Transverse Response Functions Research Articles

Role of nonthermal solar wind protons in the excitation of electromagnetic proton-cyclotron instability: a kinetic theory based exact numerical investigation

Free transverse kinetic energy i.e. perpendicular temperature anisotropy of protons excite the electromagnetic ion/proton cyclotron instability which is pertained to waves associated with prevalent electromagnetic ion/proton cyclotron emissions in various natural regions of plasmas. The transverse dielectric response function of left hand circularly polarized electromagnetic proton cyclotron (EPC) instability is calculated for two models of nonthermal Cairns distributed plasmas. These models are distinguished according to the effective thermal velocities of protons. For the energetic nonthermal protons populations, nonthermality dependent effective temperature model is proposed which significantly contributes in the excitation of aforementioned plasma mode and cause an appreciable enhancement in the instability growth rate. Exact numerical solution of dispersion relation yields oscillatory real frequency and growth rate of instability. A comparative analysis is also carried out to examine the instability behavior in distinct nonthermal and thermal plasma models. Contemporary numerical investigations are highly beneficial to understand the intricate dynamics of space plasmas.

Measurement of the 12C(e,e′)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm {{}^{12}C}(e,e')$$\\end{document} Cross Sections at Q2=0.8GeV2/c2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^2=0.8\\,\ extrm{GeV}^2/c^2$$\\end{document}

We present the findings of a study based on a new inelastic electron-scattering experiment on the 12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${}^{12}$$\\end{document}C nucleus focusing on the kinematic region of Q2=0.8GeV2/c2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q^2=0.8\\,\ extrm{GeV}^2/{c}^2$$\\end{document}. The measured cross section is sensitive to the transverse response function and provides a stringent test of theoretical models, as well as of the theoretical assumptions made in Monte-Carlo event-generator codes developed for the interpretation of neutrino-nucleus experiments, such as DUNE and HyperK. We find that modern generators such as GENIE and GiBUU reproduce our new experimental data within 10%\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\%$$\\end{document}.

Kinetic numerical analysis of electromagnetic ion cyclotron instability in non-thermal Vasyliunas-Cairns distributed plasmas

Enhanced fluctuations driven by non-thermal features of particle-distributions are reported frequently in the variety of space plasma observations. In the rare-collisional plasmas, these amplified fluctuations scatter the particles in various direction and governs the dynamics of space plasma environments effectively. Electromagnetic ion cyclotron (EMIC) waves usually responsible for low frequency interplanetary magnetic field fluctuations. These are natural emissions in numerous natural environments of plasmas which usually operates underneath the ion/proton cyclotron frequencies. These are identified as left hand circular polarization (L-mode) with a propagation directed towards the ambient magnetic field. Various space missions and in situ measurements unveil the perpendicular temperature anisotropies of non-thermal populations of ions/protons i.e. in heliospheric regions and solar wind. These proton temperature anisotropies excite EMIC instability which in turn the pitch angle scatters the ions and restrained the anisotropy in certain ranges. In Vasyliunas-Cairns distributed hybrid non-thermal electromagnetic proton plasma, the transverse dielectric response function (TDERF) is calculated for L-mode. It is then numerically solved in order to show the impact of non-thermal populations due to non-thermal parameters α and κ on the dispersion and growth rates of EMIC instability in low and high plasma beta β regimes. Possible variation in the real oscillatory and imaginary frequencies spectrum is also analyzed with the variation in the values of other pertinent parameters i.e. temperature anisotropy τ and β. The parametric numerical analysis of the present work has relevance about that plasma phenomena of space regions where non-thermal distributed populations are prevalent.

Exact numerical analysis of EMEC mode instability in more realistic Cairns distributed non-thermal plasmas

Non-thermal plasma systems beyond the state of thermal equilibrium must have non-thermality dependent effective temperatures. These particle populations cannot have Maxwellian temperatures T∥,⊥e(M) which are typically considered at thermal equilibrium in the context of Maxwellian plasmas. Previously, in such dilute environments, numerous non-thermal distributions incorporating the concept of Maxwellian temperature T∥,⊥e(M) have been utilized, one of them is Cairns distribution (here termed as type-A). To ameliorate this inconsistency, we propose a more realistic form of Cairns distribution (type-B) with the vigorous definition of effective temperature and effective thermal velocity. Both Cairns distributions (A and B) are utilized to calculate the transverse dielectric response function (TDERF) of electromagnetic electron cyclotron (EMEC) mode. The exact numerical solution of TDERFs of EMEC instability reveals interesting and more promising repercussions in the case of Cairns-B i.e. an augmentation in the behavior of oscillatory and imaginary frequencies of the instability.

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.''

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.

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.

Superscaling analysis of quasielastic electron scattering with relativistic effective mass

We provide a parametrization of a new phenomenological scaling function obtained from a chi-square fit to a selected set of (e,e') cross section data expanding a band centered around the quasielastic peak. We start from a re-analysis of quasielastic electron scattering from nuclear matter within the relativistic mean field model. The cross section depends on the relativistic effective mass of the nucleon, $m_N^*$, and it scales with respect to a new scaling variable, $\psi^*$. This suggests a new superscaling approach with effective mass (SuSAM*) for predicting quasielastic cross sections within an uncertainty band. The model reproduces previously established results on the enhancement of the transverse response function as compared to the traditional relativistic Fermi gas.

Transverse isospin response function of asymmetric nuclear matter from a local isospin density functional

The time dependent local isospin density approximation (TDLIDA) has been extended to the study of the transverse isospin response function in nuclear matter with an arbitrary neutron-proton asymmetry parameter $\ensuremath{\xi}$. The energy density functional has been chosen in order to fit existing accurate quantum Monte Carlo calculations with a density dependent potential. The evolution of the response with $\ensuremath{\xi}$ in the $\mathrm{\ensuremath{\Delta}}{T}_{z}=\ifmmode\pm\else\textpm\fi{}1$ channels is quite different. While the strength of the $\mathrm{\ensuremath{\Delta}}{T}_{z}=+1$ channel disappears rather quickly by increasing the asymmetry, the $\mathrm{\ensuremath{\Delta}}{T}_{z}=\ensuremath{-}1$ channel develops a stronger and stronger collective mode that in the regime typical of neutron star matter at $\ensuremath{\beta}$ equilibrium almost completely exhausts the excitation spectrum of the system. The neutrino mean free paths obtained from the TDLIDA responses are strongly dependent on $\ensuremath{\xi}$ and on the presence of collective modes, leading to a sizable difference with respect to the prediction of the Fermi gas model.

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.

Hydrodynamics on the lowest Landau level

Using the recently developed approach to quantum Hall physics based on Newton-Cartan geometry, we consider the hydrodynamics of an interacting system on the lowest Landau level. We rephrase the non-relativistic fluid equations of motion in a manner that manifests the spacetime diffeomorphism invariance of the underlying theory. In the massless (or lowest Landau level) limit, the fluid obeys a force-free constraint which fixes the charge current. An entropy current analysis further constrains the energy response, determining four transverse response functions in terms of only two: an energy magnetization and a thermal Hall conductivity. Kubo formulas are presented for all transport coefficients and constraints from Weyl invariance derived. We also present a number of Středa-type formulas for the equilibrium response to external electric, magnetic and gravitational fields.

Transverse (e,e′) Response Functions for 4He

This poster presentation is intended to show preliminary results from calculations of the inclusive (e,e′) transverse response functions of 4He. Up to now we have only included the E1 and M1 multipoles and therefore no comparison with experiment is shown. That will be done once all relevant multipoles have been calculated. Details of the calculation are summarized in the text below.

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.

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.

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 ...

Δ Isobar Degrees of Freedom in the 3He Transverse Electron Scattering Response Function

The importance of Δ(1232) isobar degrees of freedom is investigated for the transverse (e, e′) response of 3He in the quasi-elastic peak region and beyond (considered momentum transfer range: 500 ≤ q ≤ 1,000 MeV/c). Besides Δ isobar currents (Δ-IC) meson exchange currents and relativistic corrections to the nucleonic one-body current are included. The calculation is carried out by using the Lorentz integral transform (LIT) method. Results for the transverse response function RT are presented up to q = 700 MeV/c, whereas for higher q only some preliminary results for the LIT of RT are discussed. In the quasi-elastic peak region Δ-IC enhance RT by about 5% and tend to cancel three-nucleon force effects. One observes an excellent agreement with experimental RT results. Particularly strong Δ-IC contributions are found for transitions into the final state with isospin T = 3/2, which is only reachable in three-body break-up reactions.

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.

Nuclear Electro-disintegration with Antisymmetrized Molecular Dynamics

The extended antisymmetrized molecular dynamics (AMD) wave function is used to study the two-body nuclear electro-disintegration. The final-state interactions are included using the Glauber multiple scattering approximation. Non-relativistic nuclear charge and current operators are employed when calculating longitudinal and transverse nuclear response functions. It is found that the AMD model gives a very good description of experimental data for the 4He response functions.

NaI (Tl) calorimeter calibration and simulation for Coulomb sum rule experiment in Hall-A at Jefferson Lab

A precision measurment of inclusive electron scattering cross sections is carried out at Jefferson Lab in the quasi-elastic region for 4He, 12C, 56Fe and 208Pb targets. The longitudinal (RL) and transverse (RT) response functions of the nucleon need to be extracted precisely in the momentum transfer range 0.55 GeV/c ≤ |q| ≤ 1.0 GeV/c. To achieve the above goal, a NaI (Tl) calorimeter is used to distinguish good electrons from background, including pions and low energy electrons rescattered from the walls of the spectrometer magnets. Due to a large set of kinematics and changes in HV settings, a number of calibrations are performed for the NaI (Tl) detector. Corrections for a few blocks of NaI (Tl) with bad or no signal are applied. The resolution of the NaI (Tl) detector after calibration reached at E = 1 GeV. The performance of the NaI (Tl) detector is compared with a simulation. The good calibration and background analysis for the NaI(Tl) detector are very important for the reduction of the systematic error of cross sections and the separation of RL and RT.

Collective excitations and response functions of two-band band-singlet and spin-tripletsuperconductors

The two-band band-singlet and spin-triplet superconductors are studied in the frameworkof functional integrals with a focus on collective excitations and their influences on responsefunctions. The long range Coulomb interaction has been included to preserve the electromagneticU(1) gaugeinvariance. The U(1) phase fluctuation and the spin wave are identified as the collective excitations.The longitudinal spin response function turns out to be solely determined byquasiparticle excitation. The transverse spin response function is determinedby both the quasiparticle excitation and the spin wave. The spin wave is foundnot to be renormalized by long range Coulomb interaction. The densityresponse function is determined by both the quasiparticle excitation and theU(1) phase fluctuation, but in contrast to the case of spin response functions, both of them arestrongly renormalized by the long range Coulomb interaction. The nondegeneracy of theband energy can affect the response functions significantly through the contribution bycollective excitations.