Electronic Response Function Research Articles

Relativistic random-phase approximation longitudinal response functions for quasielastic electron scattering with nonlinear models

The longitudinal response functions for quasielastic electron scattering on ${}^{12}\mathrm{C},$ ${}^{40}\mathrm{Ca},$ and ${}^{56}\mathrm{Fe}$ have been calculated taking into account relativistic RPA correlations. For these calculations relativistic nonlinear models, providing a good description of ground state properties of finite nuclei, have been used. The effect of the nonlinear terms on the longitudinal response has been discussed.

Electronic raman scattering on under-doped mercurate high-Tc superconductors: the symmetry of the order parameter

In order to obtain electronic Raman spectra of a high- Tc superconductor compound, comparable with existing model, we have studied polished, under-doped HgBa 2 CuO 6+ δ and HgBa 2 Ca 2 Cu 3 O 8+ δ . This choice was made such as to i) minimize the over- stoichiometry of oxygen δ ii) avoid the need of phonon background subtraction from the raw data iii) eliminate traces of parasitic phases from the crystal surface. Under these experimental conditions we present the pure electronic Raman response function in the B 2 g and B 1 g channels. The B 2 g spectrum exhibits a linear frequency dependence (exponent n = 1.12 ± 0.03) at low energy whereas the B 1 g one shows a cubic-like dependence ( n = 3.02 ± 0.1). As compared to previous data on more optimally doped, less stoichiometric Hg - 1223 compounds, this work reconciles the electronic Raman spectra of under-doped Hg - 1223 crystals with the d x 2− y 2 model, provided that the oxygen doping δ is not too strong. This surprisingly strong sensitivity of the electronic Raman spectra to oxygen doping in the superconducting state in emphasized here and remains an open question.

Ground state correlations and mean field in16O.II. Effects of a three-nucleon interaction

We continue the investigations of the $^{16}$O ground state using the coupled-cluster expansion [$\exp({\bf S})$] method with realistic nuclear interaction. In this stage of the project, we take into account the three nucleon interaction, and examine in some detail the definition of the internal Hamiltonian, thus trying to correct for the center-of-mass motion. We show that this may result in a better separation of the internal and center-of-mass degrees of freedom in the many-body nuclear wave function. The resulting ground state wave function is used to calculate the "theoretical" charge form factor and charge density. Using the "theoretical" charge density, we generate the charge form factor in the DWBA picture, which is then compared with the available experimental data. The longitudinal response function in inclusive electron scattering for $^{16}$O is also computed.

Electronic Raman scattering on the underdopedHgBa2Ca2Cu3O8+δhigh-Tcsuperconductor: The symmetry of the order parameter

In order to obtain high quality, reliable electronic Raman spectra of a high-${T}_{c}$ superconductor compound, comparable with existing models, we have studied strongly underdoped ${\mathrm{HgBa}}_{2}{\mathrm{Ca}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{8+\ensuremath{\delta}}$ with well prepared surface conditions. This choice was made such as to (i) minimize the overstoichiometry of oxygen $\ensuremath{\delta},$ (ii) avoid the need of phonon background subtraction from the raw data, and (iii) eliminate traces of parasitic phases identified and monitored on the crystal surface. Under these experimental conditions we are able to present the pure electronic Raman response function in the ${B}_{2g},$ ${B}_{1g},$ ${A}_{1g}{+B}_{2g},$ and ${A}_{1g}{+B}_{1g}$ channels. The ${B}_{2g}$ spectrum exhibits a linear frequency dependence (exponent $n=1.12\ifmmode\pm\else\textpm\fi{}0.03)$ at low energy whereas the ${B}_{1g}$ one shows a cubiclike dependence $(n=3.02\ifmmode\pm\else\textpm\fi{}0.1).$ The ${B}_{2g}$ and ${B}_{1g}$ spectra display a single well defined maximum at ${5.6k}_{B}{T}_{c}$ and ${9k}_{B}{T}_{c},$ respectively. In mixed ${A}_{1g}$ channels an intense electronic peak centered around ${6.4k}_{B}{T}_{c}$ is observed. The low-energy parts of the spectra (below $350 {\mathrm{cm}}^{\ensuremath{-}1})$ correspond to the electronic response expected for a pure ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ gap symmetry (and can be fitted up to the gap energy for the ${B}_{1g}$ channel). However, in the upper parts (above $350 {\mathrm{cm}}^{\ensuremath{-}1}),$ the relative position of the ${B}_{1g}$ and ${B}_{2g}$ peaks needs expanding the ${B}_{2g}$ Raman vertex to second-order Fermi surface harmonics to fit the data with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ model. The sharper and more intense ${A}_{1g}$ peak appears to challenge the Coulomb screening efficiency present for this channel. As compared to previous data on more optimally doped, less stoichiometric Hg-1223 compounds, this work reconciles the electronic Raman spectra of underdoped Hg-1223 crystals with the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ model, provided that the oxygen doping $\ensuremath{\delta}$ is not too strong. This surprisingly strong sensitivity of the electronic Raman spectra to the low lying excitations induced by oxygen doping in the superconducting state is emphasized here and remains an open question.

Coulomb distortion measurements by comparing electron and positron quasielastic scattering off12Cand208Pb

Positron and electron quasielastic cross sections on ${}^{12}\mathrm{C}$ and ${}^{208}\mathrm{Pb}$ were measured at the Saclay linear accelerator (ALS) to test Coulomb corrections to the plane-wave Born approximation. The positron and electron response functions at the same effective kinematics were found to be equal within a 3% experimental uncertainty, which allows us to discriminate between different theoretical models of Coulomb distortions. Our result strongly supports the effective momentum approximation, even for nuclei as heavy as ${}^{208}\mathrm{Pb}$.

Energy loss of fast protons specularly reflected from metal surfaces

We have calculated the mean energy lost by protons of 120 keV that are specularly reflected at an aluminum (1 1 1) surface. For this impact energy, the main contribution to the energy loss is due to the excitation of conduction band electrons. The response of these electrons to the proton electric field can be accurately treated within linear response theory. Therefore, we have studied the importance of improving the model for the response function of conduction band electrons by using two different models. One of the models considered here is semiclassical whereas the other is fully quantum mechanical. The results obtained with both models have been compared with each other and recent experimental data. For this particular impact energy, the more realistic quantum mechanical model provides better agreement with experiment at the higher incidence angles, where the calculated ion trajectories are more reliable.

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σs(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σs(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σs(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σs(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π −1 Im D s (q, ω), where D s (q, ω) is the phonon Green’s function, at temperatures T<T c .

Time-domain separation of nuclear and electronic contributions to the third-order nonlinearity in glasses

The electronic and nuclear contributions to the third-order nonlinearity of glasses are separated by use of 100-fs pulses in a time-resolved heterodyne optical Kerr effect technique. A direct estimate of the relative strengths of electronic and nuclear contributions was made by the comparison between the nuclear contribution deduced from the Raman spectra with the Kerr signal. The ratio between the electronic and nuclear response functions was ∼5/1 in a tellurium oxide glass sample. The time evolution of the nuclear contribution is in good agreement with results deduced from the Raman spectra.

Nuclear response in electron scattering at high momentum transfer

Nuclear response functions for high energy electron scattering were calculated over a wide region of excitation energies. Three typical regions were studied: the quasi-elastic region, the Δ-excitation region, and the intermediate region where the meson-exchange currents make significant for finite-size nuclei by taking into account relativistic kinematics. Contributions from meson-exchange currents were calculated in the relativistic Fermi-gas model. The results were compared with electron scattering data from 12C and 16O at high momentum transfer.

Double particle resolution in STAR silicon drift detectors

The inner tracking detector of the STAR experiment at the BNL Relativistic Heavy Ion Collider will consist of a three layer barrel structure of 216 silicon drift detectors. Calculations of the two-hit resolution achievable for these detectors are presented in this article. The effects on two-hit resolution of the electronic's response function, frequency of signal digitization and noise level are discussed.

Light spectra sum rule

Fourier analysis is applied to a statistical model of photon detector behaviour. An interesting sum rule relating the characteristic function for photoelectron spectra and for the single electron response function is derived. This suggests the design of new strategies for photoelectron spectra analysis. Some of them are described in the case of experiments performed with electrostatically focused hybrid photomultiplier tubes.

Nonlinear electronic responses, Fukui functions and hardnesses as functionals of the ground-state electronic density

The exact equations for the variations of the electronic density induced by an adiabatic external potential are derived to an arbitrary perturbation order in the framework of density-functional-theory. The formal solutions of these density perturbation equations are given and the exact relations between the electronic response functions and the Hohenberg–Kohn functional are derived. Using these relations, the static nonlinear electronic response functions are constructed from the linear one. Nonconserving electron number perturbations are also directly included in the formalism to all perturbation orders. In this way the well-known results of the density-functional reactivity theory are generalized beyond the first and the second-order. This makes it possible to derive the exact relations between the Hohenberg–Kohn functional and the linear and nonlinear Fukui responses, the nonlinear Fukui functions and the nonlinear hardnesses. These relations allow us to reformulate all the derivatives of the electronic energy relative to the external potential and to the particle number in terms of the linear response kernel and in terms of the linear Fukui function. The formalism is applied to the Thomas–Fermi–Dirac-λ von Weiszäcker model of the Hohenberg–Kohn functional.

Intrinsic Auger signal profiles derived by Monte Carlo analysis

A Monte Carlo simulation with cascade secondary electron generation has recently enabled us to obtain the background formed by backscattered electrons in Auger spectra. Applying this approach to experimentalEN(E)-spectrameasured by Goto et al. with a novel CMA, we have derived the Cu-LMM spectrum with the background fully subtracted. Further Monte Carlo calculation of the response function for Auger electrons has then yielded the background due to inelastically scattered Auger electrons. Compared to Tougaard's background subtraction method, the intrinsic Auger signal profile obtained by the present Monte Carlo analysis shows stronger Auger electron intensities at the lower energy side and describes much better the experimental spectrum.

Electrons in anharmonic phonon fields of low-dimensional high- Tc superconductors

A general Mathematical formulation is developed for calculating the electron response function of layered superconductors. A model Hamiltonian for the low-dimensional superconducting system is developed which includes (i) bare electron interactions, (ii) harmonic phonon fields, (iii) electron-phonon interactions, (iv) anharmonic phonons and (v) effects of localized phonon fields. Quantum dynamics of electrons is studied adopting the Green's function theory via this advanced Hamiltonian in order to describe the many-body problem. This work remarkably describes that the electron-phonon coupling coefficient shows its inevitable presence in all sectors of phonon fields, namely, the fields of (i) anharmonic phonons (ii) localized phonons and (iii) the impurity-anharmonicity interaction. The expressions for electron density of states and electron heat capacity are also obtained in the new framework.

Relativistic RPA response functions for quasielastic electron scattering with a density-dependent NN interaction

Abstract The longitudinal and transverse response functions as well as the Coulomb sum for quasielastic electron scattering on 12C, 40Ca, 48Ca, 56Fe and 208Pb have been calculated taking into account relativistic RPA correlations. For these calculations a density-dependent relativistic NN interaction reproducing the saturation curve of a Dirac-Brueckner calculation providing a good description of nuclear matter has been used. The agreement with experiment is considerably improved for nuclei ranging from 40Ca to 208Pb, but not for a relatively light nucleus like 12C.

Investigations into the origin of the spurious 17 keV neutrino signal observed in35S beta decay

An exhaustive study has been made of the β spectrum of35S, recorded with a Si(Li) detector. The object was to identify the origin of a distortion in the35S β spectrum some 17 keV below the end point, reported over three years ago and interpreted then as evidence for a 17 keV neutrino. Measurements with different source-detector spacings and with varied collimation have shown that there is a long range curvature in the Kurie plot which is a sensitive function of configuration, but the principal origin of the distortion is energy loss in the35S sources. The35S sources, prepared by chemical adsorption of Ba35SO4 on a gold substrate, are clumped and locally thick. Electrons near the end point lose ∼0.3 keV in the source material and if this is taken into account the spectra are well fitted without any admixture of 17 keV neutrino. The source thickness has been investigated with a proton microprobe and determined from both source tilting and the yield of bariumK X-rays; these studies are discussed in detail. The uncertainties in and justification for the form of the electron response function employed are also thoroughly discussed. If there is no systematic error common to the majority of 14 independent sets of35S data, the admixture of 17 keV neutrino is <10−3 (95% CL). A simple search for a kink at 150 keV in the combined data from all 14 runs yielded a limit of 1.8×10−3 (95% CL). The end point of the35S β spectrum is found to be 167.60±0.05 keV.

Coulomb sum rule: Is there a missing charge?

Translational and Galilean invariant approaches to the charge form factor for elastic electron scattering from nuclei as well as to the longitudinal and transverse response functions for inclusive electron scattering are presented. The results indicate that the proper treatment of these invariances is rather essential for the analysis of such experiments.

Subthreshold response function in the Delta -resonance region.

Nuclear response functions for quasielastic electron scattering are studied in the \ensuremath{\Delta}-resonance region below threshold. We find that the slow falloff below threshold required by the data in the dip region can be understood in a general way that depends only on kinematics and the approximate mass and width of the \ensuremath{\Delta}.

Role of the surface electronic response function on treatments of the liquid-vapor interface of alkali metals.

We present a treatment of the surface of liquid alkali metals based on a perturbative expansion to second order in the electron-ion pseudopotential. We make a simple direct approximation for the inhomogeneous electronic response function, in contrast to previous work which approximates the effective pair interaction. It is found that the surface tension, obtained by using a nonmonotonic parametrization of the ionic profile, is in good agreement with the experimental value and improves the results of the previous approaches.

Detector response and the 17 keV neutrino

The 17 keV neutrino, proposed by Simpson in 1985 [1], may be an artifact of the data analysis which includes an oversimplified response function for monoenergetic electrons. This function was assumed to contain a backscatter fraction that is independent of energy. It is demonstrated that, when artificial “data” are simulated for an external-source beta decay experiment with a realistic response function containing an energy-dependent backscatter fraction, but are analyzed with a response function containing a constant backscatter fraction, an artifact roughly equivalent to a 17 keV neutrino emerges.