projected-Hartree-Fock-Bogoliubov Research Articles

Limits on Effective Masses of Light and Heavy Majorana Neutrinos for Positron Emitting Modes of Double Beta Decay

Double beta decay is a rare weak interaction process in which two identical nucleons inside the nucleus decay with or without the emission of neutrinos. If the neutrinoless double beta decay is observed, the (e+DBD) processes will play a crucial role in discriminating the finer issues like the dominance of Majorana neutrino mass or the right-handed current. In the present work, we have obtained the limits on the effective mass of light and heavy Majorana neutrinos for the electron-positron conversion and double positron-emitting modes of 96Ru, 106Cd, 124Xe, and 130Ba isotopes, using the nuclear transition matrix elements NTMEs M(0ν) and M(0N) for light and heavy Majorana neutrinos obtained in projected Hartree-Fock Bogoliubov (PHFB) model. The predicted half-lives and corresponding extracted limits on heavy neutrino mass <MN> is discussed. We have also calculated nuclear sensitivities ξ(0ν) and ξ(0N) due to the light and heavy neutrino exchange, respectively. Finally, the mass limits are obtained using various phase space factors (PSF), and the effect of this PSF on mass limits is discussed.

Nuclear transition matrix elements for neutrinoless double-β decay of 76Ge isotope within PHFB approach

Employing projected–Hartree–Fock–Bogoliubov (PHFB) model, nuclear transition matrix elements (NTMEs) [Formula: see text] for the neutrinoless double-[Formula: see text] decay of [Formula: see text]Ge isotope are calculated within mechanisms involving light as well as heavy Majorana neutrinos, and classical Majorons. By considering the spin-tensor decomposition of realistic KUO and empirical JUN45 effective two-body interactions, it is noticed that the effect due to SRC on NTMEs [Formula: see text] and [Formula: see text] involving the exchange of light and heavy Majorana neutrinos, respectively, is maximally incorporated by the central part of the effective two-body interaction, which varies by a small amount with the inclusion of spin-orbit and tensor components. Presently, the model-dependent uncertainties in the average NTMEs [Formula: see text] and [Formula: see text] turn out to be about 10% and 37%, respectively.

Nuclear Transition Matrix Elements for Double-β Decay Within PHFB Model

Employing the projected-Hartree-Fock-Bogoliubov (PHFB) approach, nuclear transition matrix elements (NTMEs) have been calculated to study the three complementary modes of $\beta ^{-}\beta ^{-}$ decay, namely two neutrino $% \beta ^{-}\beta ^{-}$ (2$\nu \beta ^{-}\beta ^{-}$) decay, neutrinoless $% \beta ^{-}\beta ^{-}$ (0$\nu \beta ^{-}\beta ^{-}$) decay within mass mechanism and Majoron accompanied 0$\nu \beta ^{-}\beta ^{-}$ (0$\nu \beta ^{-}\beta ^{-}\chi $) decay. Reliability of HFB wave functions generated with four different parametrizations of the pairing plus multipolar type of effective two-body interaction has been ascertained by comparing a number of nuclear observables with the available experimental data. Specifically, the calculated NTMEs $M^{(2\nu )}$ of 2$\nu \beta ^{-}\beta ^{-}$ decay have been compared with the observed data. Effects due to different parametrizations of effective two-body interactions, form factors and short-range correlations have been studied. It has also been observed that deformation plays a crucial role in the nuclear structure aspects of 0$\nu \beta ^{-}\beta ^{-}$ decay. Uncertainties in NTMEs calculated with wave functions generated with four different parametrizations of the pairing plus multipolar type of effective two-body interaction, dipole form factor and three different parametrizations of Jastrow type of short-range correlations within mechanisms involving light Majorana neutrinos, heavy Majorona neutrinos, sterile neutrinos and Majorons have been statistically estimated.

Nuclear transition matrix elements for neutrinoless double-β decay within mechanisms involving light Majorana neutrino mass and right-handed current

Employing the projected-Hartree-Fock-Bogoliubov (PHFB) model in conjunction with four different parametrizations of pairing plus multipolar effective two-body interaction and three different parametrizations of Jastrow short-range correlations, nuclear transition matrix elements for the neutrinoless double-[Formula: see text] decay of [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] isotopes are calculated within mechanisms involving light Majorana neutrino mass and right-handed current. Statistically, model specific uncertainties in sets of twelve nuclear transition matrix elements are estimated by calculating the averages along with the standard deviations. For the considered nuclei, the most stringent extracted on-axis limits on the effective light Majorana neutrino mass [Formula: see text], the effective weak coupling of right-handed leptonic current with right-handed hadronic current [Formula: see text], and the effective weak coupling of right-handed leptonic current with left-handed hadronic current [Formula: see text] from the observed limit on half-life [Formula: see text] of [Formula: see text] isotope are [Formula: see text][Formula: see text]eV, [Formula: see text] and [Formula: see text], respectively.

Matrix Elements for Neutrinoless Double Beta Decay

The status of calculation of the neutrinoless double beta decay (0νββ-decay) nuclear matrix elements (NMEs) is reviewed. The 0νββ-decay NMEs obtained in the framework of the Quasiparticle Random Phase Approximation (QRPA), Large Scale Shell Model (LSSM), Interacting Boson Model (IBM), Projected Hartree-Fock Bogoliubov approach (P-HFB) and Energy Density Functional Method (EDF) are presented and discussed. The problem of reliable determination of the 0νββ-decay NMEs is addressed. It is manifested that the uncertainty associated with the calculation of the 0νββ-decay NMEs can be diminished by suitable chosen nuclear probes. Further, the recent development in the field of double beta decay showed that the search for the neutrinoless double electron capture process (0νECEC) may establish the Majorana nature of neutrinos. This possibility should be considered as alternative and complementary to searches for the 0νββ-decay.

Double Beta Decay, Nuclear Structure and Physics beyond the Standard Model

The Neutrinoless Double Beta Decay (0νββ) allows to determine the absolute scale of the neutrino masses. For this one must assume, that the light Majorana neutrino exchange is the leading mechanism for 0νββ and that the matrix element of this transition can ba calculated reliably. The different methods: Quasi-particle Random Phase Approximation (QRPA), Shell Model (SM), Projected Hartree-Fock-Bogoliubov (PHFB) and Interacting Boson Model (IBM2) to calculate these matrix elements are reviewed. The question, how one can determine the leading mechanism or mechanisms from the data of the 0νββ decay in different nuclei is studied in the later part of this article. Possible interference terms allow to test CP (Charge and Parity conjugation) violation.

Influence of pairing in double beta decay of 48Ca

Two-neutrino ββ decay matrix elements and half-life of 48Ca are calculated after including neutron-proton pairing correlations in projected Hartree-Fock-Bogoliubov (PHFB) formalism. The GT matrix elements in 2νββ decay are reduced due to broader smearing of Fermi surfaces. Half-life results for 2νββ decay of 48Ca with np pairing are better than without pairing.

Nuclear deformation and the two-neutrino double- β decay in 124, 126Xe , 128, 130Te , 130, 132Ba and 150Nd isotopes

The two-neutrino double-beta decay of 124, 126Xe , 128, 130Te , 130, 132Ba and 150Nd isotopes is studied in the Projected Hartree-Fock-Bogoliubov (PHFB) model. Theoretical 2ν β-β- half-lives of 128, 130Te , and 150Nd isotopes, and 2ν β+β+ , 2ν β+EC and 2ν ECEC for 124, 126Xe and 130, 132Ba nuclei are presented. Calculated quadrupolar transition probabilities B(E2 : 0+ → 2+) , static quadrupole moments and g -factors in the parent and daughter nuclei reproduce the experimental information, validating the reliability of the model wave functions. The anticorrelation between nuclear deformation and the nuclear transition matrix element M2ν is confirmed.

Functional integrals for Hartree Fock Bogoliubov many-body matrix elements

We discuss exact functional integral expressions for many-body matrix elements of the type ψ, A|e−βĤ|ψ, A, between particle number projected Hartree–Fock–Bogoliubov (HFB) wavefunctions with time-reversal symmetry. A proof of positivity is given for a class of Hamiltonians and when the HFB wavefunctions with time-reversal symmetry are particle number projected to an even number of particles. We show explicitly how to reduce the propagator in the functional integral to a Hermitian positive definite propagator for particle pairs. This result generalizes that previously obtained using Bardeen–Cooper–Schrieffer wavefunctions.