Fermi matrix element
$M^{2\nu}_F$ vanishes, as it should, unlike in the previous version of the
method. This is accomplished by separating the renormalization parameter
$g_{pp}$ of the particle-particle proton-neutron interaction into the isovector
and isoscalar parts. The isovector parameter $g_{pp}^{T=1}$ need to be chosen
to be essentially equal to the pairing constant $g_{pair}$, so no new parameter
is needed. For the $0\nu\beta\beta$ decay the Fermi matrix element $M^{0\nu}_F$
is substantially reduced, while the full matrix element $M^{0\nu}$ is reduced
by $\approx$ 10%. We argue that this more consistent approach should be used
from now on in the proton-neutron QRPA and in analogous methods.
02/2013;
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ABSTRACT: A formal relation between the GT part of the nuclear matrix elements
$M^0\nu}_{GT}$ of $0\nu\beta\beta$ decay and the closure matrix elements
$M^{2\nu}_{cl}$ of $2\nu\beta\beta$ decay is established. This relation is
based on the integral representation of these quantities in terms of their
dependence on the distance $r$ between the two nucleons undergoing
transformation. We also discuss the difficulties in determining the correct
values of the closure $2\nu\beta\beta$ decay matrix elements.
08/2011;
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ABSTRACT: We analyze the possibility of detection of cosmological relic neutrinos via neutrino capture on beta decaying nuclei. This reaction has no threshold in neutrino energy, which is crucial for searching for relic neutrinos possessing very low energies. We focus on tritium (3H) and rhenium (187Re) beta radioactive isotopes to be used in the Karlsruhe tritium neutrino mass (KATRIN) experiment and project, called the Microcalorimeter Arrays for a Rhenium Experiment (MARE), dedicated to the measurement of the electron neutrino mass at sub-eV scale. We examine these experiments from the viewpoint of searching for the cosmological neutrinos via neutrino capture. We conclude that even with possible gravitational clustering of relic neutrinos the prospects for their detection in these and other similar experiments are not optimistic. Nevertheless, KATRIN and MARE experiments could establish some useful constraints on the density of relic neutrinos.
Journal of Physics G Nuclear and Particle Physics 06/2011; 38(7):075202. · 4.18 Impact Factor
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ABSTRACT: The planned rhenium β-decay experiment, called the “Microcalorimeter Arrays for a Rhenium Experiment” (MARE), might probe the absolute mass scale of neutrinos with the same sensitivity as the Karlsruhe tritium neutrino mass (KATRIN) experiment, which will take commissioning data in 2011 and will proceed for 5 years. We present the energy distribution of emitted electrons for the first unique forbidden β decay of 187Re. It is found that the p-wave emission of electron dominates over the s wave. By assuming mixing of three neutrinos, the Kurie function for the rhenium β decay is derived. It is shown that the Kurie plot near the end point is within a good accuracy linear in the limit of massless neutrinos like the Kurie plot of the superallowed β decay of 3H.
Phys. Rev. C. 04/2011; 83(4).
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ABSTRACT: It is well known that there exist many mechanisms that may contribute to neutrinoless double beta decay. By exploiting the fact that the associated nuclear matrix elements are target dependent we show that, given definite experimental results on a sufficient number of targets, one can determine or sufficiently constrain all lepton violating parameters including the mass term. As a specific example we show that, assuming the observation of the 0νββ decay in three different nuclei, e.g., G76e, 100Mo, and 130Te, and just three lepton number violating mechanisms (light- and heavy-neutrino mass mechanisms as well as the R-parity breaking supersymmetry mechanism) being active, there are only four different solutions for the lepton violating parameters, provided that they are relatively real. In particular, our analysis shows that the effective neutrino Majorana mass |mββ| can be almost uniquely extracted by utilizing other existing constraints (cosmological observations and tritium β-decay experiments). We also point out the possibility that the nonobservation of the 0νββ decay for some isotopes could be in agreement with a value of |mββ| in the sub-eV region. We thus suggest that it is important to have at least two different 0νββ-decay experiments for a given nucleus. We note that obtained results are sensitive to the accuracy of measured half-lives and to uncertainties in calculated nuclear matrix elements.
Phys. Rev. D. 12/2010; 82(11).
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ABSTRACT: We show that the dominant Gamow-Teller part, $M^{0\nu}_{GT}$, of the nuclear
matrix element governing the neutrinoless $\beta\beta$ decay is related to the
matrix element $M^{2\nu}_{cl}$ governing the allowed two-neutrino $\beta\beta$
decay. That relation is revealed when these matrix elements are expressed as
functions of the relative distance $r$ between the pair of neutrons that are
transformed into a pair of protons in the $\beta\beta$ decay. Analyzing this
relation allows us to understand the contrasting behavior of these matrix
elements when $A$ and $Z$ is changed; while $M^{0\nu}_{GT}$ changes slowly and
smoothly, $M^{2\nu}$ has pronounced shell effects. We also discuss the
possibility of phenomenological determination of the
$M^{2\nu}_{cl}$ and from them of the $M^{0\nu}_{GT}$ values from the
experimental study of the $\beta^{\pm}$ strength functions.
12/2010;
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ABSTRACT: A self-consistent calculation of nuclear matrix elements of the neutrinoless double-beta decays (0νββ) of 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128Te, 130Te, and 136Xe is presented in the framework of the renormalized quasiparticle random phase approximation (RQRPA) and the standard QRPA. The pairing and residual interactions as well as the two-nucleon short-range correlations are for the first time derived from the same modern realistic nucleon-nucleon potentials, namely, from the charge-dependent Bonn potential (CD-Bonn) and the Argonne V18 potential. In a comparison with the traditional approach of using the Miller-Spencer Jastrow correlations, matrix elements for the 0νββ decay are obtained that are larger in magnitude. We analyze the differences among various two-nucleon correlations including those of the unitary correlation operator method (UCOM) and quantify the uncertainties in the calculated 0νββ-decay matrix elements.
Phys. Rev. C. 05/2009; 79(5).
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ABSTRACT: At the quark level there are basically two types of contributions of R-parity violating supersymmetry (R̸p SUSY) to neutrinoless double beta decay: the short-range contribution involving only heavy virtual superpartners and the long-range one with the virtual squark and neutrino. Hadronization of the effective operators, corresponding to these two types of contributions, may in general involve virtual pions in addition to close on-mass-shell nucleons. From the previous studies it is known that the short-range contribution is dominated by the pion exchange. In the present paper we show that this is also true for the long-range R̸p SUSY contribution. Therefore, we conclude that the R̸p SUSY contributes to the neutrinoless double beta decay dominantly via charged pion exchange between the decaying nucleons.
Phys. Rev. D. 06/2008; 77(11).
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ABSTRACT: The nuclear matrix elements M
0ν
of the neutrinoless double-beta decay (0νβ β) of most nuclei with known 2νββ-decay rates are systematically evaluated using the Quasiparticle Random Phase Approximation (QRPA) and Renormalized QRPA
(RQRPA). The experimental 2νβ β-decay rate is used to adjust the most relevant parameter, the strength of the particle-particle interaction. With such procedure
the M
0ν
values become essentially independent of single-particle basis size, the axial vector quenching factor, etc. Theoretical
arguments in favor of the adopted way of determining the interaction parameters are presented. It is suggested that most of
the spread among the published M
0ν
’s can be ascribed to the choices of implicit and explicit parameters, inherent to the QRPA method.
Czechoslovak Journal of Physics 04/2006; 56(5):495-503. · 0.42 Impact Factor
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ABSTRACT: We present a detailed analysis of the muonic analogue of neutrinoless double beta decay (μ-,μ+) conversion. We study several lepton number violating (LNV) mechanisms potentially triggering this process: exchange by light and heavy Majorana neutrinos as well as exchange by supersymmetric particles participating in R-parity violating interactions. The nuclear structure is taken into account within the renormalized quasiparticle random phase approximation method. This is the first realistic treatment of nuclear structure aspects of the (μ-,μ+) conversion. We estimate the rate of this process utilizing the existing experimental constraints on the parameters of the underlying LNV interactions and conclude that the (μ-,μ+) conversion will hardly be detectable in the near future experiments.
Phys. Rev. D. 08/2002; 66(3).
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ABSTRACT: The effect of deformation on the two-neutrino double decay (2νββ-decay) for ground state transition is studied in the framework of the deformed QRPA with separable Gamow–Teller residual interaction. We found that when the parent and daughter nuclei have different deformations, the 2νββ-decay matrix element is suppressed with respect to the case of 2νββ decay between nuclei having the same deformation, in particular, spherical going to spherical. An advantage of this suppression mechanism in comparison with that associated with ground state correlations is that it allows a simultaneous description of the single β and the 2νββ-decay. By performing a detail calculation of the 2νββ-decay of 76Ge, it is found that the states of intermediate nucleus lying in the region of the Gamow–Teller resonance contribute significantly to the matrix element of this process.
Nuclear Physics A. 733:321-350.
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ABSTRACT: The 2νββ-decay running sums for 76Ge and 150Nd nuclei are calculated within a QRPA approach with account for deformation. A realistic nucleon-nucleon residual interaction based on the Brueckner G matrix (for the Bonn CD force) is used. The influence of different model parameters on the functional behavior of the running sums is studied. It is found that the parameter gpp renormalizing the G matrix in the QRPA particle-particle channel is responsible for a qualitative change in behavior of the running sums at higher excitation energies. For realistic values of gpp a significant negative contribution to the total 2νββ-decay matrix element is found to come from the energy region of the giant Gamow-Teller resonance. This behavior agrees with results of other authors.
Phys. Rev. C. 81(3).
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ABSTRACT: The measured occupancies of valence orbits in 76Ge and 76Se are used as a guideline for modification of the effective mean field energies that results in better description of these quantities. With them, in combination with the self-consistent renormalized quasiparticle random phase approximation (SRQRPA) method that ensures conservation of the mean particle number in the correlated ground state, we show that the resulting 0νββ nuclear matrix element for the 76Ge-->76Se transition is reduced by ~25% compared to the previous QRPA value, and therefore the difference between the present approach and the interacting shell model predictions becomes correspondingly smaller. Analogous modification of the mean field energies for the A=82 system also results in a reduction of 0νββ matrix element for the 82Se-->82Kr transition, making it also closer to the shell model prediction.
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ABSTRACT: We show that the dominant Gamow-Teller part, M^(0ν)_(GT), of the nuclear matrix element governing the neutrinoless ββ decay is related to the matrix element M^(2ν)_(cl) governing the allowed two-neutrino ββ decay. That relation is revealed when these matrix elements are expressed as functions of the relative distance r between the pair of neutrons that are transformed into a pair of protons in the ββ decay. Analyzing this relation allows us to understand the contrasting behavior of these matrix elements when A and Z is changed; while M^(0ν)_(GT) changes slowly and smoothly, M^(2ν) has pronounced shell effects. We also discuss the possibility of phenomenological determination of the M^(2ν)_(cl) and from them of the M^(0ν)_(GT)values from the experimental study of the β^± strength functions.
