Nuclear Transition Matrix Elements Research Articles

Deformed Shell Model Applications to Weak Interaction Processes

The deformed shell model (DSM), based on Hartree–Fock intrinsic states with angular momentum projection and band mixing, has been found to be quite successful in describing many spectroscopic properties of nuclei in the A = 60–100 region. More importantly, DSM has been used recently with good success in calculating nuclear structure factors, which are needed for a variety of weak interaction processes. In this article, in addition to giving an overview of this, we discuss the applications of DSM to obtain cross-sections for coherent and incoherent neutrino nucleus scattering on 96,98,100Mo targets and also for obtaining two neutrino double beta decay nuclear transition matrix elements for 100Mo.

Multichannel experimental and theoretical constraints for the Cd116(Ne20,F20)In116 charge exchange reaction at 306 MeV

Charge exchange (CE) reactions offer a major opportunity to excite nuclear isovector modes, providing clues about the nuclear interaction in the medium. Moreover, double charge exchange (DCE) reactions are proving to be a tempting tool to access nuclear transition matrix elements (NME) related to double beta-decay processes. Through a multi-channel experimental analysis and a consistent theoretical approach of the $^{116}$Cd($^{20}$Ne,$^{20}$F)$^{116}$In single charge exchange (SCE) reaction at 306 MeV, we aim at disentangling from the experimental cross section the contribution of the competing mechanisms, associated with second or higher order sequential transfer and inelastic processes. We measured excitation energy spectra and absolute cross sections for elastic + inelastic, one-proton transfer and SCE channels, using the MAGNEX large acceptance magnetic spectrometer to detect the ejectiles. For the first two channels, we also extracted the experimental cross section angular distributions. The experimental data are compared with theoretical predictions obtained by performing two-step distorted wave Born approximation and coupled reaction channel calculations. We employ spectroscopic amplitudes for single-particle transitions derived within a large-scale shell model approach and different optical potentials for modeling the initial and the final state interactions. The present study significantly mitigates the possible model dependence existing in the description of these complex reaction mechanisms, thanks to the reproduction of several channels at once. In particular, our work demonstrates that the two-step transfer mechanisms produce a non negligible contribution to the total cross section of the $^{116}$Cd($^{20}$Ne,$^{20}$F)$^{116}$In reaction channel, although a relevant fraction is still missing, being ascribable to the direct SCE mechanism, which is not addressed here.

Occupation numbers and nuclear transition matrix elements for $$0\nu \beta ^{-}\beta ^{-}$$ decay within a mechanism involving neutrino mass

Occupation numbers and nuclear transition matrix elements for $$0\nu \beta ^{-}\beta ^{-}$$ decay within a mechanism involving neutrino mass

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.

Calculation of double-β decay half-lives using an improved Primakoff-Rosen formula * *Supported by the National Natural Science Foundation of China (U1731238, 11761161001, 11105079, 11535004, 11375086, 11975167, 12035011), the Science and Technology Development Fund (FDCT) of Macau (020/2014/A1, 008/2017/AFJ, 0042/2018/A2), the Science and Technology Foundation of Guizhou Province ((2016)4008, (2017)5726-37) and the foundation of Guizhou Provincial education Department (KY(2020)003)

A systematic analysis on experimental data of the half-lives of nuclear double- decays with two neutrinos ( ) is performed based on the analytical formula proposed by Primakoff and Rosen. We improve the formula by considering the shell effects and refining the energy dependence of the phase-space factor. This improved formula can closely describe all available experimental half-lives of decays, both for ground-state transitions and transitions from ground states of parent nuclei to the first excited states of daughter nuclei. The calculated half-lives agree with the experimental data of ground-state transitions of all known eleven nuclei with an average factor of 2.3. Further predictions are provided for -decay candidates with decay energies above 0.5 MeV. We compare different theoretical predictions and emphasize the importance of experimental measurements on the half-lives of double- transitions between the ground state of Ca, Ge, and Xe and the first excited states of their corresponding daughter nuclei, which will be very useful for understanding the underlying mechanisms of double- decays and for further studying the shell effects on nuclear transition matrix elements.

Nuclear transition matrix elements for neutrinoless double-β decay of 76Ge within mechanisms involving sterile neutrinos, Majorons and composite neutrinos

Using HFB wave functions generated with a realistic KUO and an empirical JUNE45 effective two-body interactions, nuclear transition matrix elements (NTMEs) [Formula: see text] for the [Formula: see text] transition of neutrinoless double-[Formula: see text] decay of [Formula: see text]Ge isotope are calculated within mechanisms involving sterile neutrinos, Majorons and compositeness scenario. Uncertainties in nuclear transition matrix elements are estimated by calculating sets of 12 NTMEs with these two sets of wave functions, two alternative forms of finite size effects (FNS) and three different parametrizations of short range correlations (SRC). Uncertainties in NTMEs within mechanisms involving sterile neutrinos, Majorons and composite neutrinos turn out to be about 10%–36% depending on the mass of sterile neutrinos, 10% and 37%, respectively.

Nuclear transition matrix elements for neutrinoless double-β decay within Rp-violating squark-neutrino mechanism

Within the squark-neutrino mechanism of [Formula: see text]-violating SUSY, sets of 12 nuclear transition matrix elements (NTMEs) are calculated for the neutrinoless double-[Formula: see text] decay [Formula: see text] of [Formula: see text]Zr, [Formula: see text]Mo, [Formula: see text]Pd, [Formula: see text]Te and [Formula: see text]Nd isotopes. Specifically, four sets of HFB wave functions generated with four different parametrizations of the pairing plus multipolar two-body interactions, dipole form factor and three different parametrizations of the Jastrow short-range correlations are employed in the calculation of NTMEs with two possible prescriptions for the hadronization, namely the two-nucleon mode and the pionic mode. Without (with) Miller–Spencer parametrization of short-range correlation, uncertainties in average NTMEs [Formula: see text] (QBM), [Formula: see text] (NRQM), [Formula: see text] (FF3) and [Formula: see text] turn out be 11–18% (29–37%), 11–16% (27–31%), 5–12% (13–17%) and 3–13% (9–15%), respectively.

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.

The Half-Life of 14C—Why Is It So Long?

ABSTRACTThe half-life of radiocarbon (14C) is 5700 ± 30 yr, which makes it particularly useful for dating in archaeology. However, only an exceptional hindrance of the beta decay from 14C to 14N—a so-called Gamow-Teller ß-decay—makes this half-life so long. A normal strength would result in a half-life of only a few days, completely useless for archaeological dating. The unusual hindrance is based on the nuclear structure of the two nuclei, resulting in strongly destructive interferences of the nuclear transition matrix element. Nuclear model calculation with great computational efforts have been performed in the literature to reproduce the very low transition probability. Here, we will attempt to describe the nuclear physics behind this most unusual half-life.

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.

Inclusive electron-nucleus cross section within the self-consistent Green's function approach

We compute inclusive electron-nucleus cross sections using ab initio spectral functions of $^4$He and $^{16}$O obtained within the Self Consistent Green's Function approach. The formalism adopted is based on the factorization of the spectral function and the nuclear transition matrix elements. This allows to provide an accurate description of nuclear dynamics and to account for relativistic effects in the interaction vertex. Our calculations use a saturating chiral Hamiltonian in order reproduce the correct nuclear sizes. When final state interactions for the struck particle are accounted for, we find nice agreement between the data and the theory for the inclusive electron-$^{16}$O cross section. The results lay the foundations for future applications of the Self Consistent Green's Function method, in both closed and open shell nuclei, to neutrino data analysis. This work also presents results for the point-proton, charge and single-nucleon momentum distribution of the same two nuclei. The center of mass can affect these quantities for light nuclei and cannot be separated cleanly in most ab initio post-Hartree-Fock methods. In order to address this, we developed a Metropolis Monte Carlo calculation in which the center of mass coordinate can be subtracted exactly from the trial wave function and the expectation values. We gauged this effect for $^4$He by removing the center of mass effect from the Optimal Reference State wave function that is generated during the Self Consistent Green's Function calculations. Our findings clearly indicate that the residual center of mass contribution strongly modifies calculated matter distributions with respect to those obtained in the intrinsic frame. Hence, its subtraction is crucial for a correct description of light nuclei.

Embedded random matrix ensembles from nuclear structure and their recent applications

Embedded random matrix ensembles generated by random interactions (of low body rank and usually two-body) in the presence of a one-body mean field, introduced in nuclear structure physics, are now established to be indispensable in describing statistical properties of a large number of isolated finite quantum many-particle systems. Lie algebra symmetries of the interactions, as identified from nuclear shell model and the interacting boson model, led to the introduction of a variety of embedded ensembles (EEs). These ensembles with a mean field and chaos generating two-body interaction generate in three different stages, delocalization of wave functions in the Fock space of the mean-field basis states. The last stage corresponds to what one may call thermalization and complex nuclei, as seen from many shell model calculations, lie in this region. Besides briefly describing them, their recent applications to nuclear structure are presented and they are (i) nuclear level densities with interactions; (ii) orbit occupancies; (iii) neutrinoless double beta decay nuclear transition matrix elements as transition strengths. In addition, their applications are also presented briefly that go beyond nuclear structure and they are (i) fidelity, decoherence, entanglement and thermalization in isolated finite quantum systems with interactions; (ii) quantum transport in disordered networks connected by many-body interactions with centrosymmetry; (iii) semicircle to Gaussian transition in eigenvalue densities with [Formula: see text]-body random interactions and its relation to the Sachdev–Ye–Kitaev (SYK) model for majorana fermions.

Two neutrino double- $\beta$ β decay of $94 \leq A \leq 150$ 94 ≤ A ≤ 150 nuclei for the $0^{+} \rightarrow 2^{+}$ 0 + → 2 + transition

Within the PHFB approach, the $ 0^{+}\rightarrow 2^{+}$ transition of two neutrino double- $ \beta$ decay of 94, 96Zr, 100Mo, 104Ru, 110Pd, 128, 130Te and 150Nd isotopes is studied employing wave functions generated with four different parametrizations of the pairing plus multipole type of two-nucleon interaction and the summation method. In comparison to the $ 0^{+}\rightarrow 0^{+}$ transition, the nuclear transition matrix elements $ M_{2\nu} (2^{+})$ are quite sensitive to the deformation of the yrast 2+ state. Consideration of the available theoretical and experimental results suggests that the observation of the $ 0^{+}\rightarrow 2^{+}$ transition of $ 2\nu \beta^{-} \beta^{-}$ decay may be possible in 96Zr, 100Mo, 130Te and 150Nd isotopes. The effect of deformation on the $ M_{2\nu} (2^{+})$ is also studied.

New limit for the half-life of double beta decay of 94Zr to the first excited state of 94Mo

Neutrinoless Double Beta Decay is a phenomenon of fundamental interest in particle physics. The decay rates of double beta decay transitions to the excited states can provide input for Nuclear Transition Matrix Element calculations for the relevant two neutrino double beta decay process. It can be useful as supplementary information for the calculation of Nuclear Transition Matrix Element for the neutrinoless double beta decay process. In the present work, double beta decay of $^{94}$Zr to the $2^{+}_{1}$ excited state of $^{94}$Mo at 871.1 keV is studied using a low background $\sim$ 230 cm$^3$ HPGe detector. No evidence of this decay was found with a 232 g.y exposure of natural Zirconium. The lower half-life limit obtained for the double beta decay of $\rm^{94}Zr$ to the $2^{+}_{1}$ excited state of $\rm^{94}Mo$ is $T_{1/2} (0\nu + 2\nu)> 3.4 \times 10^{19}$ y at 90% C.L., an improvement by a factor of $\sim$ 4 over the existing experimental limit at 90\% C.L. The sensitivity is estimated to be $T_{1/2} (0\nu + 2\nu) > 2.0\times10^{19}$ y at 90% C.L. using the Feldman-Cousins method.

Nuclear matrix elements for neutrinoless double-beta decay in covariant density functional theory

We review the first fully relativistic description for the neutrinoless double-beta decay by the beyond-mean-field covariant density functional theory. The calculations of the nuclear transition matrix elements are based on a full relativistic transition operator and nuclear wave functions in which the dynamic effects of particle-number, angular-momentum, and parity conservations as well as shape fluctuations are incorporated. We find that the commonly used nonrelativistic approximation for the transition operator is justified within the mechanism of light-Majorana-neutrino exchange. We stress that reducing the discrepancies in the predicted nuclear matrix elements by different nuclear models is a major challenge in nuclear physics.

Nuclear transition matrix elements for Majoron-accompanied neutrinoless double-βdecay within a projected-Hartree-Fock-Bogoliubov model

Nuclear transition matrix elements for Majoron-accompanied neutrinoless double-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>β</mml:mi></mml:math>decay within a projected-Hartree-Fock-Bogoliubov model

Nonquenched Isoscalar Spin-M1 Excitations in sd-Shell Nuclei.

Differential cross sections of isoscalar and isovector spin-M1 (0(+)→1(+)) transitions are measured using high-energy-resolution proton inelastic scattering at E(p)=295 MeV on (24)Mg, (28)Si, (32)S, and (36)Ar at 0°-14°. The squared spin-M1 nuclear transition matrix elements are deduced from the measured differential cross sections by applying empirically determined unit cross sections based on the assumption of isospin symmetry. The ratios of the squared nuclear matrix elements accumulated up to E(x)=16 MeV compared to a shell-model prediction are 1.01(9) for isoscalar and 0.61(6) for isovector spin-M1 transitions, respectively. Thus, no quenching is observed for isoscalar spin-M1 transitions, while the matrix elements for isovector spin-M1 transitions are quenched by an amount comparable with the analogous Gamow-Teller transitions on those target nuclei.

Deformed shell model results for neutrinoless double beta decay of nuclei in A = 60 - 90 region

Nuclear transition matrix elements (NTME) for the neutrinoless double beta decay (Oνββ or OνDBD) of 70 Zn , 80 Se and 82 Se nuclei are calculated within the framework of the deformed shell model (DSM) based on Hartree–Fock (HF) states. For 70 Zn , jj44b interaction in 2p3/2, 1f5/2, 2p1/2 and 1g9/2 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 has been found to be better for 70 Zn . The above model space was used in many recent shell model (SM) and interacting boson model (IBM) calculations for nuclei in this region. After ensuring that DSM gives good description of the spectroscopic properties of low-lying levels in these three nuclei considered, the NTME are calculated. The deduced half-lives with these NTME, assuming neutrino mass is 1 eV, are 1.1 × 1026, 2.3 × 1027 and 2.2 × 1024 yr for 70 Zn , 80 Se and 82 Se , respectively.

Deformed shell model studies of spectroscopic properties of 64Zn and 64Ni and the positron double beta decay of 64Zn

The spectroscopic properties of 64Zn and 64Ni are calculated within the framework of the deformed shell model (DSM) based on Hartree-Fock states. GXPF1A interaction in 1f7/2, 2p3/2, 1f5/2 and 2p1/2 space with 40Ca as the core is employed. After ensuring that DSM gives good description of the spectroscopic properties of low-lying levels in these two nuclei considered, nuclear transition matrix elements (NTME) for the neutrinoless positron double beta decay ( 0νβ+β+ and 0νβ+EC) of 64Zn are calculated. The two-neutrino positron double beta decay half-life is also calculated for this nucleus.