Search

The fundamental importance of searching for neutrinoless double-beta decay is widely recognized. Observation of the decay would tell us that the total lepton number is not conserved and that, consequently, neutrinos are massive Majorana fermions. The same statement could be made in the case of observing neutrinoless double-electron capture. We address the question of the sensitivity of the 0 ν e e decay to the effective mass of the Majorana neutrino. According to our estimates, in the case of 152Gd and 164Er the sensitivity can be comparable to the favored 0 ν β β decays of nuclei. The main uncertainty in the prediction of half-lives of the 0 ν e e decay stems from the lack of sufficient precision in measuring the mass difference between the parent and daughter atoms. More accurate measurements can be accomplished using the modern high-precision ion traps.

A brief review of recent progress in the field of double beta decay is presented. Different aspects from particle, nuclear and atomic physics of both two-neutrino ( 2 ν β β ) and neutrinoless ( 0 ν β β ) modes of the double β decay are discussed. It is argued that the R-parity violating supersymmetry ( ⁄ R p SUSY) contributes to the 0 ν β β -decay predominantly via charged pion-exchange between decaying nucleons. Further, a problem of reliable determination of the 0 ν β β -decay nuclear matrix elements (NMEs) is addressed. It is manifested that the uncertainty associated with the calculation of the 0 ν β β -decay NMEs can be diminished by suitably chosen nuclear probes. A new possibility for the study of lepton number non-conservation is proposed, namely oscillations plus deexcitations of neutral atoms. A phenomenological analysis of this process leads to a resonant enhancement of the neutrinoless double electron capture, that has a Breit–Wigner form.

We discuss oscillations of two neutral atoms which proceed with the violation of lepton number. One of the neutral atoms is stable, the other one represents a quasistationary state subjected to electromagnetic deexcitation. The system of neutral atoms exhibits oscillations similar to those of the system of neutral kaons and neutron-antineutron oscillations in the nuclear medium. The underlying mechanism is a transition of two protons and two bound electrons to two neutrons p + p + eb− + eb− ↔ n + n. A signature of the oscillations might be an electromagnetic deexcitation of the involved unstable nucleus and atomic shell with the electron holes. A resonant enhancement of the neutrinoless double electron capture takes place when the atomic masses tend to be degenerate. Qualitative estimates show that in searches for lepton number violation oscillations of atoms might be a possible alternative to the conventional mechanism of the neutrinoless double β decay process with emission of two electrons.

We assume that the Pauli exclusion principle is violated for neutrinos, and thus, neutrinos obey at least partly the Bose-Einstein statistics. The parameter sin^2 chi is introduced that characterizes the bosonic (symmetric) fraction of the neutrino wave function. Consequences of the violation of the exclusion principle for the two-neutrino double beta decays are considered. This violation strongly changes the rates of the decays and modifies the energy and angular distributions of the emitted electrons. Pure bosonic neutrinos are excluded by the present data. In the case of partly bosonic (or mixed-statistics) neutrinos the analysis of the existing data allows to put the conservative upper bound sin^2 chi < 0.6. The sensitivity of future measurements of the two-neutrino double beta decay to sin^2 chi is evaluated., 25 pages including 8 eps figures

Theoretical estimates for the half-life of neutrinoless double beta decay ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) in candidate nuclei are affected by both particle and nuclear physics uncertainties, which may complicate the interpretation of decay signals or limits. We study such uncertainties and their degeneracies in the following context: three $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ nuclei of great interest for large-scale experiments ($^{76}\mathrm{Ge}$, $^{130}\mathrm{Te}$, $^{136}\mathrm{Xe}$), two representative particle physics mechanisms (light and heavy Majorana neutrino exchange), and a large set of nuclear matrix elements (NME), computed within the quasiparticle random phase approximation (QRPA). It turns out that the main theoretical uncertainties, associated with the effective axial coupling ${g}_{A}$ and with the nucleon-nucleon potential, can be parametrized in terms of NME rescaling factors, up to small residuals. From this parametrization, the following QRPA features emerge: (1) the NME dependence on ${g}_{A}$ is milder than quadratic, (2) in each of the two mechanisms, the relevant lepton number violating parameter is largely degenerate with the NME rescaling factors, and (3) the light and heavy neutrino exchange mechanisms are basically degenerate in the above three nuclei. We comment on the challenging theoretical and experimental improvements required to reduce such particle and nuclear physics uncertainties and their degeneracies.

The extension of the Majorana neutrino mass mechanism of the neutrinoless double-beta decay (0νββ) with the inclusion of right-handed leptonic and hadronic currents is revisited. While only the exchange of light neutrinos is assumed, the s_(1/2) and p_(1/2) states of emitted electrons as well as recoil corrections to the nucleon currents are taken into account. Within the standard approximations the decay rate is factorized into a sum of products of kinematical phase-space factors, nuclear matrix elements, and the fundamental parameters that characterize the lepton number violation. Unlike in the previous treatments, the induced pseudoscalar term of hadron current is included, resulting in additional nuclear matrix elements. An improved numerical computation of the phase-space factors is presented, based on the exact Dirac wave functions of the s_(1/2) and p_(1/2) electrons with finite nuclear size and electron screening taken into account. The dependence of values of these phase-space factors on the different approximation schemes used in evaluation of electron wave functions is discussed. The upper limits for effective neutrino mass and the parameters ⟨λ⟩ and ⟨η⟩ characterizing the right-handed current mechanism are deduced from data on the 0νββ decay of ^(76)Ge and ^(136)Xe using nuclear matrix elements calculated within the nuclear shell model and quasiparticle random phase approximation. The differential decay rates, i.e., the angular correlations and the single electron energy distributions for various combinations of the total lepton number violating parameters that can help to disentangle the possible mechanism, are described and discussed.

Estimates of nuclear matrix elements for neutrinoless double beta decay (0nu2beta) based on the quasiparticle random phase approximations (QRPA) are affected by theoretical uncertainties, which can be substantially reduced by fixing the unknown strength parameter g_pp of the residual particle-particle interaction through one experimental constraint - most notably through the two-neutrino double beta decay (2nu2beta) lifetime. However, it has been noted that the g_pp adjustment via 2\nu2\beta data may bring QRPA models in disagreement with independent data on electron capture (EC) and single beta decay (beta^-) lifetimes. Actually, in two nuclei of interest for 0nu2beta decay (Mo-100 and Cd-116), for which all such data are available, we show that the disagreement vanishes, provided that the axial vector coupling g_A is treated as a free parameter, with allowance for g_A0) by the combination of all data. We discuss quantitatively, in each of the two nuclei, these phenomenological constraints and their consequences for QRPA estimates of the 0nu2beta matrix elements and of their uncertainties., Comment: Revised version (27 pages, including 10 figures), focussed on Mo-100 and Cd-116. To appear in J. Phys. G: Nucl. Phys. (2008)

The NEMO-3 detector, which had been operating in the Modane Underground Laboratory from 2003 to 2010, was designed to search for neutrinoless double $\beta$ ($0\nu\beta\beta$) decay. We report final results of a search for $0\nu\beta\beta$ decays with $6.914$ kg of $^{100}$Mo using the entire NEMO-3 data set with a detector live time of $4.96$ yr, which corresponds to an exposure of 34.3 kg$\cdot$yr. We perform a detailed study of the expected background in the $0\nu\beta\beta$ signal region and find no evidence of $0\nu\beta\beta$ decays in the data. The level of observed background in the $0\nu\beta\beta$ signal region $[2.8-3.2]$ MeV is $0.44 \pm 0.13$ counts/yr/kg, and no events are observed in the interval $[3.2-10]$ MeV. We therefore derive a lower limit on the half-life of $0\nu\beta\beta$ decays in $^{100}$Mo of $T_{1/2}(0\nu\beta\beta)> 1.1 \times 10^{24}$ yr at the $90\%$ Confidence Level, under the hypothesis of light Majorana neutrino exchange. Depending on the model used for calculating nuclear matrix elements, the limit for the effective Majorana neutrino mass lies in the range $\langle m_{\nu} \rangle < 0.33$--$0.62$ eV. We also report constraints on other lepton-number violating mechanisms for $0\nu\beta\beta$ decays.

Ground states of even-even Ge isotopes with mass number $A=64\text{--}76$ have been studied in the deformed Bardeen-Cooper-Schrieffer (BCS) theory by taking neutron-proton $(np)$ pairing correlations as well as neutron-neutron $(nn)$ and proton-proton $(pp)$ pairing correlations. The $np$ pairing has two different modes $J=0,\phantom{\rule{4pt}{0ex}}T=1$ (isotriplet) and $J=1,\phantom{\rule{4pt}{0ex}}T=0$ (isosinglet). In this work, the Brueckner $G$ matrix, based on the CD-Bonn potential, has been exploited to reduce the ambiguity regarding nucleon-nucleon interactions inside nuclei compared to the results by a simple schematic phenomenological force. We found that the $G$ matrix plays important roles to obtain reasonable descriptions of even-even nuclei compared to the schematic force. The $np$ pairing strength has been shown to have a clear correlation with quadrupole deformation parameter ${\ensuremath{\beta}}_{2}$ for the isotopes, and affects the smearing of the Fermi surfaces of not only $N=Z$ nuclei but also $N\ensuremath{\ne}Z$ nuclei. In particular, the coexistence of the like particle ($nn$ and $pp$) and the $np$ pairing modes was found to become more salient by the $G$-matrix approach than by the schematic force approach.

In this work, we calculate the matrix elements for the $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay of $^{150}\mathrm{Nd}$ using the deformed quasiparticle random-phase approximation $(pn$-QRPA) method. We adopted the approach introduced by Rodin and Faessler [Phys. Rev. C 84, 014322 (2011)] and Simkovic et al. [Phys. Rev. C 87, 045501 (2013)] to restore the isospin symmetry by enforcing ${M}_{F}^{2\ensuremath{\nu}}=0$. We found that with this restoration, the Fermi matrix elements are reduced in the strongly deformed $^{150}\mathrm{Nd}$ by about 15 to 20%, while the more important Gamow-Teller matrix elements remain the same. The results of an enlarged model space are also presented. This enlargement increases the total (Fermi plus Gamow-Teller) matrix elements by less than 10%.

International audience; A new experimental run of searching for double beta decay of (106)Cd was performed at the Modane underground laboratory (LSM, France, 4800 m w.e.) using the TGV-2 spectrometer, consisting of 32 planar type HPGe detectors with a total sensitive volume of ~400 cm(3). 16 foils of (106)Cd with an enrichment of 99.57% and a total mass of ~ 23.2 g were inserted between the entrance windows of face-to-face detectors. The limit on 2vEC/EC decay of (106)Cd - T(1/2) > 3.7 × 10(20) y at 90% C.F was obtained from the preliminary calculation of experimental data accumulated for 8198 h of measurement. The limits on the resonance OvEC/EC decay of (106)Cd were obtained from the measurement of ~23.2 g of (106)Cd with the low-background HPGe spectrometer Obelix lasted 395 h -T(1/2) (KF, 2741 keV) > 0.9 × 10(20) y and T(1/2) (KK, 2718 keV) > 1.4 × 10(20) y at 90% C.L.

The two-neutrino double-β Gamow-Teller and Fermi transitions are studied within an exactly solvable model, which allows a violation of both spin-isospin SU(4) and isospin SU(2) symmetries, and is expressed with generators of the SO(8) group. It is found that this model reproduces the main features of realistic calculation within the quasiparticle random-phase approximation with isospin symmetry restoration concerning the dependence of the two-neutrino double-β decay matrix elements on isovector and isoscalar particle-particle interactions. By using perturbation theory an explicit dependence of the two-neutrino double-β decay matrix elements on the like-nucleon pairing, particle-particle T = 0 and T = 1, and particle-hole proton-neutron interactions is obtained. It is found that double-β decay matrix elements do not depend on the mean field part of Hamiltonian and that they are governed by a weak violation of both SU(2) and SU(4) symmetries by the particleparticle interaction of Hamiltonian. It is pointed out that there is a dominance of two-neutrino double-β decay transition through a single state of intermediate nucleus. The energy position of this state relative to energies of initial and final ground states is given by a combination of strengths of residual interactions. Further, energy-weighted Fermi and Gamow-Teller sum rules connecting ∆Z = 2 nuclei are discussed. It is proposed that these sum rules can be used to study the residual interactions of the nuclear Hamiltonian, which are relevant for charge-changing nuclear transitions.

Ho to 163 Dy is probably due to the small Q value of about 2.5 keV the best case to determine the neutrino mass by electron capture. The energy of the Q value is distributed between the excitation of Dysprosium (and the neglected small recoil of Holmium) and the relativistic energy of the emitted neutrino including the rest mass. The reduction of the upper end of the deexcitation spectrum of Dysprosium below the Q value allows to determine the neutrino mass. The excitation of Dysprosium can be calculated in the sudden approximation of the overlap of the electron wave functions of Holmium minus the captured electron and one- , two-, three- and multiple hole- excitations in Dysprosium. Robertson (R. G. H. Robertson, Phys. Rev. C91, 035504 (2015) and arViv: 1411.2906) and Faessler and Simkovic (Amand Faessler, Fedor Simkovic, accepted for Phys. Rev. C, March 2015 and arXiv: 1501.04338) have calculated the influence of the two-hole states on the Dysprosium spectrum. Here for the first time the influence of the three-hole states on the deexcitation bolometer spectrum of 163 Dysprosium is presented. The electron wave functions and the overlaps are calculated selfconsistently in a fully relativistic and antisymmetrized Dirac- Hartree-Fock approach in Holmium and in Dysprosium. The electron orbitals in Dy are determined including the one-hole states in the selfconsistent iteration. The influence of the three-hole states on the Dy deexcitation (by X-rays and Auger electrons) can hardly be seen. The three-hole states seem not to be relevant for the determination of the electron neutrino mass.

The atomic pair $^{163}\mathrm{Ho}$ and $^{163}\mathrm{Dy}$, because of its small $Q$ value of about 2.5 keV, seems to be the best pair to use to determine the neutrino mass by electron capture. The bolometer spectrum measures the full deexcitation energy of dysprosium (by x rays and Auger electrons plus the recoil of holmium, which can be neglected). The spectrum has an upper limit given by the $Q$ value minus the neutrino mass. Till now this spectrum has been calculated in dysprosium allowing excitations with $3{s}_{1/2}, 3{p}_{1/2}, 4{s}_{1/2}, 4{p}_{1/2}, 5{s}_{1/2}$, and $5{p}_{1/2}$ (and $6{s}_{1/2}$) holes only. Robertson [R. G. H. Robertson, arXiv:1411.2906v1] also recently calculated the spectrum with two-electron-hole excitations in Dy. He took the probability for the excitation for the second electron hole from the work of Carlson and Nestor [T. A. Carlson, C. W. Nestor, T. C. Tucker, and F. B. Malik, Phys. Rev. 169, 27 (1968); T. A. Carlson and C. W. Nestor, Phys. Rev. A 8, 2887 (1973)] for $Z=54$ xenon. The neutrino mass must finally be obtained by a simultaneous fit of the $Q$ value, together with the properties of the relevant resonances, and the neutrino mass to the the upper end of the spectrum. Under the assumption that only one resonance (independent of its nature: one-hole, two-hole, multihole, or of other origin) near the $Q$ value determines the upper end of the spectrum and that the profile of this leading state is Lorentzian, one has to fit simultaneously four parameters (neutrino mass, strength, distance of the leading resonance to the $Q$ value, and width). If more than one resonance is of comparable importance for the upper end of the spectrum, it might be difficult or even impossible to extract the neutrino mass reliably. Compared to the work of Robertson this work includes the following improvements. (i) The two-hole probabilities are calculated in the Dirac-Hartree-Fock (DHF) approach for holmium and dysprosium but not for xenon. (ii) In calculating the probability for the second electron hole in dysprosium the $n{s}_{1/2}$ or $n{p}_{1/2}$ ($n\ensuremath{\ge}3$) one-hole states are included self-consistently in the DHF iteration. (iii) Because dysprosium has $Z=66$ electrons and xenon only has $Z=54$ electrons, one has at least eight additional two-hole states that do not exist in xenon and thus their probabilities have not been calculated by Carlson and Nestor and have not been included by Robertson. They are included here. (iv) For the probabilities of the one-hole states, which determine the main structure of the spectrum, the overlap and exchange corrections are taken into account. (v) In solving the DHF electron wave functions the finite size of the nuclear charge distribution is included. (vi) The nuclear matrix elements for electron capture integrate the charge of the captured electron over the nucleus with the weight $\ensuremath{\psi}{(r)}_{e,n,\ensuremath{\ell},j}^{2}{r}^{2}$. Thus, for the capture probability the value ${\ensuremath{\psi}}_{e,n,\ensuremath{\ell},j}^{2}(R){R}^{2}$ is taken at the nuclear radius and not the value ${\ensuremath{\psi}}_{e,n,\ensuremath{\ell},j}^{2}(r=0.0)$ at $r=0.0$, which has the weight ${r}^{2}$ zero. (vii) The formulas are derived in second quantization including automatically the antisymmetrization.

The longitudinal form factors of the weak vector current of particles with spin $ J = 1/2 $ and isospin $ I = 1/2 $ are determined by the mass difference and the charge radii of members of the isotopic doublets. The most promising reactions to measure these form factors are the reactions with large momentum transfers involving the spin-1/2 isotopic doublets with a maximum mass splitting. Numerical estimates of longitudinal form factors are given for nucleons and eight nuclear spin-1/2 isotopic doublets., Comment: 6 pages. Talk given at the 10th MEDEX'15 meeting Matrix Elements for the Double-beta-decay Experiments, Prague, June 9-12, 2015

International audience; A new experimental run of searching for EC/EC decay of Cd-106 was performed at the Modane underground laboratory (4800 m w.e.) using the TGV-2 spectrometer and similar to 23.2 g Cd-106 with enrichment of 99.57%. The limit on 2 nu EC/EC decay of Cd-106 -T-1/2(2 nu EC/EC) > 3.1x10(20) y, at 90% C. L was obtained from the preliminary calculation of experimental data accumulated for 7018 h of measurement. The limits on the resonance neutrino-less double electron capture decay of Cd-106 were obtained from the measurement of similar to 23.2 g of Cd-106 with the low-background HPGe spectrometer OBELIX lasted 395 h -T-1/2(KL, 2741 keV) > 0.9x10(20) y and T-1/2(KK, 2718 keV) > 1.4x10(20) y at 90% C.L.

The measurement of the electron energy spectrum in single β decays close to the endpoint provides a direct determination of the neutrino masses. The most sensitive experiments use β decays with low Q value, e.g. KATRIN (tritium) and MARE (rhenium). We present the theoretical spectral shape of electrons emitted in the first, second, and fourth unique forbidden β decays. Our findings show that the Kurie functions for these unique forbidden β transitions are linear in the limit of massless neutrinos like the Kurie function of the allowed β decay of tritium.

We propose a novel extension of the standard quasiparticle random phase approximation (QRPA) with a new form of phonon operator, which allows to describe also states of multiphonon origin. We denote this method as QRPA with non-linear phonon operator (nlQRPA) and apply it to the proton-neutron Lipkin model. We consider the simplest non-linear extension of a phonon operator where the RPA equation can be transformed into a standard form. That guarantees the orthonormality and completeness of the QRPA states of one-phonon and three-phonon origin. A rather good agreement is found both for energies and beta transition amplitudes with those obtained by a diagonalization of the schematic Hamiltonian. There is straightforward way to extend this approach also for a realistic nuclear structure calculations.

Double electron capture has been of interest of many theoretical and experimental works as a possible extension of double beta-decay investigations. The neutrinoless double-electron capture, similarly as the neutrinoless double beta-decay may help to clarify if neutrinos are Majorana or Dirac particles. Results obtained in several double electron capture experiments are reviewed and new experiments to be carried out in deep underground laboratories using enriched sources and multidimensional HPGe-HPGe gamma-ray spectrometry with a few years of counting time are proposed, which should be able to improve half-lives limits by at least an order of magnitude.

We present a derivation of the total cross section for inelastic scattering of low-energy solar neutrinos and reactor antineutrinos on bound electrons, resulting in a transition of the electron to an excited state. The atomic-shell structure of various chemical elements is treated in terms of a nonrelativistic approximation. We estimate the interaction rates for modern neutrino detectors, in particular the Borexino and GEMMA experiments. We establish that in these experiments the effect can be safely neglected, but it could be accessible to future large-volume neutrino detectors with low energy threshold.

Possible nature of strongly magnetized white dwarfs (SMWDs) is studied. It is shown that for relatively low values of the equatorial surface magnetic field $B\,\sim\,10^9\,-\,10^{11}$ G they can be good candidates for soft gamma-ray repeaters and anomalous X-ray pulsars (SGRs/AXPs). For the case of iron SMWDs the influence of a neutrinoless electron to positron conversion on the SGRs/AXPs luminosity is estimated., Comment: 4 pages, contribution to the proceedings of the Workshop on calculation of double-beta-decay matrix elements (MEDEX'15), Prague, 9-12 June 2015, eds. O. Civitarese, I. Stekl and J. Suhonen

The neutrinoless double-beta (0νββ) decay associated with light neutrino exchange mechanisms, which are due to both left-handed V-A and right-handed V+A leptonic and hadronic currents, is discussed by using the recent progress achieved by the GERDA, EXO and KamlandZen experiments. The upper limits for effective neutrino mass mββ and the parameters 〈λ〉 and 〈η〉 characterizing the right handed current mechanisms are deduced from the data on the 0νββ-decay of 76Ge and 136Xe using nuclear matrix elements calculated within the nuclear shell model and quasiparticle random phase approximation and phase-space factors calculated with exact Dirac wave functions with finite nuclear size and electron screening. The careful analysis of upper constraints on effective lepton number violating parameters assumes a competition of the above mechanisms and arbitrary values of involved CP violating phases.

The low-background multi-HPGe spectrometer TGV II installed in the Modane Underground Laboratory (France) is described in detail and the results of the background measurements are reported. The spectrometer is focused on the double beta decay measurements with two isotopes—106Cd ( 2 ν EC / EC mode) and 48Ca ( β β mode). A basic summary of the physics of β β decay (especially EC/EC mode) is also given.

After the discovery of neutrino oscillations, the search for the 0 ν β β -decay became one of the most fundamental problems of neutrino physics. In this contribution the recent developments in the field of nuclear double beta decay are reviewed. The light Majorana neutrino mass mechanism of the neutrinoless double beta decay ( 0 ν β β -decay) is discussed in the context of recent neutrino oscillation data. The expected half-lives of the 0 ν β β -decay are calculated by assuming the normal and inverted hierarchy of neutrino masses. The problem of reliable determination of the 0 ν β β -decay nuclear matrix elements is addressed. A sterile neutrino ν h contribution to the 0 ν β β -decay is investigated. From the lower bound on the 0 ν β β -decay half-life stringent constraints on the ν h − ν e mixing in a wide region of sterile neutrino masses are derived.

The nuclear matrix elements $M^{0\nu}$ of the neutrinoless double beta decay ($0\nu\beta\beta$) of most nuclei with known $2\nu\beta\beta$-decay rates are systematically evaluated using the Quasiparticle Random Phase Approximation (QRPA) and Renormalized QRPA (RQRPA). The experimental $2\nu\beta\beta$-decay rate is used to adjust the most relevant parameter, the strength of the particle-particle interaction. With such procedure the $M^{0\nu}$ values become essentially independent on 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 $M^{0\nu}$'s can be ascribed to the choices of implicit and explicit parameters, inherent to the QRPA method.

The nuclear matrix elements M 0 ν of the neutrinoless double beta decay ( 0 ν β β ) of most nuclei with known 2 ν β β -decay rates are systematically evaluated using the quasiparticle random phase approximation (QRPA) and renormalized QRPA (RQRPA). The experimental 2 ν β β -decay rate is used to adjust the most relevant parameter, the strength of the particle–particle interaction. New results confirm that with such procedure the M 0 ν values become essentially independent on the size of the single-particle basis. Furthermore, the matrix elements are shown to be also rather stable with respect to the possible quenching of the axial vector strength parametrized by reducing the coupling constant g A , as well as to the uncertainties of parameters describing the short range nucleon correlations. Theoretical arguments in favor of the adopted way of determining the interaction parameters are presented. Furthermore, a discussion of other implicit and explicit parameters, inherent to the QRPA method, is presented. Comparison is made of the ways these factors are chosen by different authors. It is suggested that most of the spread among the published 0 ν β β decay nuclear matrix elements can be ascribed to these choices.

The systematic study of (anti)neutrino accompanied β ± β ± decays and β + / EC , EC / EC electron capture is performed under the assumption of single intermediate nuclear state dominance. The corresponding half-lives are evaluated both for transitions to the ground state as well as to the 0 + and 2 + excited states of final nucleus. It is stressed that the hypothesis of single state dominance can be confirmed or ruled out by the precision measurements of the differential characteristics of the 2 ν β − β − -decays of 100 Mo and 116 Cd as well as β + / EC electron capture in 106 Cd, 130 Ba and 136 Ce.

We study nuclear mu-e conversion in the general framework of an effective Lagrangian approach without referring to any specific realization of the physics beyond the standard model (SM) responsible for lepton flavor violation (LFV). We show that vector meson exchange between lepton and nucleon currents plays an important role in this process. A new issue of this mechanism is the presence of the strange quark vector current contribution induced by the phi meson. This allows us to extract new limits on the LFV lepton-quark effective couplings from the existing experimental data., 11 pages, 1 figure, to be published in Phys. Lett. B

The effect of deformation on the two-neutrino double-beta decay (2νββ decay) for ground-state transition 76Ge → 76Se is studied in the framework of the deformed QRPA with separable Gamow-Teller residual interaction. A new suppression mechanism of the 2νββ-decay matrix element based on the difference in deformations of the initial and final nuclei is reported. 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.

The effect of deformation on the two-neutrino double decay (2 νββ -decay) for ground state transition 76 Ge → 76 Se 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 2 νββ -decay matrix element is suppressed with respect to the case of 2 νββ 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 2 νββ -decay. By performing a detail calculation of the 2 νββ -decay of 76 Ge, 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.

We investigate neutrino flux induced double beta transitions in targets built of Cd112, Cd114, Cd116 and O18 isotopes. In addition to known beta^- beta^- channel we consider new beta^- beta^+ and beta^- beta^+ gamma modes of the neutrino induced double beta process. A possibility of detection of the solar neutrinos via the induced double beta transitions of interest is discussed. We note that the beta^- part of the solar neutrino induced beta^- beta^+ process in O18 was already discussed in Ref. [9,10] in connection with a possible influence of high energy electron production of this origin on the SuperKamiokande results.

The non-photonic neutrino exchange mechanism of the lepton flavor violating muon-electron conversion in nuclei is revisited. First we determine the nucleon coupling constants for the neutrino exchange mechanism in a relativistic quark model taking into account quark confinement and chiral symmetry requirements. This includes a new, previously overlooked tree-level contribution from neutrino exchange between two quarks in the same nucleon. Then for the case of an additional sterile neutrino we reconsider the coherent mode of this process. The presence of a mixed sterile-active neutrino state heavier than the quark confinement scale Lambda_c (~1 GeV) may significantly improve the prospects for observation of this process in future experiments as compared to the conventional scenario with only light neutrinos. Turning the arguments around we derive new experimental constraints on |U_(mu h)| and |U_(e h)| mixing matrix elements from the non-observation of muon--electron conversion.

We have used a self-consistent version of the BCS + RQRPA method for a systematic study of the two-neutrino double-beta decay of nuclei with 100

The time integral representation of the many-body Green function describing the two-neutrino double-beta-decay (2νββ-decay) matrix element is used in schematic calculations within the proton-neutron Lipkin model. The two-body Hamiltonian considered includes a quadratic polynomial in bosons to describe the motion of the selected degrees of freedom. The beta-transition operators also include higher-order terms in the boson expansion. They have been shown to be of crucial importance in the determination of the 2νββ-decay matrix element M F. We have found that in the standard QRPA approach, which exploits the form of M F with denominator, there is a dominant unphysical contribution to M F arising from the non-orthogonality of the initial and final quasiparticle ground states. The physical part of M F is negligible for small values of the particle-particle interaction strength, i.e., it exhibits a different behavior as that known from the QRPA approaches.

The detection of solar-neutrinos of different origin via induced ββ process of 100Mo is investigated. The particular counting rates and energy distributions of emitted electrons are presented. A discussion in respect to the solar-neutrino detector consisting of 10 tones of 100Mo is included. Both the cases of the standard solar model and neutrino oscillation scenarios are analyzed. Moreover, new β-β+ and β-/EC channels of the double-beta process are introduced and possibilities of their experimental observation are addressed.

Present status of the experiment TGV II is given. The experiment TGV II is devoted to the measurement of double-beta decay of 106Cd and 48Ca. The new HPGe multi-detector TGV spectrometer has been constructed and installed in the Modane underground laboratory (in France). Preliminary results of the first background measurement are presented.

A new ansatz for the correlated ground state of the many-nucleon system is proposed which results in obtaining a modified Quasiparticle Random Phase Approximation (QRPA). An additional degree of freedom is introduced which allows to determine variationally the ground state simultaneously with solving the QRPA equations. This new approach, QRPA with an optimal ground state, is studied within the proton-neutron Lipkin model. New solutions have been found, in the range of the interaction strength where the standard QRPA formalism does not work. A relation between one of them and the solution obtained within a semi-classical approach is established. A detailed study of the expectation value of the quasiparticle number operator in the ground state and the transition amplitude for the two-neutrino double beta Fermi decay, is also presented.

The neutrinoless double-beta decay (0νββ decay) to the first excited 0+ collective final state is examined for A = 76, 82, 100 and 136 nuclei by assuming light Majorana neutrino exchange mechanism. Realistic calculations of nuclear matrix elements are performed within the renormalized Quasiparticle Random Phase Approximation. Transitions to the first excited two-quadrupole phonon 0+ state are described within a boson expansion formalism. It is found that the 100Mo is a good candidate for experimental study of the 0νββ decay to excited 0+ state due to small suppression of this transition relative to the transition to the ground state.

Many new 0νββ-decay experiments are planned or in preparation. If the 0νββ-decay will be detected, the key issue will be what is the dominant mechanism of this process. By measuring only transitions to the ground state one can not distinguish among many of the 0νββ-decay mechanisms (the light and heavy Majorana neutrino exchange mechanisms, the trilinear R-parity breaking mechanisms etc.). We show that if the ratio of the 0νββ-decay half-lifes for transitions to the 0+ first excited and ground states is determined both theoretically and experimentally, it might be possible to determine, which 0νββ-decay mechanisms is dominant. For that purpose the corresponding nuclear matrix elements have to be evaluated with high reliability. The present work is giving strong motivations for experimental studies of the 0νββ-decay transitions to the first excited 0+ states of the final nuclei.

It is shown that the random-phase approximation (RPA) method with its nonlinear generalization, which was previously considered as approximation, reproduces the exact solutions of the Lipkin model. The nonlinear RPA is based on an equation nonlinear on eigenvectors and includes many-particle-many-hole components in the creation operator of the excited states. We demonstrate the exact character of solutions analytically for the particle number $N$ = 2 and, numerically, for $N$ = 20. This finding indicates that the nonlinear RPA is equivalent to the exact Schr\"{o}dinger equation, which opens up new possibilities for realistic calculations in many-body problems., Comment: 17 pages, 9 figures

We revisit the mechanism of neutrinoless double beta (NLDBD) decay mediated by the exchange with the heavy Majorana neutrino N of arbitrary mass mN, slightly mixed with the electron neutrino. By assuming the dominance of this mechanism, we update the well-known NLDBD-decay exclusion plot in the mass-mixing angle plane taking into account recent progress in the calculation of nuclear matrix elements within quasiparticle random phase approximation and improved experimental bounds on the NLDBD-decay half-life of Ge-76 and Xe-136. We also consider the known formula approximating the mN dependence of the NLDBD-decay nuclear matrix element in a simple explicit form. We analyze its accuracy and specify the corresponding parameters, allowing one to easily calculate the NLDBD-decay half-life for arbitrary mN for all the experimentally interesting isotopes without resorting to real nuclear structure calculations., Published version, title modified

Holmium 163 offers perhaps the best chance to determine the neutrino mass by electron capture (EC). This contribution treats the EC in Holmium completely relativistic for the overlap and exchange corrections and the description of the bolometer spectrum. The theoretical expressions are derived consistently in second quantization with the help of Wickʼs theorem assuming single Slater determinants for the initial Ho and the final Dy atoms with holes in the final and states. One needs no hand waving arguments to derive the exchange terms. It seems, that for the first time the multiplicity of electrons in the orbital overlaps are included in the numerical treatment. Electron capture is proportional to the probability to find the captured electron in the parent atom at the nucleus. Non-relativistically this is only possible for electron states. Relativistically also electrons have a probability due to the lower part of the relativistic electron spinor, which does not disappear at the origin. Moreover relativistic effects increase by contraction the electron probability at the nucleus. Capture from other states are suppressed. However they can be allowed with smaller intensity due to finite nuclear size. These probabilities are at least three orders smaller than the EC from and states. The purpose of this work is to give a consistent relativistic formulation and treatment of the overlap and exchange corrections for EC in Ho to excited atomic states in Dy and to show the influence of the different configurations in the final Dy states. The overlap and exchange corrections are essential for the calorimetric spectrum of the de-excitation of the hole states in dysprosium. The slope of the upper end of the spectrum, which contains the information on the electron neutrino mass, is different. In addition the effect of the finite energy resolution on the spectrum and on the determination of the neutrino mass is studied. The neutrino mass must finally be determined by maximum likelihood methods to fit the theoretical spectra at the upper end near the Q value varying the neutrino mass, the Q-value and probably also the energy resolution, because at the moment Q and the energy resolution are not known to the accuracy needed.

We test the effects of an approximate treatment of two-body contributions to the axial-vector current on the quasiparticle random-phase approximation (QRPA) matrix elements for neutrinoless double-beta decay in a range of isotopes. The form and strength of the two-body terms come from chiral effective-field theory. The two-body currents typically reduce the matrix elements by about 20%, not as much as in shell-model calculations. One reason for the difference is that standard practice in the QRPA is to adjust the strength of the isoscalar pairing interaction to reproduce two-neutrino double-beta decay lifetimes. Another may be the larger QRPA single-particle space. Whatever the reasons, the effects on neutrinoless decay are significantly less than those on two-neutrino decay, both in the shell model and the QRPA.

We report the results of a search for the neutrinoless double-$\beta$ decay (0$\nu\beta\beta$) of $^{100}$Mo, using the NEMO-3 detector to reconstruct the full topology of the final state events. With an exposure of 34.7 kg.y, no evidence for the 0$\nu\beta\beta$ signal has been found, yielding a limit for the light Majorana neutrino mass mechanism of $T_{1/2}(0\nu\beta\beta)>1.1 \times 10^{24}$ years (90% C.L.) once both statistical and systematic uncertainties are taken into account. Depending on the Nuclear Matrix Elements this corresponds to an upper limit on the Majorana effective neutrino mass of $ < 0.3-0.8$ eV (90% C.L.). Constraints on other lepton number violating mechanisms of 0$\nu\beta\beta$ decays are also given. Searching for high-energy double electron events in all suitable sources of the detector, no event in the energy region [3.2-10] MeV is observed for an exposure of 47 kg.y.

We discuss a novel effect in neutrinoless double beta (0{\nu}{\beta}{\beta}) decay related with the fact that its underlying mechanisms take place in the nuclear matter environment. We study the neutrino exchange mechanism and demonstrate the possible impact of nuclear medium via Lepton Number Violating (LNV) 4-fermion interactions of neutrino with quarks from decaying nucleus. The net effect of these interactions is generation of an effective in-medium Majorana neutrino mass matrix. The enhanced rate of the 0{\nu}{\beta}{\beta}-decay can lead to the apparent incompatibility of observations of the 0{\nu}{\beta}{\beta}-decay with the value of the neutrino mass determined or restricted by the {\beta}-decay and cosmological data. The effective neutrino masses and mixing are calculated for the complete set of the relevant 4-fermion neutrino-quark operators. Using experimental data on the 0{\nu}{\beta}{\beta}-decay in combination with the {\beta}-decay and cosmological data we evaluate the characteristic scales of the LNV operators: {\Lambda} > 2.4 TeV., Comment: 5 pages REVTeX, accepted for publication in PRL

Double beta decay of $^{100}$Mo to the excited states of daughter nuclei has been studied using a 600 cm$^3$ low-background HPGe detector and an external source consisting of 2588 g of 97.5% enriched metallic $^{100}$Mo, which was formerly inside the NEMO-3 detector and used for the NEMO-3 measurements of $^{100}$Mo. The half-life for the two-neutrino double beta decay of $^{100}$Mo to the excited 0$^+_1$ state in $^{100}$Ru is measured to be $T_{1/2}=[7.5 \pm{0.6}(stat) \pm {0.6}(syst)]\cdot 10^{20}$ yr. For other $(0\nu + 2\nu)$ transitions to the 2$^+_1$, 2$^+_2$, 0$^+_2$, 2$^+_3$ and 0$^+_3$ levels in $^{100}$Ru, limits are obtained at the level of $\sim (0.25-1.1)\cdot 10^{22}$ yr., Comment: 19 pages, 4 figures. arXiv admin note: text overlap with arXiv:0904.1924

A model many-body Hamiltonian describing a heterogenous system of paired protons and paired neutrons and interacting among themselves through monopole particle–hole and monopole particle–particle interactions is used to study the double beta decay of Fermi type. The states are described by time-dependent approaches choosing as trial functions coherent states of the symmetry groups underlying the model Hamiltonian. One formalism, VP1, is fully equivalent with the standard proton–neutron quasiparticle random phase approximation and therefore fails at a critical value of the particle–particle interaction strength while another one, VP2, corresponds to a two-step Bardeen–Cooper–Schrifed (BCS) treatment, i.e., the proton quasiparticles are paired with the neutron quasiparticles. In this way a harmonic description for the double beta transition amplitude is provided for any strength of the particle–particle interaction. The approximation quality is judged by comparing the actual results with the exact result as well as with those corresponding to various truncations of the boson-expanded Hamiltonian and transition operator. Finally, it is shown that the dynamic ground states provided by VP1 and VP2 are reasonably well approximated by solutions of a variational principle. This remark constitutes a step forward in finding an approach where the random phase approximation ground state is a solution of a variational principle equation.

The modern theories of Grand Unification (GUT) and supersymmetric (SUSY) extensions of standard model (SM) suppose that the conservation laws of the SM may be violated to some small degree. The nuclei are well-suited as a laboratory to test fundamental symmetries and fundamental interactions like lepton flavor (LF) and lepton number (LN) conservation. A prominent role between experiments looking for LF and total LN violation play yet not observed processes of neutrinoless double beta decay (0νββ-decay). The GUT's and SUSY models offer a variety of mechanisms which allow 0νββ-decay to occur. They are based on mixing of Majorana neutrinos and/or R-parity violation hypothesis. Although the 0νββ-decay has not been seen it is possible to extract from the lower limits of the lifetime upper limits for the effective electron Majorana neutrino mass, effective right handed weak interaction parameters, the effective Majoron coupling constant, R-parity violating SUSY parameters etc. A condition for obtaining reliable limits for these fundamental quantities is that the nuclear matrix elements governing this process can be calculated correctly. The nuclear structure wave functions can be tested by calculating the two neutrino double beta decay (2νββ-decay) for which we have experimental data and not only lower limits as for the 0νββ-decay. For open shell nuclei the method of choice has been the Quasiparticle Random Phase Approximation, which treats Fermion pairs as bosons. It has been found that by extending the QRPA including Fermion commutation relations better agreement with 2νββ-decay experiments is achieved. This increases also the reliability of conclusions from the upper limits on the 0νββ-decay transition probability. In this work the limits on the LN violating parameters extracted from current 0νββ-decay experiments are listed. Studies in respect to future 0νββ-decay experimental projects are also presented.