Coulomb Distortion Effects Research Articles

Uncertainty quantification for μ → e conversion in nuclei: charge distributions

Predicting the rate for μ → e conversion in nuclei for a given set of effective operators mediating the violation of lepton flavor symmetry crucially depends on hadronic and nuclear matrix elements. In particular, the uncertainties inherent in this non-perturbative input limit the discriminating power that can be achieved among operators by studying different target isotopes. In order to quantify the associated uncertainties, as a first step, we go back to nuclear charge densities and propagate the uncertainties from electron scattering data for a range of isotopes relevant for μ → e conversion in nuclei, including 40,48Ca, 48,50Ti, and 27Al. We provide as central results Fourier-Bessel expansions of the corresponding charge distributions with complete covariance matrices, accounting for Coulomb-distortion effects in a self-consistent manner throughout the calculation. As an application, we evaluate the overlap integrals for μ → e conversion mediated by dipole operators. In combination with modern ab-initio methods, our results will allow for the evaluation of general μ → e conversion rates with quantified uncertainties.

Neutrino-nucleus cross-sections at supernova neutrino energies

The inclusive neutrino/antineutrino-induced charged and neutral current reaction cross-sections in [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in the energy region of supernova neutrinos/antineutrinos are studied. The calculations are performed in the local density approximation (LDA) taking into account the effects due to Pauli blocking, Fermi motion and the renormalization of weak transition strengths in the nuclear medium. The effect of Coulomb distortion of the lepton produced in the charged current reactions has also been included. The numerical results for the energy dependence of the cross-section [Formula: see text] as well as the flux averaged cross-section and event rates for the charged lepton production in the case of some supernova neutrino/antineutrino fluxes recently discussed in the literature have been presented. We have also given the flux-averaged angular and energy distributions of the charged leptons corresponding to these fluxes.

Electroweak charge density distributions with parity-violating electron scattering

Parity-violating electron scattering (PVS) is an accurate and model-independent way to investigate the weak-charge density distributions of nuclei. In this paper, we study parity-violating electron scattering with the Helm model where the effects of spin-orbit currents on nuclear weak skins are taken into account. The conditions of two PVS measurements to constrain the surface thickness ${\ensuremath{\sigma}}_{W}$ of Helm weak-charge densities are investigated. According to the plane wave Born approximation, ${A}_{\mathrm{pv}}$ is expressed in terms of parameters of the corresponding Helm charge and weak-charge densities. After fitting the results of ${A}_{\mathrm{pv}}$ calculated from the phase-shift analysis method where the Coulomb distortion effects are incorporated, an empirical formula in terms of Helm model parameters for calculating ${A}_{\mathrm{pv}}$ is obtained. If two PVS measurements with different scattering angles are carried out, the modeled weak-charge density distributions with two parameters could be extracted from this empirical formula.

Asymmetry in the neutrino and anti-neutrino reactions in a nuclear medium

We study the effect of the density-dependent axial and vector form factors on the electron–neutrino (νe) and anti-neutrino (ν¯e) reactions for a nucleon in nuclear matter or in 12C. The nucleon form factors in free space are presumed to be modified for a bound nucleon in a nuclear medium. We adopt the density-dependent form factors calculated by the quark–meson coupling (QMC) model, and apply them to the νe and ν¯e induced reactions with the initial energy E=8–80 MeV. We find that the total νe cross sections on 12C as well as on a nucleon in nuclear matter are reduced by about 5% at the nuclear saturation density, ρ0. This reduction is caused by the modification of the nucleon structure in matter. Although the density effect for both cases is relatively small, it is comparable with the effect of Coulomb distortion on the outgoing lepton in the ν-reaction. In contrast, the density effect on the ν¯e reaction reduces the cross section significantly in both nuclear matter and 12C cases, and the amount maximally becomes of about 35% around ρ0. Such large asymmetry in the νe and ν¯e cross sections, which seems to be nearly independent of the target, is originated from the differences in the helicities of ν¯e and νe. It is expected that the asymmetry influences the r-process and also the neutrino-process nucleosynthesis in core-collapse supernovae.

Parity Violation in Electron Quasielastic Scattering

From the leading order of the interference of the electromagnetic current and weak neutral current, parity violating electron scattering in the quasielastic region is investigated by using a relativistic single particle model including final state interactions. The possible strangeness and the Coulomb distortion effects of incident and outgoing electrons are discussed within that framework.

Eikonal analysis of Coulomb distortion in quasi-elastic electron scattering

An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order 1/k 2, where k is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. A form of effective-momentum approximation is obtained using trajectory-dependent eikonal phases and focusing factors. Fixing the Coulomb distortion effects at the center of the nucleus, the often-used ema approximation is recovered. Comparisons of these approximations are made with full calculations using the electron eikonal wave functions. The ema results are found to agree well with the full calculations.

Coulomb excitation at intermediate energies

Straight line trajectories are commonly used in semiclassical calculations of the first-order Coulomb excitation cross section at intermediate energies, and simple corrections are often made for the distortion of the trajectories that is caused by the Coulomb field. These approximations are tested by comparing to numerical calculations that use exact Coulomb trajectories. In this paper a model is devised for including relativistic effects in the calculations. It converges at high energies toward the relativistic straight-line trajectory approximation and approaches the non-relativistic Coulomb trajectory calculation at low energies. The model is tested against a number of measurements and analyses that have been performed at beam energies between 30 and 70 MeV/nucleon, primarily of quadrupole excitations. Remarkably good agreement is achieved with the previous analyses, and good agreement is also achieved in the few cases, where the $B$($E\ensuremath{\lambda}$) value is known from other methods. The magnitudes of the relativistic and Coulomb distortion effects are discussed.

Coulomb distortion effects in quasi-elastic [formula omitted] scattering on heavy nuclei

The influence of the Coulomb distortion for quasi-elastic ( e , e ′ ) scattering on highly charged nuclei is investigated in distorted wave Born approximation for electrons. The Dirac equation is solved numerically in order to obtain exact electron continuum states in the electrostatic field generated by the charge distribution of an atomic nucleus. Different approximate models are used to describe the nucleon current in order to show that, at high electron energies and energy–momentum transfer, the influence of Coulomb distortions on ( e , e ′ ) cross sections can be reliably described by the effective momentum approximation, irrespective of details concerning the description of the nuclear current.

Investigating the Suppressions for the Longitudinal Structure Function in High Energy Quasielastic Scattering from 56Fe

We investigate the cross sections for inclusive (e, e') reaction from 56 Fe in quasielastic region at large electron energies (2-4GeV) and large three momentum transfer (0.5-1.5 GeV/c). We use a relativistic mean-field single particle model for the bound and continuum nucleon wave functions based on the σ-ω model and we include the effects of electron Coulomb distortion in the calculation. The results are compared to high energy data from SLAC and more recent data from Jefferson Laboratory, particularly for the kinematics where the quasielastic process is expected to dominate the cross section with the energy transfer less than 500 to 600 MeV. The effects of the predicted weakening of the strong scalar and vector potentials of the σ-ω model at high energy are discussed. Possible evidence for longitudinal suppression or modifications of nucleon form factors in the medium is considered, but neither is necessary to explain the quasielastic data for four momentum transfers less than 1 (GeV/c) 2 .

Extraction of structure functions from quasielastic electron scattering(e,e')off medium and heavy nuclei

Using a relativistic mean-field single particle knock-out model for (e,e') reactions on nuclei, we investigate approximate treatments of Coulomb distortion effects and the extraction of longitudinal and transverse structure functions. We show that an effective momentum approximation (EMA) when coupled with a focusing factor provides a good description of the transverse contributions to the (e,e') cross sections for electron energies above 300 MeV on 208Pb. This approximation is not as good for the longitudinal contributions even for incident electron eneriges above 1 GeV and if one requires very precise extraction of longitudinal and transverse structure functions in the quasielastic region it is necessary to utilize distortion factors based on a nuclear model and a more accurate inclusion of Coulomb distortion effects.

Neutrino nucleus cross sections for low energy neutrinos at SNS facilities

We calculate the neutrino nucleus cross sections for charged lepton production relevant for the experiments proposed with the stopped muon neutrinos using neutron spallation source facility. The calculations are done in local density approximation taking into account Pauli blocking, Fermi motion effects and renormalization of weak transition strengths in the nuclear medium. The effect of Coulomb distortion of the lepton produced in charge current reactions is taken into account by using the Fermi function as well as in a model where an effective momentum has been used for the lepton moving in the local Coulomb field of the final nucleus. The numerical results for the neutrino nucleus total cross sections averaged over Michel spectrum are presented for various nuclei.

Supernova neutrino induced inclusive reactions onFe56in terrestrial detectors

The calculations for the neutrino absorption cross sections for supernova neutrinos in $^{56}\mathrm{Fe}$ have been done in the local density approximation (LDA) taking into account Pauli blocking and Fermi motion effects. The renormalization of weak transition strengths in the nuclear medium and the effect of Coulomb distortion of the final lepton are taken into account. The numerical results for the cross sections averaged over the Michel spectrum of neutrinos and various supernova neutrino spectra are presented and compared with other theoretical results.

Coulomb corrections for quasielastic [formula omitted] scattering: eikonal approximation

We address the problem of including Coulomb distortion effects in inclusive quasielastic ( e , e ′ ) reactions using the eikonal approximation. Our results indicate that Coulomb corrections may become large for heavy nuclei for certain kinematical regions. The issues of our model are presented in detail and the results are compared to calculations of the Ohio group, where Dirac wave functions were used both for electrons and nucleons. Our results are in good agreement with those obtained by exact calculations.

Coulomb distortion in high-Q2elastice‐pscattering

Recently, there has been a significant amount of activity to try and understand the discrepancy between Rosenbluth and polarization transfer measurements of the proton form factors. It has been suggested that the standard use of plane-wave Born approximation in extracting the form factors is insufficient, and that higher-order terms must also be included. Of the corrections missing in standard prescriptions, Coulomb distortion is the most well understood. In this paper, we examine the effect of Coulomb distortion on the extraction of the proton form factors.

Formula omitted]–40Ar absorption cross sections for supernova neutrinos

The calculations for the neutrino absorption cross sections for supernova neutrinos in 40Ar have been done in the local density approximation (LDA) taking into account Pauli blocking and Fermi motion effects. The renormalization of weak transition strengths in the nuclear medium and the effect of Coulomb distortion of the lepton produced in charged current reactions are taken into account. The expected event rates for electrons (positrons) have been calculated for a 3 kT liquid argon detector for a supernova occurring at 10 kpc from earth.

?40Ar absorption cross sections for supernova neutrinos

The calculations for the neutrino absorption cross sections for supernova neutrinos in 40Ar have been done in the local density approximation (LDA) taking into account Pauli blocking and Fermi motion effects. The renormalization of weak transition strengths in the nuclear medium and the effect of Coulomb distortion of the lepton produced in charged current reactions are taken into account. The expected event rates for electrons (positrons) have been calculated for a 3 kT liquid argon detector for a supernova occurring at 10 kpc from earth.

Laser-assisted Mott scattering in the Coulomb approximation

We investigate the influence of the Coulomb interaction on laser-assisted Mott scattering. This is done by using an approximation in which the initial state of the electron is described by a Coulomb function modulated by the laser in the same way as a relativistic Volkov state. Numerical calculations are carried out for medium field intensity, and compared with the corresponding results obtained within the first-order Born approximation (where Coulomb distortion effects are neglected). It is found that the differential cross sections of the present treatment agree well with the Born predictions at small angles. With increasing scattering angles, however, including the Coulomb interaction enhances the cross section, as compared to the first-Born results. Furthermore, we show that the Coulomb distortion of the electron motion leads to a qualitatively different dependence of the cross sections on the laser frequency at high frequencies. The dependences of the differential cross section on the other field parameters, impact energy and the charge state of the residual ion are also studied.

Quasielastic electron scattering at high energy from12C,56Fe,and197Au

A relativistic mean-field single particle knockout model is compared to inclusive electron scattering ${(e,e}^{\ensuremath{'}})$ from a range of nuclei ${(}^{12}\mathrm{C},$ ${}^{56}\mathrm{Fe},$ and ${}^{197}\mathrm{Au})$ at high electron energy, but in kinematics where the cross section is dominated by the quasielastic response. These experiments were done with incident electron energies of approximately 2 GeV at SLAC with four-momentum transfer squared of approximately $0.20--0.30(\mathrm{GeV}{/c)}^{2}.$ We include the effects of electron Coulomb distortion in the calculation, and propose a simple way of including Coulomb distortion at high energies which can be used to analyze newer ${(e,e}^{\ensuremath{'}})$ experiments at Jefferson Lab. The effects of the predicted weakening of the strong scalar and vector potentials of the $\ensuremath{\sigma}\ensuremath{-}\ensuremath{\omega}$ model at high nucleon kinetic energy are included in our model.

Effects of the form factor on inclusive(e,e′)reactions in the quasielastic region

We discuss the effect of nuclear medium on the inclusive ${(e,e}^{\ensuremath{'}})$ reactions for ${}^{40}\mathrm{Ca}$ and ${}^{208}\mathrm{Pb}$ targets by introducing the form factors of the nucleons inside nuclei in the quasielastic region. These form factors include the change of nucleon properties in nuclear medium. Longitudinal and transverse structure functions for given momenta and energy transfers are extracted from the cross section calculated by using the form factors with the Rosenbluth separation method. A relativistic Hartree single particle model for the bound state and continuum nucleon wave functions is used and the effects of the electron Coulomb distortion are included in the calculation. We compare the results with the experimental data measured at Bates and Saclay.

Relativistic Hartree-Bogoliubov model with density-dependent meson-nucleon couplings

The relativistic Hartree-Bogoliubov (RHB) model is extended to include density dependent meson-nucleon couplings. The effective Lagrangian is characterized by a phenomenological density dependence for the $\sigma$, $\omega$ and $\rho$ meson-nucleon vertex functions, adjusted to properties of nuclear matter and finite nuclei. Pairing correlations are described by the pairing part of the finite range Gogny interaction. The new density-dependent effective interaction DD-ME1 is tested in the analysis of the equations of state for symmetric and asymmetric nuclear matter, and of ground-state properties of the Sn and Pb isotopic chains. Results of self-consistent RHB calculations are compared with experimental data, and with results previously obtained in the RHB model with non-linear self-interactions, as well as in the density dependent relativistic hadron field (DDRH) model. Parity-violating elastic electron scattering on Pb and Sn nuclei is calculated using a relativistic optical model with inclusion of Coulomb distortion effects, and the resulting asymmetry parameters are related to the neutron ground-state density distributions.