Longitudinal Response Functions Research Articles

Polarization effects on the dielectric properties of molten AgI

The results are reported of molecular dynamics simulations of the static longitudinal dielectric and response functions for molten AgI at 923 K using two ionic models. The first one is a rigid ion model, while in the second the induced dipole moments of the anions are added to the effective pair potentials of the first. It is derived theoretically that the dielectric functions for the polarizable ion model are determined by spatial correlations of charge and dipole moment densities. The charge structure factor at long wavelengths is also studied.

Kinetic equation for finite systems of fermions with pairing

The solutions of the Wigner-transformed time-dependent Hartree–Fock–Bogoliubov equations are studied in the constant-Δ approximation. This approximation is known to violate particle-number conservation. As a consequence, the density fluctuation and the longitudinal response function given by this approximation contain spurious contributions. A simple prescription for restoring both local and global particle-number conservation is proposed. Explicit expressions for the eigenfrequencies of the correlated systems and for the density response function are derived and it is shown that the semiclassical analogous of the quantum single-particle spectrum has an excitation gap of 2Δ, in agreement with the quantum result. The collective response is studied for a simplified form of the residual interaction.

Extraction of the longitudinal and transverse response functions in(e,e'p)reactions

In this Brief Report we extract the longitudinal and transverse response functions from exclusive $(e,{e}^{'}p)$ cross sections at fixed squared four-momentum transfer ${Q}^{2}$ in the quasielastic region. They are extracted in parallel kinematics by applying the Rosenbluth separation to the $(e,{e}^{'}p)$ reactions. The distorted Coulomb effects are also taken into account on each extracted response functions. The Coulomb effects in the response functions are different from those of the corresponding cross sections.

Inclusive electron scattering offHe4

Inclusive electron scattering off $^{4}\mathrm{He}$ is investigated for low and medium energy and momentum transfers. The final state interaction, given by the simple semirealistic Malfliet-Tjon potential, is treated rigorously applying the Lorentz integral transform (LIT) method. In addition to the nonrelativistic one-body current a consistent meson exchange current is constructed and implemented. Results are presented for both longitudinal and transverse response functions at various momentum transfers. Good agreement with experimental data is found for the longitudinal response function, whereas some strength is missing in the transverse response function on the low energy side of the quasi-elastic peak.

Inclusive electron scattering off 4He

Inclusive electron scattering off 4 He is calculated exactly with a complete treatment of the final state interaction within a simple semirealistic potential model. We discuss results for both the longitudinal and the transverse response functions, at various momentum transfers. A consistent meson exchange current is implemented. Good agreement with available experimental data is found for the longitudinal response function, while some strength is still missing in the transverse response function.

Recent experimental results for the π+ electric form factor from Jefferson Lab

The pion holds a special role in our quest to understand hadrons in terms of the underlying degrees of freedom of QCD. It is the lightest mass QCD system and is used as a test case for all models of hadronic structure. While the π+ form factor (Fπ) can be calculated using perturbative QCD at large Q2, its calculation in the intermediate Q2 transition region is more complex and model-dependent. Over the past several years, two experiments have been mounted at Jefferson Lab to measure Fπ over the range of Q2 = 0.6 to 2.45 GeV2. The technique utilizes a precision Rosenbluth separation of the p(e, e′π+)n reaction at low −t. Fπ is then extracted from the separated longitudinal response function (σL) with the aid of a model. The recent Jefferson Lab data are reviewed, with special emphasis on the extraction of the form factor from the σL data.

The production of matter from curvature in a particular linearized high order theory ofgravity and the longitudinal response function of interferometers

The strict analogy between scalar–tensor theories of gravity and high order gravity iswell known in the literature. In this paper it is shown that, from a particularhigh order gravity theory known in the literature, it is possible to produce, inthe linearized approach, particles which can be seen like massive scalar modesof gravitational waves, and the response of interferometers to such particles isanalysed. The presence of the mass generates a longitudinal force in addition of thetransverse one which is appropriate to the massless gravitational waves and theresponse of an arm of an interferometer to this longitudinal effect in the frameof a local observer is computed. This longitudinal response function is directlyconnected to the function of the Ricci scalar in the particular action of this highorder theory. Important consequences from a theoretical point of view could arisefrom this approach, because it opens up the possibility of using the signals seenfrom interferometers to understand which is the correct theory of gravitation.The presence of the mass could also have important applications in cosmology because ofthe fact that gravitational waves can have mass and could give a contribution to the darkmatter of the Universe.

Coulomb sums of the 4He nucleus at q=0.88 to 1.25 fm−1

Abstract Spectra of electrons scattered by 4He nuclei have been processed. Response functions of the 4He nucleus were found at effective 3-momentum transfers q = 0.875 , 1.000, 1.125 and 1.250 fm−1. The data on the longitudinal response function were used to determine the Coulomb sum values. The data obtained here are compared with the theoretical values.

SCALAR GRAVITATIONAL WAVES FROM SCALAR-TENSOR GRAVITY: PRODUCTION AND RESPONSE OF INTERFEROMETERS

Scalar-tensor gravity admits the existence of scalar modes of gravitational waves (SGWs). The mechanism of production and the response of interferometers to these scalar components of gravitational waves can be studied in three different gauges in the massless case: the transverse-traceless (TT) gauge, the so-called "Shibata, Nakao and Nakamura" (SNN) gauge, and the local Lorentz gauge. The response of interferometers to massless SGWs is invariant in these different gauges. Our work generalizes previous results which, in the study of the coupling between interferometers and massless SGWs, started from the assumption that the wavelength of the SGW is much larger than the distance between the test masses. Furthermore, considering situations motivated by string-dilaton gravity, the effect of a small mass term on the response of the interferometer is taken into account. In this case (massive SGW), we have a longitudinal effect, the response of an arm of an interferometer, which is aligned in the wave propagation direction is computed. The value of the longitudinal response function for non-relativistic massive SGW at high frequencies is very high: this fact opens the doors to the interesting possibility of detection of "massive" part of the signal, if advanced projects will achieve high sensitivities. Finally, by using previous results and the geometry of the system, the generalized coupling between interferometers (like VIRGO or LIGO) and massless SGWs is studied. The total frequency response function to massless SGWs incoming from arbitrary directions is studied.

Relativistic quantum plasma dispersion functions

Relativistic quantum plasma dispersion functions are defined and the longitudinal and transverse response functions for an electron (plus positron) gas are written in terms of them. The dispersion is separated into Landau-damping, pair-creation and dissipationless regimes. Explicit forms are given for the RQPDFs in the cases of a completely degenerate distribution and a nondegenerate thermal (J\"uttner) distribution. Particular emphasis is placed on the relation between dissipation and dispersion, with the dissipation treated in terms of the imaginary parts of RQPDFs. Comparing the dissipation calculated in this way with the existing treatments leads to the identification of errors in the literature, which we correct. We also comment on a controversy as to whether the dispersion curves in a superdense plasma pass through the region where pair creation is allowed.

Medium modifications of nucleon electromagnetic form factors

We use the Nambu–Jona-Lasinio model as an effective quark theory to investigate the medium modifications of the nucleon electromagnetic form factors. By using the equation of state of nuclear matter derived in this model, we discuss the results based on the naive quark–scalar diquark picture, the effects of finite diquark size, and the meson cloud around the constituent quarks. We apply this description to the longitudinal response function for quasielastic electron scattering. RPA correlations, based on the nucleon–nucleon interaction derived in the same model, are also taken into account in the calculation of the response function.

Quasielastic electron scattering in relativistic mean-field theory

The density-dependent relativistic hadron (DDRH) field theory proposed recently is extended to investigate the longitudinal response function and the Coulomb sum rule in quasielastic electron scattering in the relativistic random phase approximation (RPA). The results in the DDRH model are compared with those in other models systematically. It is found that meson effective masses induced by the nonlinear terms in the nonlinear Walecka model should be used to obtain the meson Green’s functions when the longitudinal response function and the Coulomb sum rule are calculated. The effects of the δ and ρ mesons are clearly shown in quasielastic electron scattering, and the isospin-dependent attractive potential between nucleons due to the exchange of the δ-meson cancels the isospin-dependent repulsive contribution of the ρ-meson to a certain extent. The obtained results in the DDRH model are in good agreement with experimental data except for the Coulomb sum rule in 208Pb.

Is the proton electromagnetic form factor modified in nuclei?

Guided by the recent experimental confirmation of the validity of the Effective Momentum Approximation (EMA) in quasi-elastic scattering off nuclei, we have re-examined the extraction of the Longitudinal and Transverse Response Functions in medium-weight and heavy nuclei. In the EMA we have performed a Rosenbluth separation of the available world data on 40Ca, 48Ca, 56Fe and 208Pb. We find that the Longitudinal Response Function for these nuclei is ”quenched” and that the Coulomb sum is not saturated, at odds with recent claims in the literature.

The role of the Δ(1232) on the longitudinal response in the inclusive electron scattering reaction

We have performed a many-body calculation of the longitudinal nuclear ( e, e′) reaction employing a Second RPA (SRPA) formalism which contains the Δ(1232). More explicitly, our scheme contains RPA correlations as well as Hartree–Fock and second order self-energies, where an accurate evaluation of exchange terms is achieved. Using this formalism we have evaluated the longitudinal response function for 40Ca. We give final results at momentum transfers ranging from 300 up to 500 MeV/ c, obtaining a good agreement with data.

Some considerations on the restoration of Galilei invariance in the nuclear many-body problem

The effects of the restoration of Galilei invariance on many-nucleon states with one nucleon in the continuum are investigated within a simple knock-out model for quasi-elastic electron scattering using a Woods-Saxon partial-wave expansion for the continuum nucleon and simple Slater determinants for the bound states. For the total longitudinal response functions of the three nuclei 4 He, 16 O and 40 Ca, as seen in inclusive experiments, a rather good agreement of the Galilei-invariant prescription and the usual spectral-function approximation is obtained, provided that in the latter the momentum transfer is quenched by a factor (A - 1)/A, and furthermore relative motion wave functions are used for the various hole states. The agreement is worse if exclusive scattering is considered. Then the above modifications of the spectral-function approximation still yield the right positions and shapes for the partial longitudinal response functions of the various residual hole states. However, as expected from the different spectroscopic factors obtained for the Galilei invariant with respect to the normal approximation in the first of the present series of papers, for holes out of the last occupied shell the corrected spectral-function approach underestimates the Galilei-invariant strengths, while for holes from the lower shells a considerable overestimation of the strengths is observed.

Dynamics of viscoelastic membranes.

We determine both the in-plane and out-of-plane dynamics of viscoelastic membranes separating two viscous fluids in order to understand microrheological studies of such membranes. We demonstrate the general viscoelastic signatures in the dynamics of shear, bending, and compression modes. We show that these modes remain independent in the presence of hydrodynamic interactions. The full response functions for motion both in-plane and out-of-plane are derived for the general case of viscoelastic films in contact with arbitrary viscous fluids. Specifically, we derive closed-form expressions for the in-plane longitudinal and transverse response functions for viscous membranes embedded in fluid media. We also find a screening of the otherwise two-dimensional character of the response to point forces due to the presence of the solvent.

Bound nucleon properties through 3He( e, e′ p) at high Q2

Electron scattering cross-sections for the reaction {sup 3}He(e,e{prime}p)d have been measured in parallel kinematics for three values of the recoil momentum (0 and {+-} 300 MeV/c) and for different values of the virtual photon squared mass Q{sup 2} up to 4.1 GeV{sup 2}. The goal is to probe the electromagnetic properties of the proton when embedded in a nucleus, by studying the Q{sup 2} dependence of the longitudinal and transverse response functions.

Kinematic response functions and dynamic stiffnesses of bridge embankments

AbstractRecognizing that soil–structure interaction affects appreciably the earthquake response of highway overcrossings, this paper compares approximate analytical solutions and finite element results to conclude on a simple procedure that allows for the estimation of the kinematic response functions and dynamic stiffnesses of approach embankments. It is shown that the shear‐wedge model yields realistic estimates for the amplification functions of typical embankments and reveals the appropriate levels of dynamic strains which are subsequently used to estimate the stiffness and damping coefficients of embankments. The shear‐wedge model is extended to a two‐dimensional model in order to calculate the transverse static stiffness of an approach embankment loaded at one end. The formulation leads to a sound closed‐form expression for the critical length, Lc, that is the ratio of the transverse static stiffness of an approach embankment and the transverse static stiffness of a unit‐width wedge. It is shown through two case studies that the transverse dynamic stiffness (‘spring’ and ‘dashpot’) of the approach embankment can be estimated with confidence by multiplying the dynamic stiffness of the unit‐width wedge with the critical length, Lc. The paper concludes that the values obtained for the transverse kinematic response function and dynamic stiffness can also be used with confidence to represent the longitudinal kinematic response function and dynamic stiffness, respectively. Copyright © 2002 John Wiley & Sons, Ltd.

Scaling behavior of anomalous Hall effect and longitudinal nonlinear response in high-Tcsuperconductors

Based on existing theoretical model and by considering our longitudinal nonlinear response function, we derive a nonliear equation in which the mixed state Hall resistivity can be expressed as an analytical function of magnetic field, temperature and applied current. This equation enables one to compare quantitatively the experimental data with theoretical model. We also find some new scaling relations of the temperature and field dependency of Hall resistivity. The comparison between our theoretical curves and experimental data shows a fair agreement.

Dynamical exchange-correlation potentials for an electron liquid

The imaginary parts of the exchange-correlation kernels ${f}_{\mathrm{xc}}^{L,T}(\ensuremath{\omega})$ in the longitudinal and transverse current-current response functions of a homogeneous electron liquid are calculated exactly at low frequency, to leading order in the Coulomb interaction. Combining these new results with the previously known high-frequency behaviors of $\mathrm{Im}{f}_{\mathrm{xc}}^{L,T}(\ensuremath{\omega})$ and with the compressibility and the third moment sum rules, we construct simple interpolation formulas for $\mathrm{Im}{f}_{\mathrm{xc}}^{L,T}(\ensuremath{\omega})$ in three and two spatial dimensions. A feature of our interpolation formulas is that they explicitly take into account the two-plasmon component of the excitation spectrum: our longitudinal spectrum $\mathrm{Im}{f}_{\mathrm{xc}}^{L}(\ensuremath{\omega})$ is thus intermediate between the Gross-Kohn interpolation, which ignores the two-plasmon contribution, and a recent approximate calculation by Nifos\`{\i}, Conti, and Tosi, which probably overestimates it. Numerical results for both the real and imaginary parts of the exchange-correlation kernels at typical electron densities are presented, and compared with those obtained from previous approximations. We also find an exact relation between $\mathrm{Im}{f}_{\mathrm{xc}}^{L}(\ensuremath{\omega})$ and $\mathrm{Im}{f}_{\mathrm{xc}}^{T}(\ensuremath{\omega})$ at small $\ensuremath{\omega}.$