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![(Color online) The 0νββ matrix element as a function of maximum seniority included in the SM wave functions for 82 Se-82 Kr and of 128 Te-128 Xe. The contributions of seniority 6 and 10 states are appreciably smaller in agreement with the philosophy of the Random Phase Approximation. The data in the figure are taken from Caurier et al. [8].](profile/Fedor-Simkovic/publication/45896387/figure/fig3/AS:669095376736269@1536536177862/Color-online-The-0nbb-matrix-element-as-a-function-of-maximum-seniority-included-in-the.png)
(Color online) The 0νββ matrix element as a function of maximum seniority included in the SM wave functions for 82 Se-82 Kr and of 128 Te-128 Xe. The contributions of seniority 6 and 10 states are appreciably smaller in agreement with the philosophy of the Random Phase Approximation. The data in the figure are taken from Caurier et al. [8].
Source publication
The methods used till now to calculate the neutrinoless double beta decay matrix elements are: the Quasiparticle Random Phase Approximation (QRPA), the Shell Model (SM), the angular momentum projected Hartee-Fock-Bogoliubov approach (HFB) and the Interacting Boson Model (IBM). The different approaches are compared specifically concerning the the an...
Contexts in source publication
Context 1
... [8,10,11]. However, contributions of the seniority six and ten admixtures to the neutrinoless double beta decay probability are suppressed according to the philosophy of the Random Phase Approach, that the ring diagrams are the leading ones (see also figure 4). ...
Context 2
... the RPA is approximately correct, since the ring diagrams give the most important ground state correlations. The contributions of seniority 6 and 10 to M 0ν are suppressed compared to the others (see figure 4). Figures 2 and 3 show the QRPA contributions of different angular momenta of the neutron pairs, which are changed in proton pairs with the same angular momenta. ...
Context 3
... radius parameter is chosen to be r 0 = 1.2 fm. Figure 4 shows for 82 Se and for 128 Te the influence of different seniority states in the SM [8]. A seniority zero pair corresponds to a zero angular momentum neutron pair, which can be changed into a zero seniority proton pair. ...
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... To explore the β-decay properties and get a better knowledge of the stellar dynamics, numerous attempts have been made previously. The calculations of Takahashi et al [10] based on gross theory, QRPA-based computations (e.g., [11][12][13][14]), and shell model calculations (e.g., [15]), are noticeable mentions. The gross theory computations failed to give structural information about each nucleus. ...
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... The neutrinoless DBDs occur in medium-mass nuclei that are often far from closed shells and, as a consequence, the calculations are mostly made in the proton-neutron quasiparticle random phase approximation (pn-QRPA), since this tool is computationally much simpler than the SM. As discussed in Ref. [8], the kind of correlations that these two methods include are not the same. The pn-QRPA deals with a large fraction of nucleons in a large single-particle space, but within a modest configuration space. ...
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... (3) The F strengths S {2} 00 deviate quite significantly from the sum rule strengths S {2} 00 -24% and 40%, respectively, within the spe spaces e expt j and e j in 48 Ca, 8 Note that the present calculations were done in a single-particle space consisting of the 2p-1 f -2s-1d shells for both protons and neutrons. and 14% in 96 Ru. ...
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... Deficiencies of the pnQRPA formalism have been analyzed against the ISM formalism, e.g., in [199] by using a seniority-based scheme where the pnQRPA was considered to be a low-seniority approximation of the ISM. On the other hand, the ground-state correlations of the pnQRPA introduce higher-seniority components to the pnQRPA wave functions and the deficiencies stemming from the incomplete seniority content of the pnQRPA should not be so severe [200]. Schematic or G-matrix-based boson-exchange Hamiltonians have widely been used in the calculations. ...
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... In that work the pnQRPA was considered to be a low-seniority approximation of the ISM. But on the other hand, the ground-state correlations of the pnQRPA introduce higher-seniority components to the pnQRPA wave functions and the deficiencies stemming from the incomplete seniority content of the pnQRPA should not be so bad [108]. Also the renormalization problems of the two-body interaction are not so severe as in the ISM due to the possibility to use large single-particle model spaces. ...
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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
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Clearly, the accuracy of the determination of the effective Majorana neutrino
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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.
A new model, based on the BCS approach, is specially designed to describe nuclear phenomena $(A,Z)\rightarrow (A,Z\pm 2)$ of double-charge exchange (DCE). After being proposed, and applied in the particle-hole limit, by one of the authors (F. Krmpoti\'c [1]), so far it was never been applied within the BCS mean-field framework, nor has its ability to describe DCE processes been thoroughly explored. It is a natural extension of the pn-QRPA model, developed by Halbleib and Sorensen [2] to describe the single $\beta$-decays $(A,Z)\rightarrow (A,Z\pm 1)$, to the DCE processes. As such, it exhibits several advantages over the pn-QRPA model when is used in the evaluation of the double beta decay (DBD) rates. For instance, i) the extreme sensitivity of the nuclear matrix elements (NMEs) on the model parametrization does not occur, ii) it allows to study NMEs, not only for the fundamental state in daughter nuclei, as the pn-QRPA model does, but also for all final $0^+$ and $2^+$ states, accounting at the same time their excitation energies and the corresponding DBD Q-values, iii) together with the DBD-NMEs it provides also the energy spectra of Fermi and Gamow-Teller DCE transition strengths, as well as the locations of the corresponding resonances and their sum rules, iv) the latter are relevant for both the DBD and the DCE reactions, since the involved nuclear structure is the same; this correlation does not exist within the pn-QRPA model. As an example, detailed numerical calculations are presented for the $(A,Z)\rightarrow (A,Z+ 2)$ process in $^{48}$Ca $\rightarrow ^{48}$Ti and the $(A,Z)\rightarrow (A,Z- 2)$ process in $^{96}$Ru $\rightarrow ^{96}$Mo, involving all final $0^+$ states and $2^+$ states.
We use the available experimental Gamow-Teller β− and β+/EC (electron-capture) decay rates between 0+ and 1+ ground states in neighboring even-even and odd-odd nuclei, combined with 2νββ half-lives, to analyze the influence of the nuclear environment on the weak axial-vector strength gA. For this purpose, the proton-neutron deformed quasiparticle random-phase approximation (pn-dQRPA), with schematic dipole residual interaction is employed. The Hamiltonian contains particle-hole (ph) and particle-particle (pp) channels with mass-dependent strengths. In deriving the equations of motion we use a self-consistent procedure in terms of a single-particle basis with projected angular momentum provided by the diagonalization of a spherical mean field plus the quadrupole-quadrupole interaction. Our analysis evidenced a quenched average effective value 〈gA〉≈0.7 with a root-mean-square deviation of σ≈0.3 for transitions from even-even emitters and σ≈0.6 for transitions from odd-odd emitters.
In this paper, with restored isospin symmetry, we evaluated the neutrinoless double-β-decay nuclear matrix elements for Ge76, Se82, Te130, Xe136, and Nd150 for both the light and heavy neutrino mass mechanisms using the deformed quasiparticle random-phase approximation approach with realistic forces. We give detailed decompositions of the nuclear matrix elements over different intermediate states and nucleon pairs, and discuss how these decompositions are affected by the model space truncations. Compared to the spherical calculations, our results show reductions from 30% to about 60% of the nuclear matrix elements for the calculated isotopes mainly due to the presence of the BCS overlap factor between the initial and final ground states. The comparison between different nucleon-nucleon (NN) forces with corresponding short-range correlations shows that the choice of the NN force gives roughly 20% deviations for the light exchange neutrino mechanism and much larger deviations for the heavy neutrino exchange mechanism.
We apply the proton-neutron deformed quasiparticle random-phase approximation (pn-dQRPA) to describe the low-lying (E≤6 MeV) 1+ Gamow-Teller (GT) strength functions in odd-odd deformed nuclei which participate as intermediate nuclei in two-neutrino double-β-decay (2νββ) transitions within the mass range A=70-176. In deriving equations of motion we use a single-particle basis with projected angular momentum, provided by the diagonalization of a spherical mean field furnished with a quadrupole-quadrupole interaction. The schematic residual Hamiltonian contains pairing and proton-neutron interaction terms in particle-hole (ph) and particle-particle (pp) channels, with constant strengths. By adopting constant particle-hole and particle-particle strengths we are able to describe the positions of the giant GT resonance and the measured half-lives of the 2νββ decays over the whole mass range A=70-176. At the same time we obtain a good agreement with the measured low-lying GT β- strength functions. By using the adopted ph and pp strengths, we predict the half-lives of a number of deformed 2νββ emitters and the low-lying GT strength functions of the corresponding odd-odd intermediate nuclei for their possible experimental tests in the future.
