Renormalized Quasiparticle Random Phase Research Articles

Study of the exotic μ-e conversion in nuclei using RQRPA

The neutrinoless muon-to-electron conversion in nuclei is studied by using the renormalized quasiparticle random-phase approximation (RQRPA). This generalization of RPA is more reliable for the extremely small (μ-,e-) transition matrix elements than the ordinary QRPA because it restores the Pauli principle to a large extent. We apply the method to a set of nuclei throughout the periodic table, but we specifically investigate the 48Ti and 208Pb nuclei which are currently used as stopping targets at the PSI μ-e conversion experiments with the SINDRUM II spectrometer.

Multiple CP non-conserving mechanisms of (ββ)0ν -decay and nuclei with largely different nuclear matrix elements

We investigate the possibility to discriminate between different pairs of CP non-conserving mechanisms inducing the neutrinoless double beta $\betabeta$-decay by using data on $\betabeta$-decay half-lives of nuclei with largely different nuclear matrix elements (NMEs). The mechanisms studied are: light Majorana neutrino exchange, heavy left-handed (LH) and heavy right-handed (RH) Majorana neutrino exchanges, lepton charge non-conserving couplings in SUSY theories with R-parity breaking giving rise to the "dominant gluino exchange" and the "squark-neutrino" mechanisms. The nuclei considered are $^{76}$Ge, $^{82}$Se, $^{100}$Mo, $^{130}$Te and $^{136}$Xe. Four sets of nuclear matrix elements (NMEs) of the decays of these five nuclei, derived within the Self-consistent Renormalized Quasiparticle Random Phase Approximation (SRQRPA), were employed in our analysis. While for each of the five single mechanisms discussed, the NMEs for $^{76}$Ge, $^{82}$Se, $^{100}$Mo and $^{130}$Te differ relatively little, the relative difference between the NMEs of any two nuclei not exceeding 10%, the NMEs for $^{136}Xe$ differ significantly from those of $^{76}$Ge, $^{82}Se$, $^{100}$Mo and $^{130}$Te, being by a factor $\sim (1.3 - 2.5)$ smaller. This allows, in principle, to draw conclusions about the pair of non-interfering (interfering) mechanisms possibly inducing the $\betabeta$-decay from data on the half-lives of $^{136}Xe$ and of at least one (two) more isotope(s) which can be, e.g., any of the four, $^{76}Ge$, $^{82}Se$, $^{100}Mo$ and $^{130}Te$. Depending on the sets of mechanisms considered, the conclusion can be independent of, or can depend on, the NMEs used in the analysis. The implications of the EXO lower bound on the half-life of $^{136}Xe$ for the problem studied are also exploited.

0νββ-decay nuclear matrix elements with self-consistent short-range correlations

A self-consistent calculation of nuclear matrix elements of the neutrinoless double-beta decays ($0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$) of $^{76}\mathrm{Ge}$, $^{82}\mathrm{Se}$, $^{96}\mathrm{Zr}$, $^{100}\mathrm{Mo}$, $^{116}\mathrm{Cd}$, $^{128}\mathrm{Te}$, $^{130}\mathrm{Te}$, and $^{136}\mathrm{Xe}$ 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 the 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 $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$ decay are obtained that 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 $0\ensuremath{\nu}\ensuremath{\beta}\ensuremath{\beta}$-decay matrix elements.

0νββnuclear matrix elements and the occupancy of individual orbits

The measured occupancies of valence orbits in 76Ge and 76Se 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 self-consistent 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 0νββ nuclear matrix element for the 76Ge-->76Se transition is reduced by ~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 0νββ matrix element for the 82Se-->82Kr transition, making it also closer to the shell model prediction.

Anatomy of the0νββnuclear matrix elements

We show that, within the quasiparticle random phase approximation (QRPA) and the renormalized QRPA (RQRPA) based on the Bonn-CD nucleon-nucleon interaction, the competition between the pairing and the neutron-proton particle-particle and particle-hole interactions causes contributions to the neutrinoless double-beta decay matrix element to nearly vanish at internucleon distances of more than 2 or 3 fermis. As a result, the matrix element is more sensitive to short-range/high-momentum physics than one naively expects. We analyze various ways of treating that physics and quantify the uncertainty it produces in the matrix elements, with three different treatments of short-range correlations.

Uncertainties in the 0νββ-decay nuclear matrix elements

The nuclear matrix elements M 0ν of the neutrinoless double-beta decay (0νβ β) of most nuclei with known 2νββ-decay rates are systematically evaluated using the Quasiparticle Random Phase Approximation (QRPA) and Renormalized QRPA (RQRPA). The experimental 2νβ β-decay rate is used to adjust the most relevant parameter, the strength of the particle-particle interaction. With such procedure the M 0ν values become essentially independent of single-particle basis size, the axial vector quenching factor, etc. Theoretical arguments in favor of the adopted way of determining the interaction parameters are presented. It is suggested that most of the spread among the published M 0ν’s can be ascribed to the choices of implicit and explicit parameters, inherent to the QRPA method.

Neutrinoless double [formula omitted]-decay nuclear matrix elements within the SRQRPA

The nuclear matrix elements associated with the light Majorana neutrino mass mechanism of the neutrinoless double beta decay of 48Ca, 76Ge, 82Se, 96Zr, 100Mo, 116Cd, 128Te, 130Te, 136Xe, and 150Nd have been calculated within the self-consistent renormalized quasiparticle random phase approximation (SRQRPA). By following a recently proposed procedure, where data on the two-neutrino double β decay half-lives are used to derive appropriate value of the particle–particle strength of the nuclear Hamiltonian, we have found that the SQRPA results are comparable with those from the QRPA and the RQRPA approaches. This constitutes an additional argument in favor of the convergence of the QRPA-like results.

Assessment of uncertainties in QRPA [formula omitted]-decay nuclear matrix elements

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

Neutrinoless doubleβ-decay and neutrino mass hierarchies

In the framework of the seesaw mechanism the normal hierarchy is favorable for the neutrino mass spectrum. For this spectrum we present a detailed calculation of the half-lives of neutrinoless double $\ensuremath{\beta}$-decay for several nuclei of experimental interest. The half-lives are evaluated by considering the most comprehensive nuclear matrix elements, which were obtained within the renormalized quasiparticle random phase approximation by the Bratislava--Caltech--Tuebingen group. The dependence of the half-lives on ${sin}^{2}{\ensuremath{\theta}}_{13}$ and the lightest neutrino mass is studied. We present also the results of the calculations of the half-lives of neutrinoless double $\ensuremath{\beta}$-decay in the case of the inverted hierarchy of neutrino masses.

Test of consistency of the so-called fully renormalized quasiparticle random phase approximation

The validity of the so-called fully renormalized quasiparticle random phase approximation is tested, under schematic model conditions. It is shown that this approximation does not fulfill the consistency required by the linealization procedure. The results are illustrated by the analysis of Fermi-type transitions.

Uncertainty in the0νββdecay nuclear matrix elements

The nuclear matrix elements $M^{0\nu}$ of the neutrinoless double beta decay ($0\nu\beta\beta$) are evaluated for $^{76}$Ge,$^{100}$Mo, $^{130}$Te, and $^{136}$Xe within the Renormalized Quasiparticle Random Phase Approximation (RQRPA) and the simple QRPA. Three sets of single particle level schemes are used, ranging in size from 9 to 23 orbits. When the strength of the particle-particle interaction is adjusted so that the $2\nu\beta\beta$ decay rate is correctly reproduced, the resulting $M^{0\nu}$ values become essentially independent on the size of the basis, and on the form of different realistic nucleon-nucleon potentials. Thus, one of the main reasons for variability of the calculated $M^{0\nu}$ within these methods is eliminated.

Energies of the ground state and first excited 0+ state in an exactly solvable pairing model

Several approximations are tested by calculating the ground-state energy and the energy of the first excited 0+ state using an exactly solvable model with two symmetric levels interacting via a pairing force. They are the BCS approximation (BCS), Lipkin-Nogami (LN) method, random-phase approximation (RPA), quasiparticle RPA (QRPA), the renormalized RPA (RRPA), and renormalized QRPA (RQRPA). It is shown that, in the strong-coupling regime, the QRPA which neglects the scattering term of the model Hamiltonian offers the best fit to the exact solutions. A recipe is proposed using the RRPA and RQRPA in combination with the pairing gap given by the LN method. Applying this recipe, it is shown that the superfluid-normal phase transition is avoided, and a reasonably good description for both of the ground-state energy and the energy of the first excited 0+ state is achieved.

(μ−,μ+)conversion in nuclei as a probe of new physics

We present a detailed analysis of the muonic analogue of neutrinoless double beta decay $({\ensuremath{\mu}}^{\ensuremath{-}},{\ensuremath{\mu}}^{+})$ conversion. We study several lepton number violating (LNV) mechanisms potentially triggering this process: exchange by light and heavy Majorana neutrinos as well as exchange by supersymmetric particles participating in R-parity violating interactions. The nuclear structure is taken into account within the renormalized quasiparticle random phase approximation method. This is the first realistic treatment of nuclear structure aspects of the $({\ensuremath{\mu}}^{\ensuremath{-}},{\ensuremath{\mu}}^{+})$ conversion. We estimate the rate of this process utilizing the existing experimental constraints on the parameters of the underlying LNV interactions and conclude that the $({\ensuremath{\mu}}^{\ensuremath{-}},{\ensuremath{\mu}}^{+})$ conversion will hardly be detectable in the near future experiments.

Self-consistent renormalized quasiparticle random phase approximation and its application to 2νββ and 0νββ decays

We have used a self-consistent version of the BCS + RQRPA method for a systematic study of the two-neutrino double-beta decay of nuclei with 100<A≤150. We also applied this newly derived formalism, to the 0νββ decay of 76Ge, where the induced nucleon currents have been accounted for. The results have been compared to the previously used approaches, namely the QRPA and the RQRPA approximations. We have shown that inclusion of the quasiparticle correlations at the BCS level reduces ground state correlations in the particle-particle channel of the proton-neutron interaction. This gives the systematic and considerable reduction of the double-beta-decay matrix elements, resulting in less stringent limits for the effective neutrino mass.

Neutrinoless Double-Beta Decay to Excited 0+ States Mediated by Light Majorana Neutrinos

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

Neutrinoless double beta decay of76Ge,82Se,100Mo,and136Xeto excited0+states

The neutrinoless double beta decay transition to the first excited 0^+ collective final state is examined for A=76, 82, 100 and 136 nuclei by assuming light and heavy Majorana neutrino exchange mechanisms as well as the trilinear R-parity violating contributions. Realistic calculations of nuclear matrix elements have been performed within the renormalized quasiparticle random phase approximation. Transitions to the first excited two-quadrupole phonon 0^+ state are described within a boson expansion formalism and alternatively by using the operator recoupling method. We present the sensitivity parameters to different lepton number violating signals, which can be used in planning the neutrinoless double beta decay experiments. The half-life of neutrinoless double beta decay to the first excited state 0^+_1 is by a factor of 10 to 100 larger than that of the transition to the ground state.

Neutrinoless doubleβdecay within the self-consistent renormalized quasiparticle random phase approximation and inclusion of induced nucleon currents

The first, to our knowledge, calculation of neutrinoless double beta decay ($0\nu\beta\beta$-decay) matrix elements within the self-consistent renormalised Quasiparticle Random Phase Approximation (SRQRPA) is presented. The contribution from the momentum-dependent induced nucleon currents to $0\nu\beta\beta$-decay amplitude is taken into account. A detailed nuclear structure study includes the discussion of the sensitivity of the obtained SRQRPA results for $0\nu\beta\beta$-decay of $^{76}$Ge to the parameters of nuclear Hamiltonian, two-nucleon short-range correlations and the truncation of the model space. A comparision with the standard and renormalized QRPA is presented. We have found a considerable reduction of the SRQRPA nuclear matrix elements, resulting in less stringent limits for the effective neutrino mass.

Exotic [formula omitted] conversion in nuclei: energy moments of the transition strength and average energy of the outgoing [formula omitted

The first-order and zero-order energy-weighted moments of the transition strength in the inclusive μ−→e− conversion process are investigated with explicit term-by-term calculations. The required full set of intermediate states is deduced within the renormalized quasiparticle random phase approximation which considers reliably the nucleon–nucleon ground-state correlations. The results are exploited to study the average energy of the outgoing electron in the process and subsequently to test the validity of the closure approximation employed previously in inclusive μ−→e− studies. We focus our attention on the particularly interesting nuclei 48Ti and 208Pb, i.e. the stopping targets of the ongoing SINDRUM II experiments. Our conclusions are discussed in conjunction with other similar processes, like the allowed ordinary muon capture and the exotic μ−→e+ conversion.

The effect of weak magnetism and induced pseudoscalar coupling in neutrinoless double-beta decay

In calculating the amplitude of the majorana neutrino-mass mechanism of neutrinoless double-beta decay (0νββ-decay), several approximations of the nucleon current have been done. for example, effects from induced current such as weak magnetism and pseudoscalar coupling have been neglected. we shall show in this work that, although such terms do not contribute significantly to the 2νββ-decay amplitude, they are important in the case of 0νββ decay. performing calculations within the renormalized quasiparticle random phase approximation (pn-rqrpa) for all nuclei undergoing double-beta decay in the region a=76 to a=150, we have found that these additional contributions of the nucleon current reduce considerably the matrix elements in all cases for the light neutrino as well as for the heavy neutrino mass. in the light-neutrino mass, we find reductions up to thirty percent, while in the heavy-neutrino mass, up to almost a factor of five. these reductions make the limits on the lepton-number-violating parameters 〈mν〉 and ηN less stringent.

The inclusive μ− e conversion process with renormalized quasiparticle random-phase approximation

The inclusive process of the neutrinoless muon-to-electron conversion in nuclei is investigated by using the renormalized quasiparticle random-phase approximation (RQRPA). This approach is an improvement of the ordinary QRPA which restores the Pauli principle. It is a more reliable method for extremely small transition matrix elements as for the ( μ −, e −) conversion. Our calculations refer to a set of nuclei throughout the periodic table but we specifically investigate those isotopes for which experiments are done or planned. We study in particular 48 Ti which is at present used as a target at PSI in the new ongoing μ− e conversion experiment with the SINDRUM II spectrometer.