Here, we study the neutrinoless double-$β$ ($0νββ$) decay between the ground state and the first $2^+$ state of $^{76}\mbox{Ge} \rightarrow {}^{76}\mbox{Se}$, $^{82}\mbox{Se} \rightarrow{}^{82}\mbox{Kr}$, $^{130}\mbox{Te} \rightarrow {}^{130}\mbox{Xe}$ and $^{136}\mbox{Xe} \rightarrow {}^{136}\mbox{Ba}$ systems. The relevant nuclear matrix elements (NMEs) involved in the process are calculated within the formalism of the microscopic interacting boson model (IBM-2). The IBM-2 has been widely used to obtain predictions for nuclear observables, such as the spectrum, but also to explore the possible emergence of beyond-the-Standard Model effects in the weak interactions of nuclei. Our calculations are carried out by considering the exchange of a Majorana neutrino between two nucleons ($2N$-mechanism). In addition to NMEs, we calculate the associated leptonic phase-space factors (PSFs) using electron radial wave functions, which are obtained by solving numerically the Dirac equation of a screened Coulomb potential that takes into account finite nuclear size. By combining our IBM-2 results for the NMEs with those for the PSFs along with experimental half-life limits, we can set limits on the $\langle λ\rangle$ and $\langle η\rangle$ couplings of left-right (L-R) models.
Majoron emitting neutrinoless double beta decay in the electroweak chiral gauge extensions
本文指出了SU（3）_C x G_W x U（1）模型中Majoron发射无中微子双β衰变的基本机制，其中G_W = SU（3）_L和SU（4）_L为电弱味手征扩展。这两种已知的Majoron发射过程，带电Majoron发射，其中无质量的Nambu-Goldstone玻色子本身携带轻子电荷，$L=-2$，以及普通Majoron发射，其中玻色子具有小的质量被发现是可能的。PACS编号：11.15.Ex、12.60.Fr、14.80.Cp
Neutrinoless double-$β$ decay is of fundamental importance for determining the neutrino mass. Although double electron ($β^-β^-$) decay is the most promising mode, in very recent years interest in double positron ($β^+β^+$) decay, positron emitting electron capture ($ECβ^+$), and double electron capture ($ECEC$) has been renewed. We present here results of a calculation of nuclear matrix elements for neutrinoless double-$β^+$ decay and positron emitting electron capture within the framework of the microscopic interacting boson model (IBM-2) for $^{58}$Ni, $^{64}$Zn, $^{78}$Kr, $^{96}$Ru, $^{10…
Nuclear matrix elements (NME) for exchange of arbitrary mass neutrinos are calculated in the interacting boson model (IBM-2). By combining the NME with the phase space factors (PSF), expected half-lives for neutrinos of mass $m_N$ and coupling $U_{eN}$ are estimated. Limits on sterile neutrinos with masses in the eV, keV, MeV-GeV, and TeV range are given.
Neutrinoless double-$β$ decay is of fundamental importance for the determining neutrino mass. By combining a calculation of nuclear matrix elements within the framework of the microscopic interacting boson model (IBM-2) with an improved calculation of phase space factors, we set limits on the average light neutrino mass and on the average inverse heavy neutrino mass (flavor violating parameter).
Understanding the origin of lepton number violation is one of the fundamental questions in particle physics today. Neutrinoless double beta decay provides a way in which this violation can be tested. In this article, we derive the form of hadronic and leptonic matrix elements for all possible long-range mechanisms of neutrinoless double beta decay. With these, we calculate the numerical values of the nuclear matrix elements (NME) and phase space factors (PSF) by making use of the interacting boson model of the nucleus (IBM-2) for NMEs and of exact Dirac wave functions for the PSFs. We show tha…
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 mak…
Direct determination of the neutrino mass is at the present time one of the most important aims of experimental and theoretical research in nuclear and particle physics. A possible way of detection is through neutrinoless double electron capture, $0νECEC$. This process can only occur when the energy of the initial state matches precisely that of the final state. We present here a calculation of prefactors (PF) and nuclear matrix elements (NME) within the framework of the microscopic interacting boson model (IBM-2) for $^{124}$Xe, $^{152}$Gd, $^{156}$Dy, $^{164}$Er, and $^{180}$W. From PF and N…
In this paper a microscopic state-of-the-art approach to calculation of the nuclear matrix element $M^{0ν}$ 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 …
A comprehensive analysis of the structure of the nuclear matrix elements (NMEs) of neutrinoless double beta-minus decays to the 0^+ ground and first excited states is performed in terms of the contributing multipole states in the intermediate nuclei of neutrinoless double beta-minus transitions. We concentrate on the transitions mediated by the light (l-NMEs) Majorana neutrinos. As nuclear model we use the proton-neutron quasiparticle random-phase approximation (pnQRPA) with a realistic two-nucleon interaction based on the Bonn one-boson-exchange G matrix. In the computations we include the ap…
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 (be…
Background: The interacting boson model (IBM) has been used extensively to calculate the matrix elements governing neutrinoless double-beta decay. Studies within other models indicate that a good description of neutron-proton pairing is essential for accurate calculations of those matrix elements. The usual interacting boson model is based only on like-particle pairs, however, and the extent to which it captures neutron-proton pairing is not clear. Purpose: To determine whether neutron-proton pairing should be explicitly included as neutron-proton bosons in IBM calculations of neutrinoless dou…
We study the impact of the mixing (LR mixing) between the standard model $W$ boson and its hypothetical, heavier right-handed parter $W_R$ on the neutrinoless double beta decay ($0νββ$-decay) rate. Our study is done in the minimal left-right symmetric model assuming type-II dominance scenario with charge conjugation as the left-right symmetry. We then show that the $0νββ$-decay rate may be dominated by the contribution proportional to this LR mixing, which at the hadronic level induces the leading-order contribution to the interaction between two pions and two charged leptons. The resulting lo…
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 $0νββ$ 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 …
A microscopic interpretation of the s and d bosons of the Interacting Boson Model is being suggested: the s, d bosons can be interpreted as symmetric pairs of harmonic oscillator quanta of the valence nuclear shell. Within this interpretation, the SU(3) limit of the Interacting Boson Model results to the Elliott SU(3) symmetry.
The change in the configuration of valence protons between the initial and final states in the neutrinoless double-$β$ decay of $^{130}$Te $\rightarrow$ $^{130}$Xe and of $^{136}$Xe $\rightarrow$ $^{136}$Ba has been determined by measuring the cross sections of the ($d$,$^3$He) reaction with 101-MeV deuterons. Together with our recent determination of the relevant neutron configurations involved in the process, a quantitative comparison with the latest shell-model and interacting-boson-model calculations reveals significant discrepancies. These are the same calculations used to determine the n…
Neutrinoless double beta decay searches are currently among the major foci of experimental physics. The observation of such a decay will have important implications in our understanding of the intrinsic nature of neutrinos and shed light on the limitations of the Standard Model. The rate of this process depends on both the unknown neutrino effective mass and the nuclear matrix element associated with the given neutrinoless double-beta decay transition. The latter can only be provided by theoretical calculations, hence the need of accurate theoretical predictions of the nuclear matrix element f…
The particle-hole symmetry (equivalence) of the full shell-model Hilbert space is straightforward and routinely used in practical calculations. In this work we show that this symmetry is preserved in the subspace truncated at a certain generalized seniority, and give the explicit transformation between the states in the two types (particle and hole) of representations. Based on the results, we study the particle-hole symmetry in popular theories that could be regarded as further truncations on top of the generalized seniority, including the microscopic interacting boson (fermion) model, the nu…
Nuclear transition matrix elements (NTME) for the neutrinoless double beta decay of $^{70}$Zn, $^{80}$Se and $^{82}$Se nuclei are calculated within the framework of the deformed shell model based on Hartree-Fock states. For $^{70}$Zn, jj44b interaction in $^{2}p_{3/2}$, $^{1}f_{5/2}$, $^{2}p_{1/2}$ and $^{1}g_{9/2}$ space with $^{56}$Ni as the core is employed. However, for $^{80}$Se and $^{82}$Se nuclei, a modified Kuo interaction with the above core and model space are employed. Most of our calculations in this region were performed with this effective interaction. However, jj44b interaction…
We introduce the formalism to describe heavy-ion Double-Charge-Exchange (DCE) processes in the eikonal approximation. We focus on the low-momentum-transfer limit -- corresponding to the differential cross section at $θ=0^\circ$ -- and, for the first time, we show that it is possible to factorize the DCE cross-section in terms of reaction and nuclear parts. Whereas in the $θ\neq0^\circ$ case the nuclear part is a convolution of the beam and target nuclear matrix elements (NMEs), for $θ=0^\circ$ we demonstrate - for the first time- that the transition matrix elements can be written as the sum of…
We re-analyze the compatibility of the claimed observation of neutrinoless double beta decay ($0νββ$) in $^{76}$Ge with the new limits on the half-life of $^{136}$Xe from EXO-200 and KamLAND-Zen. Including recent calculations of the nuclear matrix elements (NMEs), we show that while the claim in $^{76}$Ge is still compatible with the individual limits from $^{136}$Xe, it is inconsistent with the KamLAND-Zen+EXO-200 combined limit for all but one NME calculations. After imposing the most stringent upper limit on the sum of light neutrino masses from Planck, we find that the canonical light neut…
The angular correlation of the electrons emitted in the neutrinoless double beta decay ($0\nu2β$) is presented using a general Lorentz invariant effective Lagrangian for the leptonic and hadronic charged weak currents. We show that the coefficient $K$ in the angular correlation $dΓ/d\cos θ\propto (1-K\cos θ)$ is essentially independent of the nuclear matrix element models and present its numerical values for the five nuclei of interest ($^{76}{Ge}$, $^{82}{Se}$, $^{100}{Mo}$, $^{130}{Te}$, and $^{136}{Xe}$), assuming that the $0\nu2β$-decays in these nuclei are induced solely by a light Majora…
We propose a novel formulation of the Interacting Boson Model (IBM) for rotational nuclei with axially-symmetric strong deformation. The intrinsic structure represented by the potential energy surface (PES) of a given multi-nucleon system has a certain similarity to that of the corresponding multi-boson system. Based on this feature, one can derive an appropriate boson Hamiltonian as already reported. This prescription, however, has a major difficulty in rotational spectra of strongly deformed nuclei: the bosonic moment of inertia is significantly smaller than the corresponding nucleonic one. …
Two-neutron transfer reactions are studied within the interacting boson model based on the nuclear energy density functional theory. Constrained self-consistent mean-field calculations with the Skyrme energy density functional are performed to provide microscopic input to completely determine the Hamiltonian of the IBM. Spectroscopic properties are calculated only from the nucleonic degrees of freedom. This method is applied to study the $(t,p)$ and $(p,t)$ transfer reactions in the assorted set of rare-earth nuclei $^{146-158}$Sm, $^{148-160}$Gd, and $^{150-162}$Dy, where spherical-to-axially…
Background: Direct determination of the neutrino mass through double-$β$ decay is at the present time one of the most important areas of experimental and theoretical research in nuclear and particle physics. Purpose: We calculate nuclear matrix elements for the extraction of the average neutrino mass in neutrinoless double-$β$ decay. Methods: The microscopic interacting boson model (IBM-2) is used. Results: Nuclear matrix elements in the closure approximation are calculated for $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{110}$Pd, $^{116}$Cd, $^{124}$Sn, $^{128}$Te, $^{130}$Te, $…
Reflection asymmetric, octupole shapes in nuclei are a prominent aspect of nuclear structure, and have been recurrently studied over the decades. Recent experiments using radioactive-ion beams have provided evidence for stable octupole shapes. A variety of nuclear models have been employed for the related theoretical analyses. We review recent studies on the nuclear octupole shapes and collective excitations within the interacting boson model. A special focus is placed on the microscopic formulation of this model by using the mean-field method that is based on the framework of nuclear density …
A shape phase transition between stable octupole deformation and octupole vibrations in Th nuclei is analyzed in a microscopic framework based on nuclear density functional theory. The relativistic functional DD-PC1 is used to calculate axially-symmetric quadrupole-octupole constrained energy surfaces. Observables related to order parameters are computed using an interacting-boson Hamiltonian, with parameters determined by mapping the microscopic energy surfaces to the expectation value of the Hamiltonian in the boson condensate. The systematics of constrained energy surfaces and low-energy ex…
Shape coexistence has been a subject of great interest in nuclear physics for many decades. In the context of the nuclear shell model, intruder excitations may give rise to remarkably low-lying excited $0^+$ states associated with different intrinsic shapes. In heavy open-shell nuclei, the dimension of the shell-model configuration space that includes such intruder excitations becomes exceedingly large, thus requiring a drastic truncation scheme. Such a framework has been provided by the interacting boson model (IBM). In this article we address the phenomenon of shape coexistence and its relev…
The structure of the $N=Z$ nucleus $^{28}$Si is studied by resorting to an IBM-type formalism with $s$ and $d$ bosons representing isospin $T=0$ and angular momentum $J=0$ and $J=2$ quartets, respectively. $T=0$ quartets are four-body correlated structures formed by two protons and two neutrons. The microscopic nature of the quartet bosons, meant as images of the fermionic quartets, is investigated by making use of a mapping procedure and is supported by the close resemblance between the phenomenological and microscopically derived Hamiltonians. The ground state band and two low-lying side ban…
We investigate the emergence and evolution of shape coexistence in the neutron-deficient Lead isotopes within the interacting boson model (IBM) plus configuration mixing with microscopic input based on the Gogny energy density functional (EDF). The microscopic potential energy surface obtained from the constrained self-consistent Hartree-Fock-Bogoliubov method employing the Gogny-D1M EDF is mapped onto the coherent-state expectation value of the configuration-mixing IBM Hamiltonian. In this way, the parameters of the IBM Hamiltonian are fixed for each of the three relevant configurations (sphe…
Microscopic energy density functionals (EDF) have become a standard tool for nuclear structure calculations, providing an accurate global description of nuclear ground states and collective excitations. For spectroscopic applications this framework has to be extended to account for collective correlations related to restoration of symmetries broken by the static mean field, and for fluctuations of collective variables. In this work we compare two approaches to five-dimensional quadrupole dynamics: the collective Hamiltonian for quadrupole vibrations and rotations, and the Interacting Boson Mod…
The structure of odd-$A$ $^{(115,117)}$Rh and $^{(115,117)}$Pd isotopes is studied by means of the neutron-proton Interacting Boson-Fermion Model (IBFM-2). $J^P = \frac{1}{2}^+$ quantum number assignment for the $^{(115,117)}$Pd ground-states is critically discussed and the predicted energy levels are compared to the existing experimental data. The resulting nuclear wave functions are used to compute the $β$-decay $ft$ values of the transitions from $^{(115,117)}$Rh to $^{(115,117)}$Pd in the microscopic IBFM-2 and the results compared with the data.
γ-softness in atomic nuclei is investigated in the framework of energy density functionals. By mapping constrained microscopic energy surfaces for a set of representative non-axial medium-heavy and heavy nuclei to a Hamiltonian of the proton-neutron interacting boson model (IBM-2) containing up to three-body interactions, low-lying collective spectra and transition rates are calculated. Observables are analyzed that distinguish between the two limiting geometrical pictures of non-axial nuclei: the rigid-triaxial rotor and the γ-unstable rotor. It is shown that neither of these pictures is real…
The interacting boson model with configuration mixing, with parameters derived from the self-consistent mean-field calculation employing the microscopic Gogny energy density functional, is applied to the systematic analysis of the low-lying structure in Hg isotopes. Excitation energies, electromagnetic transition rates, deformation properties, and ground-state properties of the $^{172-204}$Hg nuclei are obtained by mapping the microscopic deformation energy surface onto the equivalent IBM Hamiltonian in the boson condensate. These results point to the overall systematic trend of the transition…
The interacting boson-fermion model (IBFM), with parameters determined from the microscopic Hartree-Fock-Bogoliubov (HFB) approximation, based on the parametrization D1M of the Gogny energy density functional (EDF), is employed to study the structural evolution in odd-mass $γ$-soft nuclei. The deformation energy surfaces of even-even nuclei, single-particle energies and occupation probabilities of the corresponding odd-mass systems have been obtained within the constrained HFB approach. Those building blocks are then used as a microscopic input to build the IBFM Hamiltonian. The coupling const…
We develop a novel theoretical method for calculating spectroscopic properties of those nuclei with odd number of nucleons, that is based on the nuclear density functional theory and the particle-boson coupling scheme. Self-consistent mean-field calculation based on the DFT is performed to provide microscopic inputs to build the Hamiltonian of the interacting boson-fermion systems, which gives excitation spectra and transition rates of odd-mass nuclei. The method is successfully applied to identify the quantum shape phase transitions and the role of octupole correlations in odd-mass nuclei, an…
A coherent state technique is used to generate an Interacting Boson Model (IBM) Hamiltonian energy surface that simulates a mean field energy surface. The method presented here has some significant advantages over previous work. Specifically, that this can be a completely predictive requiring no a priori knowledge of the IBM parameters. The technique allows for the prediction of the low lying energy spectra and electromagnetic transition rates which are of astrophysical interest. Results and comparison with experiment are included for krypton, molybdenum, palladium, cadmium, gadolinium, dyspro…
