Search

We develop the formalism for calculating the decay rate of neutrinoless double beta decay to the $2^+$ excited states within L-R symmetric model. We consider the effects from induced hadronic currents up to NLO. The QRPA method in a spherical basis is adopted for the nuclear many-body calculation and the corresponding nuclear matrix elements are given. Also, the phase space factors are obtained with numerical electron wave functions. Our results suggest that the nuclear matrix elements are nucleus dependent and they are generally smaller than that of the decay to the ground states. And finally, we give a naive analysis of how current experiment data constrains the L-R symmetric model., Comment: 9 pages, 1 figure, figure corrected

In this work we present the first beyond closure calculation for the neutrinoless double beta decay ($0\nu\beta\beta$) of $^{76}$Ge to the first $2^+$ states of $^{76}$Se. The isospin symmetry restored Quasi-particle random phase approximation (QRPA) method with the CD-Bonn realistic force is adopted for the nuclear structure calculations. We analyze the structure of the two nucleon mechanism nuclear matrix elements, and estimate the uncertainties from the nuclear many-body calculations. We find $g_{pp}$ plays an important role for the calculations and if quenching is included, suppression for the transition matrix element $M_{\lambda}$ is found. Our results for the transition matrix elements are about one order of magnitude larger than previous projected Hatree-Fock-Boglyubov results with the closure approximation., Comment: 10 pages, 4 figures

With partially restored isospin symmetry, we calculate the nuclear matrix element for a special decay mode of $2\nu\beta\beta$ (two neutrino double beta decay) -- the decay to the first $2^+$ excited states. With the realistic CD-Bonn nuclear force, we analyze the dependence of the nuclear matrix elements on the iso-vector and iso-scalar parts of proton-neutron particle-particle interaction. The dependence on the different nuclear matrix element is observed and the results are explained. We also give the phase space factors with numerical electron wave functions and properly chosen excitation energies. Finally we give our results for the half-lives of this decay mode for different nuclei., Comment: 9 pages, 3 figures, to be published in Chinese Physics C

An improved formalism of the two-neutrino double-beta decay ($2\nu\beta\beta$-decay) rate is presented, which takes into account the dependence of energy denominators on lepton energies via the Taylor expansion. Till now, only the leading term in this expansion has been considered. The revised $2\nu\beta\beta$-decay rate and differential characteristics depend on additional phase-space factors weighted by the ratios of $2\nu\beta\beta$-decay nuclear matrix elements with different powers of the energy denominator. For nuclei of experimental interest all phase-space factors are calculated by using exact Dirac wave functions with finite nuclear size and electron screening. For isotopes with measured $2\nu\beta\beta$-decay half-life the involved nuclear matrix elements are determined within the quasiparticle random phase approximation with partial isospin restoration. The importance of correction terms to the $2\nu\beta\beta$-decay rate due to Taylor expansion is established and the modification of shape of single and summed electron energy distributions is discussed. It is found that the improved calculation of the $2\nu\beta\beta$-decay predicts slightly suppressed $2\nu\beta\beta$-decay background to the neutrinoless double-beta decay signal. Further, a novel approach to determine the value of effective weak-coupling constant in nuclear medium $g^{\rm eff}_{\rm A}$ is proposed., Comment: 12 pages, 11 figures

In this work, with restored isospin symmetry, we evaluated the neutrinoless double beta decay nuclear matrix elements for $^{76}$Ge, $^{82}$Se, $^{130}$Te, $^{136}$Xe and $^{150}$Nd for both the light and heavy neutrino mass mechanisms using the deformed QRPA 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 BCS overlap factor between the initial and final ground states. The comparison between different nucleon-nucleon forces with corresponding Short-Range-Correlations (src) shows, that the choice of the NN force gives roughly $20\%$ deviations for light exchange neutrino mechanism and much larger deviations for the heavy neutrino exchange mechanism., Comment: 15 pages, 4 figures, submitted to Phys. Rev. C, adding ISM results in Table V

There are three different methods used to search the neutrino mass: - The electron antineutrino mass can probably best be determined by the Triton decay. - The neutrinoless Double Beta Decay yields information, if the neutrino is a Dirac or a Majorana particle. It can also determine the Majorana neutrino mass. - Electron capture of an atomic bound electron by a proton in a nucleus bound electron plus proton to neutron plus electron-neutrino can give the mass of the electron neutrino. This contribution summarizes our theoretical work on the possibility to determine the electron neutrino mass by electron capture. One expects the largest influence of the neutrino mass on this decay for a small Q = 2.8 keV for electron capture in Holmium. The energy of the Q value is distributed to the emitted neutrino and the excitation of the Dy atom. Thus the energy difference between the Q value and the upper end of the deexcitation spectrum is the electron neutrino mass. The excitation spectrum of Dy is calculate by one-, two- and three-electron hole excitations, and by the shake-off process. The electron wave functions are calculated selfconsistently by the Dirac-Hartree-Fock approach for the bound and the continuum states. To extract the neutrino mass from the spectrum one must adjust simultaneously the neutrino mass, the Q value, the position, the relative strength and the width of the highest resonance. This fit is only possible, if the background is reduced relative to the present situation. In case of a drastically reduced background a fit of the Q-value and the neutrino mass only seems also to be possible. The analysis presented here shows, that the determination of the electron neutrino mass by electron capture is difficult, but seems not to be impossible., Comment: Dedicated to the memory of Walter Greiner 1935 - 2016, five figures. arXiv admin note: substantial text overlap with arXiv:1611.00325

Electron capture can determine the electron neutrino mass, while the beta decay of Tritium measures the electron antineutrino mass and the neutrinoless double beta decay observes the Majorana neutrino mass. Electron capture e. g. on 163Ho plus bound electron to 163Dy* plus neutrino can determine the electron neutrino mass from the upper end of the decay spectrum of the excited Dy*, which is given by the Q-Value minus the neutrino mass. The Dy* states decay by X-ray and Auger electron emissions. The total decay energy is measured in a bolometer. These excitations have been studied by Robertson and by Faessler et al.. In addition the daughter atom Dy can also be excited by moving in the capture process one electron into the continuum. The escape of these continuum electrons is automatically included in the experimental bolometer spectrum. Recently a method developed by Intemann and Pollock was used by DeRujula and Lusignoli for a rough estimate of this shake-off process for "s" wave electrons in capture on 163Ho. The purpose of the present work is to give a more reliable description of "s" wave shake-off in electron capture on Holmium. For that one needs very accurate atomic wave functions of Ho in its ground state and excited atomic wave functions of Dy* including a description of the continuum electrons. In the present approach the wave functions of Ho and Dy* are determined selfconsistently with the antisymmetrized relativistic Dirac-Hartree-Fock approach. The relativistic continuum electron wave functions for the ionized Dy* are obtained in the corresponding selfconsistent Dirac-Hartree-Fock-Potential. In this improved approach shake-off can hardly be seen after electron capture in 163Ho and thus can probably not affect the determination of the electron neutrino mass., Comment: 20 pages, 9 figures

The Cosmic Microwave Background (CMB) yields information about our Universe at around 380 000 years after the Big Bang (BB). Due to the weak interaction of the neutrinos with matter the Cosmic Neutrino Background (CNB) should give information about a much earlier time of our Universe, around one second after the Big Bang. Probably the most promising method to `see' the Cosmic Neutrino Background is the capture of the electron neutrinos from the Background by Tritium, which then decays into 3He and an electron with the energy of the the Q-value = 18.562 keV plus the electron neutrino rest mass. The `KArlsruhe TRItium Neutrino' (KATRIN) experiment, which is in preparation, seems presently the most sensitive proposed method for measuring the electron antineutrino mass. At the same time KATRIN can also look by the reaction: electron neutrino (~1.95 Kelvin) + 3H --> 3He + e- (with the energy Q = 18.6 keV + electron neutrino mass). The capture of the Cosmic Background Neutrinos (CNB) should show in the electron spectrum as a peak by the electron neutrino rest mass above Q. Here the possibility to see the CNB with KATRIN is studied. A detection of the CNB by KATRIN seems not to be possible at the moment. But KATRIN should be able to determine an upper limit for the local electron neutrino density of the CNB., Comment: 13 pages and two figures

In this work, we calculate the matrix elements of $0\nu\beta\beta$-decay of $^{150}$Nd with the deformed pn-QRPA method. We adopted the approach introduced by Rodin, Faessler [Phys. Rev. C84, 014322 (2011)] and Simkovic {\it et. al.} [Phys. Rev. C87,045501(2013)] to restore the isospin symmetry by enforcing $M^{2\nu}_F=0$. We found that with this restoration, the Fermi matrix elements are reduced by about 30\% while the more important Gamow-Teller matrix elements remains the same. The results of an enlarged model space is also presented, which changes the matrix elements by less than 10\%., Comment: 5 pages, 1 figure, accepted by Phys. Rev. C

The two-neutrino double-$\beta$ 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-$\beta$ decay matrix elements on isovector and isoscalar particle-particle interactions. By using perturbation theory an explicit dependence of the two-neutrino double-$\beta$ 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-$\beta$ 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 particle-particle interaction of Hamiltonian. It is pointed out that there is a dominance of two-neutrino double-$\beta$ 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 Delta 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., Comment: 12 pages, 4 figures

163 Holmium to 163 Dysprosium 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 restmass. 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 and the author have calculated the influence of the two-hole states on the Dysprosium deexitation 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 selfconsitently in a fully relativistic and antisymmetrized Dirac-Hartree-Fock approach in Holmium and in Dysprosium. The electron orbitals in Dysprosium are determined including the one-hole states in the selfconsistent iteration. The influence of the three-hole states on the deexcitation (by X-rays and Auger electrons) spectrum is hardly visible. The three-hole states seem not to be important for the determination of the neutrino mass., Comment: 4 figures. arXiv admin note: text overlap with arXiv:1501.04338

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., Comment: Published version, title modified

Holmium 163 offers perhaps the best chance to determine the neutrino mass by electron capture. This contribution treats the electron capture in 163 Holmium completely relativistic for the overlap and exchange corrections and the description of the bolometer Spectrum. The theoretical expressions are derived assuming single Slater determinants for the initial Ho and the final Dy Atoms. 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 ns(1/2) electron states. Relativistically also p(1/2) 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. The purpose of this work is to give a consistent relativistic formulation and treatment of the overlap and exchange corrections for electron capture in 163 Ho to excited atomic states in 163 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 deexcitation 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 Generalized Coherent State Model, proposed previously for a unified description of magnetic and electric collective properties of nuclear systems, is extended to account for the chiral like properties of nuclear systems. To a phenomenological core described by the GCSM a set of interacting particles are coupled. Among the particle-core states one identifies a finite set which have the property that the angular momenta carried by the proton and neutron quadrupole bosons and the particles respectively, are mutually orthogonal. All terms of the model Hamiltonian satisfy the chiral symmetry except for the spin-spin interaction. The magnetic properties of the particle-core states, where the three mentioned angular momenta are orthogonal, are studied. A quantitative comparison of these features with the similar properties of states, where the three angular momenta belong to the same plane, is performed., Comment: 35 pages, 14 figures, to appear in Journal of Physics G: Nucl. Part. Phys

An exactly solvable model for a description of the two-neutrino double beta decay transition of the Fermi type is considered. By using perturbation theory an explicit dependence of the two-neutrino double beta decay matrix element on the like-nucleon pairing, particle-particle and particle-hole proton-neutron interactions by assuming a weak violation of isospin symmetry of Hamiltonian expressed with generators of the SO(5) group. It is found that there is a dominance of double beta decay transition through a single state of the intermediate nucleus. Then, an energy weighted sum rule connecting Delta Z=2 nuclei is presented and discussed. It is suggested that this sum rule can be exploited to study the residual interactions of the nuclear Hamiltonian., Comment: 8 pages, 3 figures

The spectrum of the Cosmic Microwave Background follows Planck's black body radiation formula and shows a remarkable constant temperature of T = 2.7. About 380 000 years after the Big Bang at a temperature of T = 3000 Kelvin in the matter dominated era the electrons combine with the protons and 4He and the photons move freely in the neutral universe. So the temperature and distribution of the photons give us information of the universe 380 000 years after the Big Bang. Information about earlier times can, in principle, be derived from the Cosmic Neutrino Background (relic neutrinos). The neutrinos decouple already about 1 second after the Big Bang at a temperature of around 1 MeV or 10^{10} Kelvin. Today their temperature is about 1.95 Kelvin. Registration of these neutrinos is an extremely challenging experimental problem, which can hardly be solved with the present technologies. On the other hand it represents a tempting opportunity to check one of key elements of the Big Bang Cosmology and to probe the early stages of the universe evolution. The search for the Cosmic Neutrino Background with the induced beta decay: relic neutrino + 3H --> 3He + e-, is the topic of this contribution. The signal would show up as a peak in the electron spectrum by an energy with the neutrino mass above the Q value. We discuss the prospects of this approach and argue that it is able to set limits on the Cosmic Neutrino density in our vicinity. We also discuss critically ways to increase with modifications of the present KATRIN spectrometer the Tritium source intensity by a factor 100, which would yield about 170 counts of relic neutrino captures per year. Presently such an increase of the Tritium source intensity seems not to be possible. But one should be able to find an upper limit for the local density of the relic neutrinos in our galaxy., Comment: 9 pages, no figures, contribution to the conference proceedings of the ICNFP September 2013 in Colymbari/Crete

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., Comment: 11 pages, 5 figures, typos removed, references updated, accepted in Phys. Rev. C

In a previous article [Phys. Rev. D 79, 053001 (2009)] we estimated the correlated uncertainties associated to the nuclear matrix elements (NME) of neutrinoless double beta decay (0 nu beta beta) within the quasiparticle random phase approximation (QRPA). Such estimates encompass recent independent calculations of NMEs, and can thus still provide a fair representation of the nuclear model uncertainties. In this context, we compare the claim of 0 nu beta beta decay in Ge-76 with recent negative results in Xe-136 and in other nuclei, and we infer the lifetime ranges allowed or excluded at 90% C.L. We also highlight some issues that should be addressed in order to properly compare and combine results coming from different 0 nu beta beta decay candidate nuclei., Comment: 8 pages, including 4 figures

A new generation of neutrinoless double beta decay experiments with improved sensitivity is currently under design and construction. They will probe inverted hierarchy region of the neutrino mass pattern. There is also a revived interest to the resonant neutrinoless double-electron capture, which has also a potential to probe lepton number conservation and to investigate the neutrino nature and mass scale. The primary concern are the nuclear matrix elements. Clearly, the accuracy of the determination of the effective Majorana neutrino mass from the measured 0\nu\beta\beta-decay half-life is mainly determined by our knowledge of the nuclear matrix elements. We review recent progress achieved in the calculation of 0\nu\beta\beta and 0\nu ECEC nuclear matrix elements within the quasiparticle random phase approximation. A considered self-consistent approach allow to derive the pairing, residual interactions and the two-nucleon short-range correlations from the same modern realistic nucleon-nucleon potentials. The effect of nuclear deformation is taken into account. A possibility to evaluate 0\nu\beta\beta-decay matrix elements phenomenologically is discussed., Comment: 24 pages; 80 references. arXiv admin note: substantial text overlap with arXiv:1101.2149

A novel approach is developed to find the three-body breakup amplitudes and cross sections within the modified Faddeev equation framework. The method is based on the lattice-like discretization of the three-body continuum with a three-body stationary wave-packet basis in momentum space. The approach makes it possible to simplify drastically all the three- and few-body breakup calculations due to discrete wave-packet representations for the few-body continuum and simultaneous lattice representation for all the scattering operators entering the integral equation kernels. As a result, the few-body breakup can be treated as a particular case of multi-channel scattering in which part of the channels represents the true few-body continuum states. As an illustration for the novel approach, an accurate calculations for the three-body breakup process $n+d\to n+n+p$ with non-local and local $NN$ interactions are calculated. The results obtained reproduce nicely the benchmark calculation results using the traditional Faddeev scheme which requires much more tedious and time-consuming calculations., Comment: 17 pages, 13 figures

The Neutrinoless double beta Decay allows to determine the effectice Majorana electron neutrino mass. For this the following conditions have to be satisfied: (i) The neutrino must be a Majorana particle, i. e. identical to the antiparticle. (ii) The half life has to be measured. (iii)The transition matrix element must be reliably calculated. (iv) The leading mechanism must be the light Majorana neutrino exchange. The present contribution studies the accuracy with which one can calculate by different methods: (1) Quasi-Particle Random Phase Approach (QRPA), (2) the Shell Model (SM), (3) the (before the variation) angular momentum projected Hartree-Fock-Bogoliubov method (PHFB)and the (4) Interacting Boson Approach (IBA). In the second part we investigate how to determine experimentally the leading mechanism for the Neutrinoless Double Beta Decay. Is it (a) the light Majorana neutrino exchange as one assumes to determine the effective Majorana neutrino mass, ist it the heavy left (b) or right handed (c) Majorana neutrino exchange allowed by left-right symmetric Grand Unified Theories (GUT's). Is it a mechanism due to Supersymmetry e.g. with gluino exchange and R-parity and lepton number violating terms. At the end we assume, that Klapdor et al. have indeed measured the Neutrinoless Double Beta Decay(, although contested,)and that the light Majorana neutrino exchange is the leading mechanism. With our matrix elements we obtain then an effective Majorana neutrino mass of: = 0.24 [eV], exp (pm) 0.02; theor. (pm) 0.01 [eV], Comment: 13 pages, 5 figures

Partial decay widths of various decay channels of the X(1835) are evaluated in the 3P0 quark model, assuming that the X(1835) is a nucleon-antinucleon bound state. It is found that the decays to rho+rho, omega+omega and pion+a0(1450) dominate over other channels, and that the product branching fractions of J/psi to pion+pion+eta and J/psi to pion+pion+eta' are in the same order. We suggest that the X(1835) may be searched in the pion+a0(1450) channel., Comment: Changed X(1850) to X(1835) in Abstract

We specify conditions under which the nucleon-nucleon interaction, based on the t-channel meson-exchange mechanism, is equivalent to an interaction generated via an s-channel exchange of six-quark bags. The duality is possible provided the alternation of zeros and poles of the non-dispersive part of D function takes place in the normalization where the imaginary part of D is non-negative and the CDD poles are the only poles of D., Comment: 13 pages, 1 figure, 1 table. To appear in Rom. Journ. Phys., Vol. 57, Special issue dedicated to the 80th birthday of Aureliu Sandulescu

The mean values of a many-body Hamiltonian including a proton-neutron pairing term and matrix elements of one-, two- and four-body operators within a basis of particle number projected BCS states, are analytically expressed in terms of a single function Q(N) depending on the number of particles, $N$. The function Q(N) is calculated using a recursion in $N$ in which the shells and the BCS angles are kept the same for any step of iteration. An illustrative example is numerically considered in a restricted single particle space. Some specific features for the standard BCS, the projection after variation approach as well as for the variation after projection formalism, are pointed out., Comment: 17 pages, 4 figures, 1 table

We study the resonant neutrinoless double-electron capture (0nECEC) in 152Gd, 164Er and 180W atoms, associated with the ground-state to ground-state nuclear transitions. The corresponding matrix elements are calculated within the deformed QRPA using the realistic Bonn-CD nucleon-nucleon interaction. The half-lives are estimated with the use of the most recent precision data on the Q-values of these processes. Perspectives of experimental search for the 0nECEC with the isotopes 152Gd, 164Er and 180W are discussed., Comment: 6 pages

Supplementing the Liquid Drop Model (LDM) Hamiltonian, written in the intrinsic reference frame, with a sextic oscillator plus a centrifugal term in the variable $\beta$ and a potential in $\gamma$ with a minimum in $\frac{\pi}{6}$, the Sch\"{o}dinger equation is separated for the two variables which results in having a new description for the triaxial nuclei, called Sextic and Mathieu Approach (SMA). SMA is applied for two non-axial nuclei, $^{180}$Hf and $^{182}$W and results are compared with those yielded by the Coherent State Model (CSM). As the main result of this paper we derive analytically the equations characterizing SMA from a semi-classical treatment of the CSM Hamiltonian. In this manner the potentials in $\beta$ and $\gamma$ variables respectively, show up in a quite natural way which contrasts their ad-hoc choice when SMA emerges from LDM., Comment: 13 figures, 13 pages

Analytical formulas for the excitation energies as well as for the electric quadrupole reduced transition probabilities in the ground, beta and gamma bands were derived within the coherent state model for the near vibrational and well deformed nuclei. Numerical calculations were performed for 42 nuclei exhibiting various symmetries and therefore with specific properties. Comparison of the calculation results with the corresponding experimental data shows a good agreement. The parameters involved in the proposed model satisfy evident regularities being interpolated by smooth curves. Few of them, which fall out of the curves, are interpreted as signatures for a critical point in a specific phase transition. This is actually supported also by the figures showing the excitation energy dependence on the angular momentum. The formulas provided for energies and B(E2) values are very simple, being written in a compact form, and therefore easy to be handled to explain the new experimental data., Comment: 9 figures, 50 pages

The inclusive reactions $pp \rightarrow e^+ e^- X$ and $np \rightarrow e^+ e^- X$ at the laboratory kinetic energy of 1.25 GeV are investigated in a model of dominance of nucleon and $\Delta$ resonances. Experimental data for these reactions have recently been reported by the HADES Collaboration. In the original model, the dileptons are produced either from the decays of nucleon and $\Delta$ resonances $R \rightarrow N e^+ e^-$ or from the Dalitz decays of $\pi^0$- and $\eta$-mesons created in the $R \to N\pi^0$ and $R \to N\eta$ decays. We found that the distribution of dilepton invariant masses in the $pp \rightarrow e^+ e^- X$ reaction is well reproduced by the contributions of $R \rightarrow N e^+ e^-$ decays and $R \rightarrow N \pi^0$, $\pi^0 \to \gamma e^+e^-$ decays. Among the resonances, the predominant contribution comes from the $\Delta(1232)$, which determines both the direct decay channel $R \rightarrow N e^+ e^-$ and the pion decay channel. In the collisions $np \rightarrow e^+ e^- X$, additional significant contributions arise from the $\eta$-meson Dalitz decays, produced in the $np \rightarrow np\eta$ and $np \rightarrow d\eta$ reactions, the radiative capture $np \rightarrow d e^+ e^-$, and the $np \rightarrow np e^+ e^-$ bremsstrahlung. These mechanisms may partly explain the strong excess of dileptons in the cross section for collisions of $np$ versus $pp$, which ranges from 7 to 100 times for the dilepton invariant masses of 0.2 to 0.5 GeV.

The $^{150}$Nd($^3$He,$t$) reaction at 140 MeV/u and $^{150}$Sm($t$,$^3$He) reaction at 115 MeV/u were measured, populating excited states in $^{150}$Pm. The transitions studied populate intermediate states of importance for the (neutrinoless) $\beta\beta$ decay of $^{150}$Nd to $^{150}$Sm. Monopole and dipole contributions to the measured excitation-energy spectra were extracted by using multipole decomposition analyses. The experimental results were compared with theoretical calculations obtained within the framework of Quasiparticle Random-Phase Approximation (QRPA), which is one of the main methods employed for estimating the half-life of the neutrinoless $\beta\beta$ decay ($0\nu\beta\beta$) of $^{150}$Nd. The present results thus provide useful information on the neutrino responses for evaluating the $0\nu\beta\beta$ and $2\nu\beta\beta$ matrix elements. The $2\nu\beta\beta$ matrix element calculated from the Gamow-Teller transitions through the lowest $1^{+}$ state in the intermediate nucleus is maximally about half of that deduced from the half-life measured in $2\nu\beta\beta$ direct counting experiments and at least several transitions through $1^{+}$ intermediate states in $^{150}$Pm are required to explain the $2\nu\beta\beta$ half-life. Because Gamow-Teller transitions in the $^{150}$Sm($t$,$^3$He) experiment are strongly Pauli-blocked, the extraction of Gamow-Teller strengths was complicated by the excitation of the $2\hbar\omega$, $\Delta L=0$, $\Delta S=1$ isovector spin-flip giant monopole resonance (IVSGMR). However, the near absence of Gamow-Teller transition strength made it possible to cleanly identify this resonance, and the strength observed is consistent with the full exhaustion of the non-energy-weighted sum rule for the IVSGMR., Comment: 18 pages, 13 figures, 2 tables

Neutrinoless Double Beta Decay ($0\nu\beta\beta$) is presently the only known experiment to distinguisch between Dirac neutrinos, different from their antiparticles, and Majorana neutrinos, identical with their antiparticles. In addition $0\nu\beta\beta$ allows to determine the absolute scale of the neutrino masses. This is not possible with neutrino oscillations. To determine the neutrino masses one must assume, that the light Majorana neutrino exchange is the leading mechanism for $0\nu\beta\beta$ and that the matrix element of this transition can ba calculated reliably. The experimental $0\nu\beta\beta$ transition amplitude in this mechanism is a product of the light left handed effective Majorana neutrino mass and of this transition matrix element. The different methods, Quasi-particle Random Phase Approximation (QRPA), Shell Model (SM), Projected Hartree-Fock-Bogoliubov (PHFB) and Interacting Boson Model (IBM2) used in the literature and the reliability of the matrix elements in these approaches are reviewed. In the second part it is investigated how one can determine the leading mechanism or mechanisms from the data of the $0\nu\beta\beta$ decay in different nuclei. Explicite expressions are given for the transition matrix elements. is shown, that possible interference terms allow to test CP (Charge and Parity conjugation) violation., Comment: Contribution to the EPS conference in Eilath: "Nuclear Physics in Astrophysics 5." April 3rd to 8th. 2011

We calculate nuclear matrix elements (NME) of neutrinoless double beta decay in four different candidate nuclei (Ge-76, Se-82, Mo-100, Te-130) within the quasiparticle random phase approximation (QRPA) and its uncertainties. We assume (up to) four coexisting mechanisms for neutrinoless double beta decay, mediated by light Majorana neutrino exchange, heavy Majorana neutrino exchange, R-parity breaking supersymmetry, and squark-neutrino, interfering either constructively or destructively with each other. We find that, unfortunately, current NME uncertainties appear to prevent a robust determination of the relative contribution of each mechanism to the decay amplitude, even assuming accurate measurements of decay lifetimes. The near-degeneracy of the decay mechanisms is analyzed with simple algebraic techniques, which do not involve assumptions about the statistical distribution of errors. We discuss implications of such degeneracy on prospective searches for absolute neutrino masses., Comment: Expanded discussion and bibliography; to appear in Phys. Rev. D

In the present work the sensitivity of the QRPA calculation results to a realistic residual interaction is analyzed in the framework of the approach of Refs. \cite{Rum98,Rodin05}. Both Gamow-Teller (GT) and Fermi (F) \bb-decay amplitudes $M^{2\nu}$, along with the corresponding energy-weighted sum rules $S$, are calculated. General expressions relating $S$ to a realistic residual particle-particle interaction are derived, which show a pronounced sensitivity of $S$ to the singlet-channel interaction in the case of F transitions, and to the triplet-channel interaction in the case of GT transitions. Decompositions of $M^{2\nu}$, as well as the monopole transition contributions to $M^{0\nu}$, are obtained by the method of Refs. \cite{Rum98,Rodin05}. It is shown that in most of the cases almost the whole dependence of $M^{2\nu}$ and $M^{0\nu}$ on the particle-particle renormalization parameter $g_{pp}$ is accounted for by the $g_{pp}$-dependence of the corresponding sum rules $S$. Thus, the $g_{pp}$-sensitivity of calculated $M^{2\nu}$ and $M^{0\nu}$ is unavoidable since it is dictated by the generic structure of the $\beta\beta$ amplitudes. Finally, a better isospin-consistent way of a renormalization of the realistic residual particle-particle interaction to use in QRPA calculations is suggested., Comment: 15 pages, 4 figures, to be published in PRC

The planned rhenium beta-decay experiment MARE might probe the absolute mass scale of neutrinos with the same sensitivity as the tritium beta-decay experiment KATRIN, which will start data taking in 2011 and will proceed for five years. We present the energy distribution of emitted electrons for the first unique forbidden beta-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 beta-decay is derived. It is shown that the Kurie plot near the endpoint is within a good accuracy linear in the limit of massless neutrinos like the Kurie plot of the superallowed beta-decay of 3H., Comment: 4 pages, 3 figures

In this paper a microscopic state-of-the-art approach to calculation of the nuclear matrix element $M^{0\nu}$ for neutrinoless double beta decay with an account for nuclear deformation is presented in length and applied for $^{76}$Ge, $^{150}$Nd and $^{160}$Gd. The proton-neutron quasiparticle random phase approximation (QRPA) with a realistic residual interaction [the Brueckner $G$ matrix derived from the charge-depending Bonn (Bonn-CD) nucleon-nucleon potential] is used as the underlying nuclear structure model. The effects of the short range correlations and the quenching of the axial vector coupling constant $g_A$ are analyzed. The results show that neutrinoless double beta decay of $^{150}$Nd, to be measured soon by the SNO+ collaboration, provides one of the best probes of the Majorana neutrino mass. This confirms our preliminary conclusion in Ref. {Fang10}., Comment: 14 pages, 3 figures

As shown in Ref.\cite{Rod09}, the Fermi nuclear matrix element $M^{0\nu}_F$ of neutrinoless double beta ($0\nu\beta\beta$) decay can be reconstructed if one is able to measure the isospin-forbidden single Fermi transition matrix element from the ground state of the final nucleus to the isobaric analog state (IAS) of the initial nucleus, for instance by means of charge-exchange reactions of the $(n,p)$-type. Here, simple estimates for $^{82}$Se are made which show that indeed the tiny cross section $\sigma_{np}(0_f^+\to IAS)$ is dominated by the admixture of the double IAS in the ground state of the final nucleus provided that the isospin mixing is weak and can be treated perturbatively. A measurement of such a cross section would definitely be a very difficult task, but it can advance a lot our knowledge of the $0\nu\beta\beta$ nuclear matrix element., Comment: 7 pages, 2 figures; to appear in the proceedings of the International School of Nuclear Physics: 32nd Course: Particle and Nuclear Astrophysics, Erice, Sicily, Italy, 16-24 Sep 2010

The process of neutrinoless double electron capture ($0\nu$ECEC) is revisited for those cases where the two participating atoms are nearly degenerate in mass. The theoretical framework is the formalism of an oscillation of two atoms with different total lepton number (and parity), one of which can be in an excited state so that mass degeneracy is realized. In such a case and assuming light Majorana neutrinos, the two atoms will be in a mixed configuration with respect to the weak interaction. A resonant enhancement of transitions between such pairs of atoms will occur, which could be detected by the subsequent electromagnetic de-excitation of the excited state of the daughter atom and nucleus. Available data of atomic masses, as well as nuclear and atomic excitations are used to select the most likely candidates for such resonant $0\nu$ECEC transitions. Assuming an effective mass for the Majorana neutrino of 1 eV, some half-lives are predicted to be as low as $10^{22}$ years in the unitary limit. It is argued that, in order to obtain more accurate predictions for the $0\nu$ECEC half-lives, precision mass measurements of the atoms involved are necessary, which can readily be accomplished by today's high precision Penning traps. Further advancements also require a better understanding of high-lying excited states of the final nuclei (i.e. excitation energy, angular momentum and parity) and the calculation of the nuclear matrix elements., Comment: 35 pages LaTeX, 2 eps figures, 5 tables; Sect. 3.6 extended, references to recent papers added, replaced with published version

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.

A microscopic state-of-the-art calculation of the nuclear matrix element for neutrinoless double beta decay of $^{150}$Nd with an account for nuclear deformation is performed. The proton-neutron quasiparticle random phase approximation (QRPA) with a realistic residual interaction [the Brueckner $G$ matrix derived from the charge-depending Bonn (Bonn-CD) nucleon-nucleon potential] is used as the underlying nuclear structure model. The present calculated matrix element is suppressed by about 40% as compared with our previous QRPA result for $^{150}$Nd obtained with neglect of deformation. By making use of this newest nuclear matrix element, one may conclude that neutrinoless double beta decay of $^{150}$Nd, to be measured soon by the SNO+ collaboration, provides one of the best probes of the Majorana neutrino mass., Comment: 7 pages, to be published in PRC

An isospin-selfconsistent pn-continuum-QRPA approach is formulated and applied to describe the Gamow-Teller strength distributions for $\beta\beta$-decaying open-shell nuclei. The calculation results obtained for the pairs of nuclei $^{76}$Ge-Se, $^{100}$Mo-Ru, $^{116}$Cd-Sn, and $^{130}$Te-Xe are compared with available experimental data.

A time dependent variational principle is used to dequantize a second order quadrupole boson Hamiltonian. The classical equations for the generalized coordinate and the constraint for angular momentum are quantized and then analytically solved. A generalized Holmberg-Lipas formula for energies is obtained. A similar $J(J+1)$ dependence is provided by the coherent state model (CSM) in the large deformation regime, by using an expansion in powers of $1/x$ for energies, with $x$ denoting a deformation parameter squared. A simple compact expression is also possible for the near vibrational regime. These three expressions have been used for 44 nuclei covering regions characterized by different dynamic symmetries or in other words belonging to the all known nuclear phases. Nuclei satisfying the specific symmetries of the critical point in the phase transitions $O(6)\to SU(3)$, $SU(5)\to SU(3)$ have been also considered. The agreement between the results and the corresponding experimental data is very good. This is reflected in very small r.m.s. values of deviations., Comment: 34 pages, 5 figures

Usual Woods-Saxon single particle levels with BCS pairing are not able to reproduce the experimental occupation probabilities of the proton and neutron levels 1p_{3/2}, 1p_{1/2}, 0f_{5/2}, 0g_{9/2} in the double-beta decay system 76Ge to 76Se. Shifting down the 0g_{9/2} level by hand can explain the data but it is not satisfactory. Here it is shown that a selfconsistent Hartree-Fock+BCS approach with experimental deformations for 76Ge and 76Se may decisively improve the agreement with the recent data on occupation probabilities by Schiffer et al. and Kay et al. Best agreement with available data on 76Ge and 76Se, as well as on neighbor isotopes, is obtained when the spin-orbit strength for neutrons is allowed to be larger than that for protons. The two-neutrino double-beta decay matrix element is also shown to agree with data., Comment: 10 pages, 6 figures

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 angular momenta and parities of the neutron pairs, which are changed into two protons by the $0\nu\beta\beta$ decay. The QRPA and SM involve about the same angular momentum and parity neutron pairs, while the HFB is restricted to $0^{+}, 2^{+}, 4^{+}, ...$, and IBM to $0^{+}$ and $2^{+}$ nucleon pairs. The differences in the seniority contributions for the QRPA and the SM are discussed., Comment: 14 pages, 8 figures, extensively revised to discuss the effect of different seniorities, 1 figure and 2 tables added

The $2\nu\beta\beta$-decay running sums for $^{76}$Ge and $^{150}$Nd 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 $g_{pp}$ 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 $g_{pp}$ a significant negative contribution to the total $2\nu\beta\beta$-decay matrix element is found to come from the energy region of the giant Gamow-Teller resonance. This behavior agrees with the results of other authors., Comment: 4 pages, 2 figures, to be published in PRC

A particle-core Hamiltonian is used to describe the lowest parity partner bands $K^{\pi}=1/2^{\pm}$ in $^{219}$Ra, $^{237}$U and $^{239}$Pu, and three parity partner bands, $K^{\pi}=1/2^{\pm}, 3/2^{\pm}, 5/2^{\pm}$, in $^{227}$Ra. The core is described by a quadrupole and octupole boson Hamiltonian which was previously used for the description of four positive and four negative parity bands in the neighboring even-even isotopes. The particle-core Hamiltonian consists of four terms: a quadrupole-quadrupole, an octupole-octupole, a spin-spin and a rotational $\hat{I}^2$ interaction, with $\hat {I}$ denoting the total angular momentum. The single particle space for the odd nucleon consists of three spherical shell model states, two of positive and one of negative parity. The product of these states with a collective deformed ground state and the intrinsic gamma band state generate, through angular momentum projection, the bands with $K^{\pi}=1/2^{\pm},3/2^{\pm},5/2^{\pm}$, respectively. In the space of projected states one calculates the energies of the considered bands. The resulting excitation energies are compared with the corresponding experimental data as well as with those obtained with other approaches. Also, we searched for some signatures for a static octupole deformation in the considered odd isotopes. The calculated branching ratios in $^{219}$Ra agree quite well with the corresponding experimental data., Comment: 26 pages, r figures

By making use of the isospin conservation by strong interaction, the Fermi $0\nu\beta\beta$ nuclear matrix element $M_{F}^{0\nu}$ is transformed to acquire the form of an energy-weighted double Fermi transition matrix element. This useful representation allows reconstruction of the total $M_{F}^{0\nu}$ provided a small isospin-breaking Fermi matrix element between the isobaric analog state in the intermediate nucleus and the ground state of the daughter nucleus could be measured, e.g. by charge-exchange reactions. Such a measurement could set a scale for the $0\nu\beta\beta$ nuclear matrix elements and help much to discriminate between different nuclear structure models in which calculated $M_{F}^{0\nu}$ may differ by as much as the factor of 5., Comment: 4 pages, to be published in Physical Review C

Two microscopic models, UrQMD and QGSM, are used to extract the effective equation of state (EOS) of locally equilibrated nuclear matter produced in heavy-ion collisions at energies from 11.6 AGeV to 160 AGeV. Analysis is performed for the fixed central cubic cell of volume V = 125 fm**3 and for the expanding cell that followed the growth of the central area with uniformly distributed energy. For all reactions the state of local equilibrium is nearly approached in both models after a certain relaxation period. The EOS has a simple linear dependence P/e = c_s**2 with 0.12 < c_s**2 < 0.145. Heavy resonances are shown to be responsible for deviations of the c_s**2(T) and c_s**2(mu_B) from linear behavior. In the T-mu_B and T-mu_S planes the EOS has also almost linear dependence and demonstrates kinks related not to the deconfinement phase transition but to inelastic freeze-out in the system., Comment: SQM2008 proceedings, 6 pages

Theories beyond the standard model include a number of new particles some of which might be light and weakly coupled to ordinary matter. Such particles affect equation of state of nuclear matter and can shift admissible masses of neutron stars to higher values. The internal structure of neutron stars is modified provided the ratio between coupling strength and mass squared of a weakly interacting light boson is above $g^2/\mu^2 \sim 25 ~\mathrm{GeV}^{-2}$. We provide limits on the couplings with the strange sector, which cannot be achieved from laboratory experiments analysis. When the couplings to the first family of quarks is considered the limits imposed by the neutron stars are not more stringent than the existing laboratory ones. The observations on neutron stars give evidence that equation of state of the $\beta$-equilibrated nuclear matter is stiffer than expected from many-body theory of nuclei and nuclear matter. A weakly interacting light vector boson coupled predominantly to the second family of the quarks can produce the required stiffening., Comment: 5 pages REVTeX, 2 pdf figures

A self-consistent calculation of nuclear matrix elements of the neutrinoless double beta decays (0nbb) of 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128Te, 130Te and 130Xe 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 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 0nbb-decay are obtained, which 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 0nbb-decay matrix elements., Comment: 11 pages, 5 figures

The measured occupancies of valence orbits in $^{76}$Ge and $^{76}$Se 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 selfconsitent 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 $0\nu\beta\beta$ nuclear matrix element for the $^{76}$Ge $\to$ $^{76}$Se transition is reduced by $\sim$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 $0\nu\beta\beta$ matrix element for the $^{82}$Se $\to$ $^{82}$Kr transition, making it also closer to the shell model prediction., Comment: 9 pages, 6 figures

Solvable Hamiltonians for the $\beta$ and $\gamma$ intrinsic shape coordinates are proposed. The eigenfunctions of the $\gamma$ Hamiltonian are spheroidal periodic functions, while the Hamiltonian for the $\beta$ degree of freedom involves the Davidson's potential and admits eigenfunctions which can be expressed in terms of the generalized Legendre polynomials. The proposed model goes to X(5) in the limit of $|\gamma|$-small. Some drawbacks of the X(5) model, as are the eigenfunction periodicity and the $\gamma$ Hamiltonian hermiticity, are absent in the present approach. Results of numerical applications to $^{150}$Nd, $^{154}$Gd and $^{192}$Os are in good agreement to the experimental data. Comparison with X(5) calculations suggests that the present approach provides a quantitative better description of the data. This is especially true for the excitation energies in the gamma band., Comment: 48 pages, 11 figures