We use the configuration-interaction nuc … Search for double beta decay of 106Cd with an enriched 106CdWO4 crystal scintillator in coincidence with CdWO4 scintillation counters. E~(1m+) and E(1m+) are the (absolute) energies of the mth 1+ state in a pnQRPA calculation based on the left- and right-side ground states. Finally, we compared the energy distributions of the multipole-decomposed 0νβ+β+-decay matrix elements and the average OMC matrix elements, computed in the adjusted Woods-Saxon single-particle basis. Blaum K, Eliseev S, Danevich FA, Tretyak VI, Kovalenko S, Krivoruchenko MI, et al. Most of the observed decays are of β−β− type, and there are only six isotopes known to be capable of β+β+ decaying. The ratio of P,T-violating to P-violating matrix elements is found to remain approximately constant across the nuclear mass table, thus . The test proposed allows also to check the dominance of the Majorana mass mechanism of violation of the total lepton charge. The definitions for the double Fermi, Gamow-Teller, and tensor NMEs MF(0ν), MGT(0ν), and MT(0ν) can be found e.g., in [17]. (B) Basis: “WS”. The matrix elements thus obtained have predicted theβ spectrum shape correction factor. This is most likely due to the fact that in the smaller bases we cannot reach the highly-excited intermediate states which play a non-negligible role in the 0νββ-decay process. (B) Basis: “WS”. Francesco Cappuzzello. 1. Nuclear and Particle Physics Franz Muheim 7 Feynman Rules for QED Each line and vertex in Feynman diagram corresponds to a term in the matrix element Initial and final state fermions Fermion wave functionΨ (spinor when including spin) Initial and final state bosons Boson wave functionincludes polarisation Internal virtual photons 27. From Nucleons to Nucleus deals with single-particle and collective features of spherical nuclei. Hence, the captured muon can be assumed to be initially bound in the lowest state, 1s1/2, corresponding to κ = −1 and μ=±12. Value of the axial-vector coupling strength in β and ββ decays: a review. Solar neutrinomeasurements in Super-Kamiokande-IV. Nuclear matrix elements from generator coordinate method Center for Computational Sciences, University of Tsukuba, Japan. Three of these, involving the nucleon momentum operator, replace the operators which, in the conventional representation of the theory, appeared as . The results reported in the present study are based on a spherical proton-neutron quasiparticle random-phase approximation (pnQRPA), which describes nuclear excitations in odd-odd nuclei (such as 106Ag) as proton-neutron quasiparticle pairs. This finding is in accordance with our previous work [13], where we compared the energy distributions of the multipole-decomposed 0νβ−β−-decay and OMC matrix elements for several 0νβ−β−-decay triplets in a similar manner. Furthermore, when comparing the 0νβ+β+-decay matrix elements of the present work with those computed in (much) smaller single-particle bases in [14], we noticed that the matrix elements are sensitive to the size of the single-particle basis. Contrary to this, the average value of the OMC matrix element is less dependent on the gpp(T=0). However, these figures show that even though the average OMC matrix element is quite independent of the value of gpp, the shape of the OMC spectrum depends on gpp. JK has been supported by the Academy of Finland, Grant Nos. Most of the observed decays are of two-neutrino double-beta minus (2νβ−β−) type, and there are only six isotopes capable of 2νβ+β+ decaying: 78Kr, 96Ru, 106Cd, 124Xe, 130Ba, and 136Ce. The reported ratio of double beta decay of the isotopes 128Te and 13°Te measured by geochemical techniques, coupled with an assumed equality of the nuclear matrix elements, would indicate the existence of a neutrinoless branch indicative ... However, at zero momentum transfer deviations from the CVC and PCAC values have been obtained in several analyses [29–32]. In [16], the phase-space factors for the 2νβ+β+ decay, as well as for the competing modes 2νβ+EC and 2νECEC were computed. Of course, as already mentioned, the accuracy with which nuclear matrix elements can be Kotila J, Iachello F. Phase space factors for β+β+ decay and competing modes of double-β decay. Figure 2: Schematic of different types of stickers and spacers for different systems. Therefore the Zachman matrix provides the answers to what data assets the nuclear and research facilities controls by setting up the ideal use and ideal places for these data. (1958) 111:354. doi: 10.1103/PhysRev.111.354, 29. We also compare our results for the two-neutrino double- decay nuclear matrix elements with those extracted from the measured half-lives. In the absence of a measured 2νβ+β+-decay half-life, adjusting gpp to OMC data, once measured, would help reduce the large uncertainty related to gpp. doi: 10.1063/1.3022342, 34. Adopted values of the pairing parameters of the BCS and the particle-hole and particle-particle parameters of the pnQRPA. On the other hand, the multipoles with J ≥ 6 play a minor role compared with the 0νβ+β+ decay. The exploration also paves the way for possible future adjustments of gpp using, e.g., the shape of the OMC strength function. Here, we show that scaffold attachment factor B (SAFB), a nuclear matrix (NM)-associated protein … Front. Figure 7. Over the last decade, numerical solutions of Quantum Chromodynamics (QCD) using the technique of lattice QCD have developed to a point where they are beginning to connect fundamental aspects of nuclear physics to the underlying degrees of freedom of the Standard Model. Suhonen J, Civitarese O. Comparative analyses of the nuclear matrix elements (NMEs) related to the 0νβ+β+ decay of 106Cd to the ground state of 106Pd and the ordinary muon capture (OMC) in 106Cd are performed. © 2021 World Scientific Publishing Co Pte Ltd, Nonlinear Science, Chaos & Dynamical Systems, Seventy Years of Double Beta Decay, pp. However, the ground states of the mother and daughter nuclei belong to different isospin multiplets, and due to the isospin symmetry, the Fermi contribution to the 2νββ-decay NME should vanish, leaving the Gamow-Teller NME in Equation (2) as the sole contributor to the 2νββ-decay rate. Status of calculation of nuclear matrix element 5. In Figures 3, 4, we show the multipole decompositions of the total 0νβ+β+-decay NME and the average OMC matrix element of 106Cd, respectively. Nuclear matrix elements and the connection to fundamental physics There is a version of double-beta decay (2 νββ decay, in which the emitted electrons are accompanied by two antineutrinos) that is violates none of the rules of the standard model. However, for the lack of the OMC data on the OMC in 106Cd, this is not possible in the present study. For the muon-capture calculations, we generate the pnQRPA excitations in 106Ag starting from the even-even mother nucleus, 106Cd. Phys Rev C. (2019) 100:014619. doi: 10.1103/PhysRevC.100.014619, 43. The article describes the main achievements of the NUMEN project together with an updated and detailed overview of the related R&D activities and theoretical developments. We assume that the muon is bound on the κ = −1 orbit and that the small component of the bound muon wave function is negligible, which simplifies the expressions of the matrix elements notably [see Equation (5.26) and Table 5.2 of [26] for the Bethe-Salpeter approximation and Equation (5.37) and Table 5.3 for a general muon wave function]. Salvat F, Fernández-Varea J, Williamson W Jr. (2013) 2013:703572. doi: 10.1155/2013/703572, 6. The value gpp(T=0)=0.7 is adopted for particle-particle interaction parameter. The 1− contribution is the second largest, whereas the 0+ and 0− contributions are negligible. We have chosen to plot only the absolute values of the matrix elements since they carry the essential information needed in the present comparison of the basic features of the OMC and 0νβ+β+ decay. Over the last decade, numerical solutions of Quantum Chromodynamics (QCD) using the technique of lattice QCD have developed to a point where they are beginning to connect fundamental aspects of nuclear physics to the underlying degrees of freedom of the Standard Model. View all
Naturally, these isotopes can also decay via the 2νβ+EC and 2νECEC (two-neutrino double electron capture) modes. In the present work, we have made a comparative analysis of the 0νβ+β+-decay and average OMC matrix elements of 106Cd in the pnQRPA framework using large no-core single-particle bases. Results of a search for neutrinoless double-β decay using the COBRA demonstrator. Spin-dipole (SD) nuclear matrix elements (NMEs) M ± (SD 2) for unique first forbidden β ± 2 − → 0 + ground-state-to-ground-state transitions are studied by using effective microscopic two-nucleon interactions in realistic single-particle model spaces. Here we finally compare the absolute values of the 0νβ+β+-decay and average OMC matrix elements in the same manner as in [13]. Best values and reasonable ranges for hadronic matrix elements of QCD theta term and dimension six CP-violating operators. The Gamow-Teller NME involved in Equation (1) can be written as. All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication. The expectation value in Equation (16) can be written as. Equation (14) can then be solved by means of the package RADIAL [25] by using a piecewise-exact power-series expansion of the radial functions, which then are summed up to a prescribed accuracy. Calculation of nuclear transition matrix elements of neutrinoless double-beta decay J. Terasaki, Univ. As mentioned in section 5, the particle-particle strength parameter gpp strongly affects the ββ-decay rates. Phys Rev C. (2019) 99:024327. doi: 10.1103/PhysRevC.99.024327, 10. We assume that the 0νββ decay is dominated by the light-Majorana-neutrino-exchange mechanism, and exploit the formalism presented in [17]. Front Phys. Approx size of matrix element may be estimated from thesimplest valid Feynman Diagram for given process. Phys Rev C. (1994) 50:2576. doi: 10.1103/PhysRevC.50.2576, 32. In the case of the 0νβ+β+ mode the final nucleus is (A, Z − 2), and two positrons are emitted. Abe K, Amey J, Andreopoulos C, Antonova M, Aoki S, Ariga A, et al. doi: 10.22661/AAPPSBL.2019.29.3.21, 12. Romig H., Fackelmeyer F. O., Renz A., Ramsperger U., and Richter A.Characterization of SAF-A, a novel nuclear DNA binding protein from HeLa cells with high affinity for nuclear matrix/scaffold attachment DNA elements.EMBO J.11199234313440 In Figure 6, we plot the average OMC matrix element |M(μ)|av as a function of gpp(T=0). Status of nuclear matrix element calculations Nuclear structure calculation of β + β +, β + /EC and EC/EC decay matrix elements. Charge‐exchange reactions of (n, p) and (p, n) type at intermediate energies are a powerful tool for the study of nuclear matrix element in ββ decay.The present paper reviews some of the most recent experiments in this context. Annual Review of Biophysics and Biophysical Chemistry . Outline pIntroduction pGenerator coordinate method pApplication to SO(8) model, 76Ge double-beta decay pFuture plans pSummary. In this paper we compared frequencies of simple nucleotide motifs in S/MAR sequences and in sequences extracted directly from various nuclear matrix elements, such as nuclear lamina, cores of rosette-like structures, synaptonemal complex. (B) Basis: “WS”. 314733 and 320062. (A) Basis: “Adj.”. Multipole decomposition of the total 0νβ+β+-decay matrix element in different single-particle bases. 015502. Nuclear matrix element 4. -/ -0 nuclear meson decay 20 30 40 10 NUMBER OF NEUTRONS 10 20 30 40 50 60 0,1 0,+1 BR t 1/2 Q EC Superallowed ! As shown in Figure 2C , MARs 1 to 5 all interacted with the nuclear matrix, and upon dilution of the latter, a corresponding decrease in band shift (indicated by . Some future double beta experiments (like GENIUS) will be capable to be simultaneously neutrino observatories for double beta decay and low-energy solar neutrinos, and observatories for cold dark matter of ultimate sensitivity.This ... Full matrix element requires in nite number of diagrams. Observables in muon capture on 23Na and the effective weak couplings ga and gp. Figure 4. (2019) 29:21–6. and compare this quantity, instead of OMC rate, with the 0νβ+β+-decay NME in order to reduce the phase-space effects. (2001) 497:221–7. Large mass of the captured muon allows highly-forbidden transitions and high excitation energies of the final states. As a starting point, the single-particle energies were generated by a spherical Coulomb-corrected Woods-Saxon (WS) potential with the parametrization of [33]. Belli P, Bernabei R, Brudanin VB, Cappella F, Caracciolo V, Cerulli R, et al. The half-life for such a 0νββ transition can be written as, where G0ν is a phase-space factor for the final-state leptons in units of inverse years (see [15, 16]), defined here without including the axial-vector coupling gA. (2018) 118:151801. doi: 10.1103/PhysRevLett.118.151801, 5. Figure 1. (2012) 229:232–478. Spin-dipole (SD) nuclear matrix elements (NMEs) M ± (SD 2) for unique first forbidden β ± 2 − → 0 + ground-state-to-ground-state transitions are studied by using effective microscopic two-nucleon interactions in realistic single-particle model spaces. Here, the (n, p) type reactions are realized through (d, 2 He), where 2 He refers to two protons in a singlet 1 S 0 state and where both of these are momentum . doi: 10.1016/0010-4655(95)00039-I. The energy release in the nuclear capture process is about 100 MeV, of which the largest fraction is donated to the neutrino, being the lightest particle in the process. Double-Beta Decay Experiment. (B) Basis: “WS”. Theory of allowed and forbidden transitions in Muon capture reactions. This makes sense, since looking at Figure 2, especially at r ≤ 7 fm, the behavior of the Dirac wave function, taking into account the finite size of the nucleus, differs significantly from the Bethe-Salpeter approximation. Ann Phys. In [10], on the other hand, OMC strength function and the associated giant resonances in 100Nb were studied for the first time. These anchor sequences are known as scaffold/matrix attachment regions (S/MARs). Current status and future perspectives of the COBRA experiment. Suhonen J. Neutrinoless double beta decays of 106Cd revisited. Phys Rev C. (2013) 87:045501. doi: 10.1103/PhysRevC.87.045501, 38. The nuclear matrix elements (NMEs) for the 0νββ decays from 130 Te to 130 Xe and from 136 Xe to 136 Ba are calculated in the nuclear shell model. Abstract. The different terms are listed in Table 5.1 of [26]. In both figures, the Bethe-Salpeter point-like-nucleus approximation (blue bars) results in notably larger values of the average OMC matrix element than the Dirac wave function (black and white bars). In this work we choose the slightly quenched values of gA(0)=gAeff=1.0 and gP(0) = 7.0 and keep the CVC value gV(0) = 1.0 for all the studied cases. The study employs the Hartree-Fock-Bogoliubov model to obtain the wave functions of the parent and daughter nuclei, in conjunction with the summation method to estimate the double-beta decay nuclear matrix elements. Outline pIntroduction pGenerator coordinate method pApplication to SO(8) model, 76Ge double-beta decay pFuture plans pSummary. The existence of neutron star mergers has been supported since the discovery of the binary pulsar and the observation of its orbital energy loss, consistent with General Relativity. Figure 9. Graduate students and researchers in these fields will find this book a reliable advanced text and source of reference. In the latter case also the electron capture (EC) is possible through the mode 0νβ+EC. (A) Basis: “Adj.”. Goldberger ML, Treiman SB. Modificasion of QRPA approach and my . While neutrinoless double beta decay remains hypothetical, the two-neutrino decay mode (2νββ), which is allowed by the standard model, has been observed in several isotopes. (2004) 30:2003–18. The half-life of a ground-state-to-ground-state two-neutrino double-beta decay can be written in the form. Feynman Diagrams 5 Phys Rev C. (2014) 89:064319. doi: 10.1103/PhysRevC.89.064319, 25. A survey of pion charge-exchange reactions with nuclei. Jokiniemi L, Ejiri H, Frekers D, Suhonen J. Neutrinoless ββ nuclear matrix elements using isovector spin-dipole Jπ = 2− data. Nuclear matrix elements from generator coordinate method Center for Computational Sciences, University of Tsukuba, Japan. Figure 2. Volume 13, number 2 PHYSICS LETTERS 15 November 1964 NUCLEAR MATRIX ELEMENTS FOR THE MIRROR DECAYS OF B12 AND N12* J. EICHLER, T. A. TOMBRELLO and J. N. BAHCALL California Institute of Technology, Pasadena, California Received 20 September, 1964 Recent precision experiments [1] have shown that theft-value for the beta decay of N12 is significantly larger (11 t 1%) than theft-value for the . Figures 7, 8 show similar behavior for both the multipoles Jπ = 1+ and 2+: decreasing the value of gpp(T=0) from 0.8 to 0.6 shifts the spectrum to lower energies for both the 0νβ+β+ decay and OMC. Phys Rev C. (2016) 94:024603. doi: 10.1103/PhysRevC.94.024603, 7. The NEWS 99 international symposium discusses symmetries in electroweak processes in nuclei. Many phenomena in nuclear and particle physics are related to symmetry. This, in turn, raises interest of studying the possibility of adjusting gpp to the locations of OMC giant resonances, once measured. Nuclear matrix elements (NMEs) for double beta decays (DBDs) are crucial for studying neutrino mass and neutrino properties of particle physics interest. The contributions coming from the higher multipoles decrease rather smoothly as a function of J. While there are arguments that the relative position of chromosome territories (CTs), the equivalent of condensed metaphase chromosomes at interphase, may be . The 0νββ Nuclear Matrix Elements (NMEs) are very The accurate description of reactions involving sensitive to nuclear physics involved in 0νββ probing the complex nuclei is a demanding task also for nuclear nuclear wave functions of the initial and final states, the theory. The nuclear size dependence is found to be A43 in the limit of large A, as expected. They find that the factorization is reasonably good when the momentum fraction carried by the gluon field is moderate. (2011) 701:490–5. The transcriptional coactivator p300 regulates transcription by binding to proteins involved in transcription and by acetylating histones and other proteins. calculated nuclear matrix elements do not include explicitly proton-neutron pairing correlations This effect (partially) accounted for by other degrees of freedom present in these approaches Include p-boson (L = 1) to IBM in addition to s and d bosons (L = 0;2) First IBM results in calcium region suggest nuclear matrix elements could be . The matrix elements are computed in the adjusted Woods-Saxon basis (“Adj.”) with the parameter value gpp(T=0)=0.7. The particle-hole part was scaled by a common factor gph fixed by fitting the centroid of the Gamow-Teller giant resonance (GTGR) in the 1+ channel of the calculations. Dependence of the energy distributions of the 0νβ+β+-decay and OMC matrix elements for the Jπ = 1+ multipole on the particle-particle parameter gpp(T=0) in different bases. Histone-depleted nuclei maintain sequence-specific interactions with genomic DNA at sites known as scaffold attachment regions (SARs) or matrix attachment regions. 9
In Figures 9, 10 we plot the energy-decompositions of the average OMC matrix element for the transitions to Jπ = 1+ and 2+ states, respectively. In addition, it should be noted that the same nuclear matrix elements (NMEs) are involved in the 0νβ+β+ and 0νβ+EC modes. In contrast to 0νβ+β+ decay, the strength is more evenly distributed among the few leading multipoles. Citation: Jokiniemi L, Suhonen J and Kotila J (2021) Comparative Analysis of Nuclear Matrix Elements of 0νβ + β + Decay and Muon Capture in 106 Cd. The wave function of the muon bound on an atomic orbit of the initial nucleus can be written as an expansion in terms of the normalized spherical spinors χκμ, where Gκ and Fκ are the large and small radial components of the wave functions of the bound state [21]. • In particular, the competition between the `pairing', J = 0, and the `broken pairs', J ≠ 0, contributions causes almost complete cancellation for the internucleon distance r ≥ 2-3 fm, hence making the short range behavior . NUMEN proposes an innovative technique to access the nuclear matrix elements entering the expression of the lifetime of the double beta decay by cross section measurements of heavy-ion induced Double Charge Exchange (DCE . The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation. The following reprint articles are included: A Breakthrough to the Understanding of the Matrix Elements, Double beta decay of 128Te/130Te and the question of a neutrino Majorana mass, THE QUENCHING OF LOW-ENERGETIC NUCLEAR GAMOW–TELLER STRENGTH BY Δ-EXCITATIONS, CALCULATION OF DOUBLE BETA DECAY OF 76Ge, 82Se, 128,130Te, PREDICTIONS OF 2ν AND 0ν DOUBLE BETA DECAY RATES FOR NUCLEI WITH A ≥ 70, CALCULATION OF DOUBLE BETA DECAY RATES AND THE NEUTRINO MASS, THE SHAPE OF THE BETA STRENGTH FUNCTION AND CONSEQUENCES FOR NUCLEAR PHYSICS AND ASTROPHYSICS, Beta Decay Far from Stability and Its Role in Nuclear Physics and Astrophysics, Suppression of the Two-Neutrino Double-Beta Decay by Nuclear-Structure Effects, Nuclear structure effects in double-beta decay, Effects of Ground-State Correlations on 2νββ Decay Rates and Limitations of the QRPA Approach, Nuclear Structure Effects on the Neutrinoless Double Beta Decay, Calculation of 2ν and 0ν Double-Beta Decay Rates, ββ DECAY OF 76Ge WITH RENORMALIZED EFFECTIVE INTERACTION DERIVED FROM PARIS, BONN AND REID POTENTIALS, ββ decay of 128Te, 130Te, and 76Ge with renormalized effective interactions derived from Paris and Bonn potentials, Renormalized Proton-Neutron Quasiparticle Random-Phase Approximation and Its Application to Double Beta Decay, Gamow-Teller matrix elements for two-neutrino double β decay within a second quasi-random-phase approximation, Second-QRPA Calculations for Two Neutrino Double-beta Decay, QRPA and RQRPA Calculations of Neutrinoless Double-Beta Decay beyond the Point of Collapse, A FIELD THEORY APPROACH TO TWO-NEUTRINO DOUBLE BETA DECAY, Double-beta decay matrix elements for 76Ge, Neutrinoless double-β-decay matrix elements within the second quasirandom phase approximation method, Shell Model Studies of the Double Beta Decays of 76Ge, 82Se, and 136Xe, Shell-model calculation for two-neutrino double beta decay of 48Ca, A comparative study of double beta decay by shell model and quasiparticle RPA, AN ALTERNATIVE APPROACH IN NUCLEAR DOUBLE BETA DECAY THEORY, A Discussion of the Question in Connexion with the Expansion of a Divergent Series Encountered in Calculating Nuclear 2ν-2β Decay Matrix Element, A NEW METHOD OF THE CALCULATION OF THE TWO-NEUTRINO DOUBLE BETA DECAY AMPLITUDES, Two-neutrino double beta decay with operator expansion method, Tensor force and operator expansion method for nuclear double beta decay, New Theoretical Results of 2νββ Decay with the Operator Expansion Method, Matrix elements for 0νββ decay calculated with the operator expansion method and QRPA wave functions, Operator expansion method and nuclear ββ decay, Extended operator expansion method for neutrinoless double beta decay, Two-Neutrino Double Beta Decay: Critical Analysis, Nuclear matrix elements for double positron emission, Nuclear structure calculation of β+β+, β+/EC and EC/EC decay matrix elements, Matrix Elements for Exchange of Heavy Particles, and a Superformula for Neutrinoless Double Beta Decay, e−e− → W−W− MEDIATED BY HEAVY NEUTRINO FLAVORS, HEAVY MAJORANA NEUTRINOS IN e−e− COLLISIONS, Nuclear matrix element uncertainties in short range 0νββ decay, Towards a superformula for neutrinoless double beta decay, A superformula for neutrinoless double beta decay II: the short range part. This invaluable book outlines the development of double beta research from its beginnings until its most recent achievements, and also presents the outlook for its highly exciting future. Studies in different models for nuclear matrix elements calculations in general are discussed and the connected uncertainties too are reported. Primakoff H. Theory of muon capture. Ordinary muon capture studies for the matrix elements in ββ decay. Theoretical results on the double positron decay of 106Cd. Section 5 is about ways in which matrix-element calculations should improve in the next few years, and ways in which the uncertainty in new calculations can be assessed. The nuclear matrix elements of neutrinoless double-β decay for nuclei Ge 76, Se 82, Mo 100, Te 130, and Nd 150 are studied within the triaxial projected shell model, which incorporates simultaneously the triaxial deformation and quasiparticle configuration mixing.The low-lying spectra, the B (E 2: 0 + → 2 +) values, and the occupancies of single-particle orbits are reproduced well. For the bound-muon wave function we have used the realistic exact wave function solved from the Dirac equation. The ground states of the initial and final nuclei are denoted by 0i+ and 0f+, correspondingly. Making this assumption, we can estimate the bound-muon wave function by the Bethe-Salpeter point-like-nucleus approximation formulae [22], where α is the fine-structure constant and Z the atomic number of the nucleus. Phys Rep. (2019) 797:1–102. Hence, in this section we study the effect of gpp on both the 0νβ+β+-decay and OMC matrix elements of 106Cd in detail. AAPPS Bull. The decompositions correspond to the parameter value gpp(T=0)=0.7. Phys Rev C. (1996) 54:2714. doi: 10.1103/PhysRevC.54.2714, 33.
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