Longitudinal Response Functions Research Articles

Extraction of the Coulomb sum rule, transverse enhancement, and longitudinal quenching from an analysis of all available e−C12 and e−O16 cross section data

We report on a phenomenological analysis of all available electron scattering data on $^{12}\mathrm{C}$ (about 6600 differential cross section measurements) and on $^{16}\mathrm{O}$ (about 250 measurements) within the framework of the quasielastic (QE) superscaling model (including Pauli blocking). All QE and inelastic cross section measurements are included down to the lowest momentum transfer $\mathbf{q}$ (including photoproduction data). We find that there is enhancement of the transverse QE response function (${R}_{T}^{QE}$) and quenching of the QE longitudinal response function (${R}_{L}^{QE}$) at low $\mathbf{q}$ (in addition to Pauli blocking). We extract parametrizations of a multiplicative low $\mathbf{q}$ ``longitudinal quenching factor'' and an additive ``transverse enhancement'' contribution. Additionally, we find that the excitation of nuclear states contribute significantly (up to 30%) to the Coulomb sum rule $SL(\mathbf{q})$. We extract the most accurate determination of $SL(\mathbf{q})$ to date and find it to be in disagreement with random phase approximation (RPA) based calculations but in reasonable agreement with recent theoretical calculations, such as ``first principle Green's function Monte Carlo.''

Removing center of mass effects in response function and sum rule calculations based on the harmonic oscillator basis

Response functions are at the heart of any comparison of theory with experiment in studies of the nuclear dynamics with electroweak probes. Calculations performed in the laboratory frame often suffer from center of mass contaminations that need to be removed. By confining the system in a harmonic oscillator, we derive a set of analytical formulas to subtract the center of mass effects from calculations of response functions and associated sum rules. After a general analytical derivation, we first deal specifically with the longitudinal response function appearing in electron scattering and provide expressions for the center of mass correcting functions. Next, we present a proof of principle study for the case of the electric dipole sum rules in a two-body problem with a numerical implementation of our formalism. These steps pave the way to applying the proposed method to heavier nuclei in the future.

Manifestation of one- and two-body currents in longitudinal and transverse response functions of the $$^{12}$$C nucleus at $$q = 300$$ MeV/c

The experimental values of longitudinal and transverse response functions of the 12C nucleus have been obtained at the 3-momentum transfer q = 300 MeV/c. The data are compared with the calculations made with due regard to the dynamics of all the nucleons constituting the 12C nucleus, and also, to the contributions of both the one-body currents only, and their combination with two-body currents.

AbInitio Computation of the Longitudinal Response Function in ^{40}Ca.

We present a consistent abinitio computation of the longitudinal response function R_{L} in ^{40}Ca using the coupled-cluster and Lorentz integral transform methods starting from chiral nucleon-nucleon and three-nucleon interactions. We validate our approach by comparing our results for R_{L} in ^{4}He and the Coulomb sum rule in ^{40}Ca against experimental data and other calculations. For R_{L} in ^{40}Ca we obtain a very good agreement with experiment in the quasielastic peak up to intermediate momentum transfers, and we find that final state interactions are essential for an accurate description of the data. This work presents a milestone towards abinitio computations of neutrino-nucleus cross sections relevant for experimental long-baseline neutrino programs.

Numerical and Analytical Study of Electron Plasma Waves in Nonthermal Vasyliunas‐Cairns Distributed Plasmas

AbstractThe Poison‐Vlasov model in plasma kinetic theory is taken into account to study the propagation of electron plasma waves (or Langmuir waves) in hot, un‐magnetized Vasyliunas‐Cairns distributed plasmas (VCDPs). The longitudinal dielectric plasma response function is obtained for such nonthermal plasmas. The Landau damping rate of Langmuir waves (LWs) in nonthermal VCDP, which propagates with a phase speed greater than the effective thermal speed of the electrons, is also studied. The real and imaginary parts of the wave frequency are investigated analytically as well as numerically and a comparison between the numerical and analytical results is presented. The finding reveals that the dispersion curve and damping rate of the wave are significantly influenced by the simultaneous presence of two nonthermality parameters, that is, ′′ and ′′ (spectral index) in the hybrid (Vasyliunas‐Cairns) distributed plasmas. It is discussed that results are quite distinctive from that obtained in nonthermal plasmas that have sole presence of either of the nonthermality parameters ′′ or super‐thermality spectral index ′′ in Cairns or kappa distributed electron plasmas, respectively. The more realistic form of 3D and reduced 1D distribution function of VCDP has been used to analyze LWs in describing nonthermal plasmas with more energetic electron in VCDP case.

Revisiting some analytical and numerical interpretations of Cairns and Kappa–Cairns distribution functions

In this tutorial, three-dimensional (3D) Cairns and Kappa-Cairns distribution functions are re-examined both analytically and numerically. The difference between one-dimensional (1D) and (3D) Cairns distribution functions (CDF) has been explained by deriving reduced 1D Cairns distribution function. It is noted that expressions of 1D and reduced 1D distributions such as Maxwellian and Kappa distributions are similar to each other, while the plots of 1D and reduced 1D CDF are significantly different from each other. The effect of non-thermality parameter on the 3D CDF is also studied by plotting it as a function of magnitude of the 3D velocity. It shows that the peak of the distribution function shifts toward higher speeds with an increase in the value of non-thermality parameter. The longitudinal dielectric response function is derived by using the 3D CDF for studying kinetic behavior of electrostatic waves in an unmagnetized isotropic plasma. The dielectric function is written in terms of plasma dispersion function and is then used to derive the dispersion relations and Landau damping increments for electron plasma waves, ion acoustic waves, and dust acoustic waves in a Cairns distributed plasma. The expressions of the dispersion relation and Landau damping rate of Cairns distributed plasma change into the corresponding expressions of the Maxwellian distributed plasma when the nonthermality parameter is taken equal to zero. Mathematical manipulations have been done for 3D Kappa-Cairns distribution function (KCDF) to find the correct normalization factor. An appropriate and valid range of values of the spectral index κ is obtained by calculating second moment of the velocity by integrating KCDF over 3D velocity space. The effect of non-thermality parameter and the spectral index κ on the 3D KCDF is studied by plotting it as a function of magnitude of the 3D velocity. It is also seen that the velocities where the tails of KCDF exists are much higher compared to the velocities where the tail of Kappa distribution occurs. For both 3D CDF and KCDF, it has been observed that the difference in the distribution functions becomes negligible when the value of the non-thermality parameter becomes more than 0.5.

Quantum kinetic dust acoustic waves in arbitrary degenerate quantum dusty plasma

Using kinetic formulation with a quantum plasma dynamic approach, dust acoustic waves (DAWs) in three component non-relativistic, isotropic, unmagnetized, and collisionless quantum dusty plasma are analytically analyzed. Electrons are considered as quantum mechanical, following the Fermi–Dirac distribution, while ions and dust are considered as classical, obeying Maxwell–Boltzmann statistics. The longitudinal response function, in terms of susceptibility tensors, is derived and divided into two parts, i.e., dispersion relation (real part) and Landau damping (imaginary part). The dispersion relations and Landau damping rates are analyzed with the effect of the arbitrary degree of temperature degeneracy and quantum recoil. Two cases of the DAWs are discussed regarding the arbitrary degeneracy, which are nearly non-degenerate and nearly degenerate quantum plasmas. The dispersion relations and Landau damping rates for DAWs in both cases are examined analytically and numerically, using the data of semiconductor quantum wells and dense astrophysical plasmas.

Probing uncertainties of nuclear structure corrections in light muonic atoms

Recent calculations of nuclear structure corrections to the Lamb shift in light muonic atoms are based on an expansion in a parameter eta, where only terms up to second order are retained. The parameter eta can be shown to be proportional to the square root of the muon/proton mass ratio, so that it is small and the expansion is expected to converge. However, practical implementations show that the eta convergence may be slower than expected. In this work we probe the uncertainties due to this expansion using a different formalism, which is based on a multipole expansion of the longitudinal and transverse response functions and was first introduced by Leidemann and Rosenfelder. We refer to this alternative expansion as the eta-less formalism. We generalize this formalism to account for the cancellation of elastic terms such as the third Zemach moment (or Friar moment) and embed it in a computationally efficient framework. We implement and test this approach in the case of muonic deuterium. The comparison of results in the point nucleon limit for both methods achieve sub-percent agreement. When nucleon form factors are introduced we find a 4% and 2% difference in the third Zemach moment and nuclear polarizability, respectively, compared to the eta-less expansion, indicating that the nucleon form factor approximations should be improved. However, we find that the sum of these terms removes this dependence and the uncertainty due to the eta-expansion and the related second-order approximation in the nucleon form factors amounts only to 0.2% and thus is fully justified in muonic deuterium. This computationally efficient framework paves the way to further studies in light muonic systems with more than two nucleons, where controlling and reducing uncertainties in nuclear structure corrections is key to the experimental efforts of the CREMA collaboration.

Dispersion properties of electron acoustic waves in degenerate and non‐degenerate quantum plasmas

AbstractThe longitudinal response functions are used to generalize the dispersion properties of electron acoustic waves (EAWs) in the presence of quantum recoil, for isotropic, non‐relativistic, degenerate/non‐degenerate plasmas. In order to study the EAWs, the constituents of non‐degenerate (thermal) plasma are considered to be of two groups of electrons having different number density and temperature, namely the cold electrons and the hot electrons. Similarly in degenerate (Fermi) plasma the two population of electrons are considered to be the thinly populated and the thickly populated electrons. The sparsely populated electrons are termed as cold electrons while the densely populated ones are termed as hot electrons. The ions are stationary which form the neutralizing background. The absorption coefficients for Landau damping with the inclusion of the quantum recoil in both plasmas are calculated and discussed. The results are discussed in the context of laser‐produced plasma.

Shift of the collective mode of polarized graphene on a substrate using spin-sensitive response theory

The growing precision of optical and scattering experiments necessitates a better understanding of the influence of damping onto the collective mode of sheet electrons. As spin-polarized systems are of particular interest for spintronic applications, we here report spin-sensitive linear response functions of graphene, which give access to chargeand spin-density related excitations. We further calculate the reflectivity of graphene on an SiO2 surface, a setup used in s-wave scanning near-field microscopy. Increasing the partial spin-polarization of the graphene charge carriers leads to a significant broadening and shift of the plasmon mode, due to single-particle interband transitions of the minority spin carriers. We also predict an antiresonance in the longitudinal magnetic response function, similar to that of semiconductor heterostructures.

Electromagnetic Response ofC12: A First-Principles Calculation

The longitudinal and transverse electromagnetic response functions of $^{12}$C are computed in a "first-principles" Green's function Monte Carlo calculation, based on realistic two- and three-nucleon interactions and associated one- and two-body currents. We find excellent agreement between theory and experiment and, in particular, no evidence for the quenching of measured versus calculated longitudinal response. This is further corroborated by a re-analysis of the Coulomb sum rule, in which the contributions from the low-lying $J^\pi\,$=$\, 2^+$, $0^+_2$ (Hoyle), and $4^+$ states in $^{12}$C are accounted for explicitly in evaluating the total inelastic strength.

Relativistic and Nuclear Medium Effects on the Coulomb Sum Rule.

In light of the forthcoming high precision quasielastic electron scattering data from Jefferson Lab, it is timely for the various approaches to nuclear structure to make robust predictions for the associated response functions. With this in mind, we focus here on the longitudinal response function and the corresponding Coulomb sum rule for isospin-symmetric nuclear matter at various baryon densities. Using a quantum field-theoretic quark-level approach which preserves the symmetries of quantum chromodynamics, as well as exhibiting dynamical chiral symmetry breaking and quark confinement, we find a dramatic quenching of the Coulomb sum rule for momentum transfers |q|≳0.5 GeV. The main driver of this effect lies in changes to the proton Dirac form factor induced by the nuclear medium. Such a dramatic quenching of the Coulomb sum rule was not seen in a recent quantum MonteCarlo calculation for carbon, suggesting that the Jefferson Lab data may well shed new light on the explicit role of QCD in nuclei.

Excitations in a spin-polarized two-dimensional electron gas

A remarkably long-lived spin plasmon may exist in two-dimensional electron liquids with imbalanced spin up and spin down population. Predictions for this interesting mode by Agarwal et al. [Phys. Rev. B 90, 155409 (2014)] are based on the random phase approximation. We here show how to account for spin dependent correlations from known ground state pair correlation functions and study the consequences on the various spin dependent longitudinal response functions. The spin plasmon dispersion relation and its critical wave vector for Landau damping by minority spins turn out to be significantly lowered. We further demonstrate that spin dependent effective interactions imply a rich structure in the excitation spectrum of the partially spin-polarized system. Most notably, we find a "magnetic antiresonance", where the imaginary part of both, the spin-spin as well as the density-spin response function vanish. The resulting minimum in the double-differential cross section is awaiting experimental confirmation.

Zero-Field Vortex-Induced Hall Effect and Polar Kerr Effect in Chiral p-Wave Superconductors near Kosterlitz-Thouless Transition

We discuss Hall effect and power dissipation in chiral p-wave superconductors near Kosterlitz-Thouless transition in the absence of applied magnetic field. In bound pair dynamics picture, nonzero Hall conductivity emerges when vortex-antivortex bound pair polarization has a component transverse to the direction of external perturbation. Such effect arises from the broken time reversal symmetry nature of a chiral p-wave superconducting state and does not require an applied magnetic field. A frequency-dependent matrix dielectric function $\epsilon(\omega)$ is derived to describe the screening effect due to the pair polarization. Quantities related to the Hall conductivity and power dissipation, denoted as $\epsilon^{-1}_\perp$ and $\Im (-\epsilon^{-1}_\parallel)$, are investigated in frequency and temperature domain. The imaginary part of the former can show peak structure and sign reversal as a function of frequency close to transition temperature, as well as in the temperature domain at various fixed frequencies. The latter shows peak structure near transition temperature. These features are attributed to pair-size-dependent longitudinal and transverse response function of bound pairs. Consequences due to free vortex dynamics and the resulting total conductivity tensor $\sigma$ are also discussed.

The longitudinal response function of the deuteron in chiral effective field theory

We use chiral effective field theory (χEFT) to make predictions for the longitudinal electromagnetic response function of the deuteron, f L , which is measured in d(e, e′N) reactions. In this case the impulse approximation gives the full χEFT result up to \(\mathcal{O}(P^4 )\) relative to leading order. By varying the cutoff in the χEFT calculation between 0.6 and 1 GeV we conclude that the calculation is accurate to better than 10% for values of q 2 within 4 fm−2 of the quasi-free peak, up to final-state energies E np = 60 MeV. In these regions χEFT is in reasonable agreement with predictions for f L obtained using the Bonn potential. We also find good agreement with existing experimental data on f L , albeit in a more restricted kinematic domain.

Charge Form Factor and Sum Rules of Electromagnetic Response Functions inC12

An ab initio calculation of the 12C elastic form factor and sum rules of longitudinal and transverse response functions measured in inclusive (e, e') scattering are reported, based on realistic nuclear potentials and electromagnetic currents. The longitudinal elastic form factor and sum rule are found to be in satisfactory agreement with available experimental data. A direct comparison between theory and experiment is difficult for the transverse sum rule. However, it is shown that the calculated transverse sum rule has large contributions from two-body currents, indicating that these mechanisms lead to a significant enhancement of the quasielastic transverse response. This fact may have implications for the anomaly observed in recent neutrino quasielastic charge-changing scattering experiments on 12C.

Exact evaluation of the rates of electrostatic decay and scattering off thermal ions for an unmagnetized Maxwellian plasma

Electrostatic decay of Langmuir waves into Langmuir and ion sound waves (L→L′+S) and scattering of Langmuir waves off thermal ions (L+i→L′+i′, also called “nonlinear Landau damping”) are important nonlinear weak-turbulence processes. The rates for these processes depend on the quadratic longitudinal response function α(2) (or, equivalently, the quadratic longitudinal susceptibility χ(2)), which describes the second-order response of a plasma to electrostatic wave fields. Previous calculations of these rates for an unmagnetized Maxwellian plasma have relied upon an approximate form for α(2) that is valid where two of the wave fields are fast (i.e., vϕ=ω/k≫Ve where ω is the angular frequency, k is the wavenumber, and Ve is the electron thermal speed) and one is slow (vϕ≪Ve). Recently, an exact expression was derived for α(2) that is valid for any phase speeds of the three waves in an unmagnetized Maxwellian plasma. Here, this exact α(2) is applied to the calculation of the three-dimensional rates for electrostatic decay and scattering off thermal ions, and the resulting exact rates are compared with the approximate rates. The calculations are performed using previously derived three-dimensional rates for electrostatic decay given in terms of a general α(2), and newly derived three-dimensional rates for scattering off thermal ions; the scattering rate is derived assuming a Maxwellian ion distribution, and both rates are derived assuming arc distributions for the wave spectra. For most space plasma conditions, the approximate rate is found to be accurate to better than 20%; however, for sufficiently low Langmuir phase speeds (vϕ/Ve≈3) appropriate to some spatial domains of the foreshock regions of planetary bow shocks and type II solar radio bursts, the use of the exact rate may be necessary for accurate calculations. The relative rates of electrostatic decay and scattering off thermal ions are calculated for a range of parameters using the exact expressions for the rates; electrostatic decay is found to have the larger growth rate over the whole range of parameters, consistent with previous approximate calculations.

Quasielastic electron scattering in a derivative coupling model with relativistic random phase approximation

We apply the derivative coupling model with ZM and ZM3 parameters to investigate the longitudinal response function in quasielastic electron scattering in the relativistic random phase approximation. The non-spectral method is chosen to describe the nucleon Green's function in a finite nucleus. Some remarks have been made in conclusion.

Possible Uncertainties of Parity Violation in Electron Quasi-Elastic Scattering

From the leading order of the interference of the electromagnetic current and the electroweak neutral current, parity violating electron scattering on a nucleus in the quasi-elastic region is investigated by using a relativistic single particle model. We use 208Pb as a target nucleus, and the incident electron energy range is exploited up to 1 GeV. We enumerate possible ambiguities from 208Pb by the electromagnetic form factors, the strangeness form factors, the final states interaction, and the Coulomb effects on the parity violation (PV) asymmetry in the inclusive electrons scattering on the quasi-elastic region. The effect of nucleon electromagnetic form factors is studied by comparing the standard Sachs form factors and the parameterized form recently adjusted to the world data. The effect of the strangeness in the PV asymmetry is also investigated through the recent results of the strangeness form factors. We separately calculate the asymmetries of longitudinal and transverse response functions. The ...

Two-Body Electrodisintegration of 4He Using Antisymmetrized Molecular Dynamics

The antisymmetrized molecular dynamics method is used to investigate the two-body electrodisintegration of 4He. Effects of final-state interactions are included via the Glauber multiple scattering approximation. Experimental data for the 4He longitudinal and transverse response functions are well described at high momentum transfer.