Two-body Current Contributions Research Articles

Impact of Two-Body Currents on Magnetic Dipole Moments of Nuclei.

We investigate the effects of two-body currents on magnetic dipole moments of medium-mass and heavy nuclei using the valence-space in-medium similarity renormalization group with chiral effective field theory interactions and currents. Focusing on near doubly magic nuclei from oxygen to bismuth, we have found that the leading two-body currents globally improve the agreement with experimental magnetic moments. Moreover, our results show the importance of multishell effects for ^{41}Ca, which suggest that the Z=N=20 gap in ^{40}Ca is not as robust as in ^{48}Ca. The increasing contribution of two-body currents in heavier systems is explained by the operator structure of the center-of-mass dependent Sachs term.

Ab Initio Study of (νℓ,ℓ−) and (ν¯ℓ,ℓ+) Inclusive Scattering in C12 : Confronting the MiniBooNE and T2K CCQE Data

We carry out an ab initio calculation of the neutrino flux-folded inclusive cross sections, measured on $^{12}$C by the MiniBooNE and T2K collaborations in the charged-current quasielastic (CCQE) regime. The calculation is based on realistic two- and three-nucleon interactions, and on a realistic nuclear electroweak current with one-and two-nucleon terms that are constructed consistently with these interactions and reproduce low-energy electroweak transitions. Numerically exact quantum Monte Carlo methods are utilized to compute the nuclear weak response functions, by fully retaining many-body correlations in the initial and final states and interference effects between one- and two-body current contributions. We employ a nucleon axial form factor of the dipole form with $\Lambda_A = 1.0$ or $1.15$ GeV, the latter more in line with a very recent lattice QCD determination. The calculated cross sections are found to be in good agreement with the neutrino data of MiniBooNE and T2K, and antineutrino MiniBooNE data, yielding a consistent picture of nuclei and their electroweak properties across a wide regime of energy and momenta.

Data-based two-body current contribution to the neutrino-nucleus cross section

A phenomenological model of two-body current (2p2h) contribution to neutrino cross section is introduced. Predictions of the Valencia model for 2p2h are modified using recent CC0pi measurements from T2K and MINERvA experiments. Our results suggest a significant increase of the 2p2h cross section at neutrino energies bigger than 1 GeV and also a redistribution of 2p2h events as function of energy and momentum transfer. This may have a big impact on neutrino energy reconstruction in neutrino oscillation parameters.

Bayesian analysis of capture reactions $$\varvec{^3}\hbox {He}\varvec{(\alpha ,\gamma )^7}\hbox {Be}$$ and $$\varvec{^3}\hbox {H}\varvec{(\alpha ,\gamma )^7}\hbox {Li}$$

Bayesian analysis of the radiative capture reactions $^3\mathrm{He}(\alpha,\gamma)^7\mathrm{Be}$ and $^3\mathrm{H}(\alpha,\gamma)^7\mathrm{Li}$ are performed to draw inferences about the cross sections at threshold. We do a model comparison of two competing effective field theory power countings for the capture reactions. The two power countings differ in the contribution of two-body electromagnetic currents. In one power counting, two-body currents contribute at leading order, and in the other they contribute at higher orders. The former is favored for $^3\mathrm{He}(\alpha,\gamma)^7\mathrm{Be}$ if elastic scattering data in the incoming channel is considered in the analysis. Without constraints from elastic scattering data, both the power countings are equally favored. For $^3\mathrm{H}(\alpha,\gamma)^7\mathrm{Li}$, the first power counting with two-body current contributions at leading order is favored with or without constraints from elastic scattering data.

New evaluation of the axial nucleon form factor from electron- and neutrino-scattering data and impact on neutrino-nucleus cross sections

A joint fit to neutrino-nucleon scattering and pion electroproduction data is performed to evaluate the nucleon axial form factor in the two-component model consisting of a three-quark intrinsic structure surrounded by a meson cloud. Further constrains on the model are obtained by re-evaluating the electromagnetic form factor using electron scattering data. The results of the axial form factor show sizable differences with respect to the widely used dipole model. The impact of such changes on the Charged-Current Quasi-Elastic neutrino-nucleus cross-section is evaluated in the SuSAv2 nuclear model, based on the Relativistic Mean Field and including the contribution of two-body currents. How the different parametrizations of the axial form factor affect the cross-section prediction is assessed in full details and comparisons to recent T2K and MINERvA data are presented.

Realistic spectral function model for charged-current quasielastic-like neutrino and antineutrino scattering cross sections on C12

A detailed study of charged current quasielastic neutrino and antineutrino scattering cross sections on a $^{12}\mathrm{C}$ target with no pions in the final state is presented. The initial nucleus is described by means of a realistic spectral function $S(p,\mathcal{E})$ in which nucleon-nucleon correlations are implemented by using natural orbitals through the Jastrow method. The roles played by these correlations and by final-state interactions are analyzed and discussed. The model also includes the contribution of weak two-body currents in the two-particle two-hole sector, evaluated within a fully relativistic Fermi gas. The theoretical predictions are compared with a large set of experimental data for double-differential, single-differential, and total integrated cross sections measured by the MiniBooNE, $\mathrm{MINER}\ensuremath{\nu}\mathrm{A}$, and T2K experiments. Good agreement with experimental data is found over the whole range of neutrino energies. The results are also in global good agreement with the predictions of the superscaling approach, which is based on the analysis of electron-nucleus scattering data, with only a few differences seen at specific kinematics.

Radiative 3He( $\alpha , \gamma$ α , γ )7Be reaction in halo effective field theory

In this work we study the radiative capture of 3He on 4He within the halo effective field theory (EFT) framework. At leading order the capture amplitude comprises the initial state s-wave strong and Coulomb interactions summed to all orders. At the same order in the expansion, leading two-body currents contribute as well. We find delicate cancelations between the various contributions, and the two-body current contributions can be replaced by appropriately enhancing the asymptotic normalizations of the 7Be ground and first excited state wave functions. The next-to-leading order corrections come from the s-wave shape parameter and the pure Coulomb d-wave initial state interactions. We fit the EFT parameters to available scattering data and most recent capture data. Our zero-energy astrophysical S-factor estimate, $S_{34}\sim 0.55$ keV b, is consistent within error bars with the average in the literature.

Recent Developments in Neutrino/Antineutrino-Nucleus Interactions

Recent experimental results and developments in the theoretical treatment of neutrino-nucleus interactions in the energy range of 1–10 GeV are discussed. Difficulties in extracting neutrino-nucleon cross sections from neutrino-nucleus scattering data are explained and significance of understanding nuclear effects for neutrino oscillation experiments is stressed. Detailed discussions of the status of two-body current contribution in the kinematic region dominated by quasielastic scattering and specific features of partonic nuclear effects in weak DIS scattering are presented.

RQM description of the charge form factor of the pion and its asymptotic behavior

The pion charge and scalar form factors, $F_1(Q^2)$ and $F_0(Q^2)$, are first calculated in different forms of relativistic quantum mechanics. This is done using the solution of a mass operator that contains both confinement and one-gluon-exchange interactions. Results of calculations, based on a one-body current, are compared to experiment for the first one. As it could be expected, those point-form, and instant and front-form ones in a parallel momentum configuration fail to reproduce experiment. The other results corresponding to a perpendicular momentum configuration (instant form in the Breit frame and front form with $q^+=0$) do much better. The comparison of charge and scalar form factors shows that the spin-1/2 nature of the constituents plays an important role. Taking into account that only the last set of results represents a reasonable basis for improving the description of the charge form factor, this one is then discussed with regard to the asymptotic QCD-power-law behavior $Q^{-2}$. The contribution of two-body currents in achieving the right power law is considered while the scalar form factor, $F_0(Q^2)$, is shown to have the right power-law behavior in any case. The low-$Q^2$ behavior of the charge form factor and the pion-decay constant are also discussed.}

Quantum Monte Carlo calculations of magnetic moments andM1transitions inA⩽7nuclei including meson-exchange currents

Green's function Monte Carlo calculations of magnetic moments and M1 transitions including two-body meson-exchange current (MEC) contributions are reported for A<=7 nuclei. The realistic Argonne v18 two-nucleon and Illinois-2 three-nucleon potentials are used to generate the nuclear wave functions. The two-body meson-exchange operators are constructed to satisfy the continuity equation with the Argonne v18 potential. The MEC contributions increase the A=3,7 isovector magnetic moments by 16% and the A=6,7 M1 transition rates by 17--34%, bringing them into very good agreement with the experimental data.

Baryon magnetic moments in the effective quark Lagrangian approach

An effective quark Lagrangian is derived from first principles through bilocal gluon field correlators. It is used to write down equations for baryons, containing both perturbative and nonperturbative fields. As a result one obtains magnetic moments of octet and decuplet baryons without introduction of constituent quark masses and using only string tension as an input. Magnetic moments come out on average in reasonable agreement with experiment, except for nucleons and $\Sigma^-$. The predictions for the proton and neutron are shown to be in close agreement with the empirical values once we choose the string tension such to yield the proper nucleon mass. Pionic corrections to the nucleon magnetic moments have been estimated. In particular, the total result of the two-body current contributions are found to be small. Inclusion of the anomalous magnetic moment contributions from pion and kaon loops leads to an improvement of the predictions.

Weak transitions inA=6and 7 nuclei

The ${}^{6}\mathrm{He}$ $\ensuremath{\beta}$ decay and ${}^{7}\mathrm{Be}$ electron capture processes are studied using variational Monte Carlo wave functions, derived from a realistic Hamiltonian consisting of the Argonne ${v}_{18}$ two-nucleon and Urbana-IX three-nucleon interactions. The model for the nuclear weak axial current includes one- and two-body operators with the strength of the leading two-body term---associated with $\ensuremath{\Delta}$-isobar excitation of the nucleon---adjusted to reproduce the Gamow-Teller matrix element in tritium $\ensuremath{\beta}$ decay. The measured half-life of ${}^{6}\mathrm{He}$ is underpredicted by theory by $\ensuremath{\simeq}8%,$ while that of ${}^{7}\mathrm{Be}$ for decay into the ground and first excited states of ${}^{7}\mathrm{Li}$ is overpredicted by $\ensuremath{\simeq}9%.$ However, the experimentally known branching ratio for these latter processes is in good agreement with the calculated value. Two-body axial current contributions lead to a $\ensuremath{\simeq}1.7%$ (4.4%) increase in the value of the Gamow-Teller matrix element of ${}^{6}\mathrm{He}$ ${(}^{7}\mathrm{Be}),$ obtained with one-body currents only, and slightly worsen (appreciably improve) the agreement between the calculated and measured half-life. Corrections due to retardation effects associated with the finite lepton momentum transfers involved in the decays, as well as contributions of suppressed transitions induced by the weak vector charge and axial current operators, have also been calculated and found to be negligible.

Weak capture of protons by protons

The cross section for the proton weak capture reaction ${}^{1}\mathrm{H}{(p,e}^{+}{\ensuremath{\nu}}_{e}{)}^{2}\mathrm{H}$ is calculated with wave functions obtained from a number of modern, realistic high-precision interactions. To minimize the uncertainty in the axial two-body current operator, its matrix element has been adjusted to reproduce the measured Gamow-Teller matrix element of tritium $\ensuremath{\beta}$ decay in model calculations using trinucleon wave functions from these interactions. A thorough analysis of the ambiguities that this procedure introduces in evaluating the two-body current contribution to the $\mathrm{pp}$ capture is given. Its inherent model dependence is in fact found to be very weak. The overlap integral ${\ensuremath{\Lambda}}^{2}(E=0)$ for the $\mathrm{pp}$ capture is predicted to be in the range 7.05--7.06, including the axial two-body current contribution, for all interactions considered.

Exchange current contributions to the octet baryon magnetic moments

In quark potential models, two-body current contributions to electromagnetic observables are needed to satisfy the continuity equation for the electromagnetic current. On the other hand, the naïve additive quark model predicts the experimental octet magnetic moments to within 5%. We discuss that consistently derived two-body current contributions to the octet baryon magnetic moments are individually large, but tend to cancel each other globally.

Magnetic moments of the octet baryons in a chiral quark potential model

In quark potential models, two-body current contributions to baryon magnetic moments arise necessarily to satisfy the continuity equation for the electromagnetic current. On the other hand, the naive additive quark model predicts the experimental octet magnetic moments to within 5%. We demonstrate that consistently derived two-body current contributions to the octet baryon magnetic moments are individually large, but tend to cancel each other globally.

Nucleon-nucleon bremsstrahlung at intermediate energies.

Energetic photon production in proton-neutron as well as in proton-proton collisions at intermediate bombarding energies are investigated in a meson-exchange potential model calculation in an effort to provide a more reliable basis for calculations of hard photon production in heavy-ion collisions. Special attention is paid to the role of the one-body rescattering contribution, which has been neglected in previous work. It is shown that this contribution enhances the cross section for photon energies only near the maximum value allowed kinematically. As a function of photon energy, both pn and pp bremsstrahlung inclusive cross sections are shown to be rather flat except in the low photon energy region. The shape of the angular distribution is, to a large extent, determined by the convection current contribution, which in the soft-photon limit has a well-known dipole shape in the case of pn bremsstrahlung and a quadrupole shape in the case of pp bremsstrahlung. For photon energies above \ensuremath{\sim}150 MeV where the magnetic current contribution dominates over the convection contribution, the shape of the angular distribution is roughly of a ${\mathrm{cos}}^{2}$\ensuremath{\theta} form. The internal current gives rise to a nearly isotropic angular distribution. The pp\ensuremath{\gamma} cross section is shown to be very small compared to the pn\ensuremath{\gamma} cross section, even for considerably high-energy photons, because of the two-body current contribution, which is mostly absent in pp bremsstrahlung. The present calculation yields np bremsstrahlung cross sections which still tend to underpredict the data, although the measurements have large uncertainties.

Hard photons in proton-nucleus collisions.

A calculation of energetic photon production in proton-nucleus reactions at intermediate bombarding energies is performed assuming the first chance nucleon-nucleon collisional mechanism. The elementary nucleon-nucleon bremsstrahlung amplitude is calculated within a meson exchange potential model which includes the one-body as well as the two-body current contributions. The results are in reasonable agreement with the recent data by the Grenoble group at the proton incident energy of ${T}_{\mathrm{lab}}$=168 MeV and indicate that these energetic photons are created in a relatively low-density region in the nucleus (\ensuremath{\sim}40% of the nuclear matter normal density). The present model, however, cannot account for the strong angular dependence observed at ${T}_{\mathrm{lab}}$=72 MeV.

Potential model calculation of energetic photon production from heavy ion collisions.

A simple parametrization has been developed for the proton-neutron bremsstrahlung amplitude which reproduces the results of a meson exchange potential model including the convection, magnetization, and the two-body current contributions. Our parametrization maintains the important role of exchange contributions at high photon energies. We apply the model to the description of energetic photon production in heavy ion induced reactions.

Particle-vibration coupling and exchange-current effects on the magnetic electron-scattering form factor

Inelastic electron-scattering form factors of magnetic states in closed-shell nuclei are calculated taking into account the combined effect of the mesonic degrees of freedom and the two-particle-two-hole components of the nuclear wave functions which come from the particle-core vibration coupling. The one-body nucleon- and two-body meson-exchange current contributions to the form factor are evaluated with the same realistic mean field. Application to various high-spin magnetic states of oxygen and lead is made. The comparison with experiment shows an excellent agreement for the states 14 −(6.74 MeV) and 12 1 −(7.06 MeV) in lead, while such is not the case for the second 12 2 −(6.43 MeV) state in lead and the 4 −(18.98MeV) state in oxygen essentially due to mixing configuration effects and the non-consideration of 3p3h excitations, respectively.

Desirability of measurements on the asymmetry function at low energies in theH2(γ,n)H1reaction

Theoretical results on the asymmetry function are provided to encourage measurements to further test the recent unexpected conclusion that nucleon polarization measurements in the photodisintegration of the deuteron at low gamma-ray energies do not appear to require the two-body exchange current contributions.