Transverse Spectral Functions Research Articles

On the existence of a second branch of transverse collective excitations in liquid metals

It was found recently that the liquid dynamics of several metals (Li, Zn, Ni, Fe, Tl, Pb) under pressure is characterized by transverse spectral functions containing an additional high-frequency peak. To rationalize the pressure dependence of the contributions from different propagating processes to transverse spectral functions in liquid metals, ab initio molecular dynamics simulations were performed for two typical liquid metals (Na and Al) in a wide range of pressures. The influence of density/pressure is investigated for Na by considering four pressures ranging from 15 to 147 GPa, while the temperature influence is considered for Al between 600 K in the deep supercooled liquid up to 1700 K well above the melting point at ambient pressure. Both temperature and density dependence of the spectra of collective excitations are analyzed with a focus on the appearance of a second high-frequency mode in the transverse spectra. A correspondence between spectra of transverse collective excitations and the peak positions of the Fourier-spectra of velocity autocorrelation functions (vibrational density of states) is found.

Virtual photon polarization in ultrarelativistic heavy-ion collisions

The polarization of direct photons produced in an ultrarelativistic heavy-ion collision reflects the momentum anisotropy of the quark-gluon plasma created in the collision. This paper presents a general framework, based on the photon spectral functions in the plasma, for analyzing the angular distribution and thus the polarization of dileptons in terms of the plasma momentum anisotropies. The rates of dilepton production depend, in general, on four independent spectral functions, corresponding to two transverse polarizations, one longitudinal polarization, and -- in plasmas in which the momentum anisotropy is not invariant under parity in the local rest frame of the matter -- a new spectral function, $\rho_n$, related to the anisotropy direction in the collision. The momentum anisotropy appears in the difference of the two transverse spectral functions, as well as in $\rho_n$. As an illustration, we delineate the spectral functions for dilepton pairs produced in the lowest order Drell-Yan process of quark-antiquark annihilation to a virtual photon.

Quasielastic(e,e′p)reaction onC12,Fe56, andAu197

We report the results from a systematic study of the quasielastic $(e,{e}^{\ensuremath{'}}p)$ reaction on $^{12}\mathrm{C},\phantom{\rule{0.5em}{0ex}}^{56}\mathrm{Fe}$, and $^{197}\mathrm{Au}$ performed at Jefferson Lab. We have measured nuclear transparency and extracted spectral functions (corrected for radiation) over a ${Q}^{2}$ range of $0.64--3.25\phantom{\rule{0.5em}{0ex}}{(\text{GeV}∕c)}^{2}$ for all three nuclei. In addition, we have extracted separated longitudinal and transverse spectral functions at ${Q}^{2}$ of 0.64 and $1.8\phantom{\rule{0.5em}{0ex}}{(\text{GeV}∕c)}^{2}$ for these three nuclei (except for $^{197}\mathrm{Au}$ at the higher ${Q}^{2}$). The spectral functions are compared to a number of theoretical calculations. The measured spectral functions differ in detail but not in overall shape from most of the theoretical models. In all three targets the measured spectral functions show considerable excess transverse strength at ${Q}^{2}=0.64\phantom{\rule{0.5em}{0ex}}{(\text{GeV}∕c)}^{2}$, which is much reduced at $1.8\phantom{\rule{0.5em}{0ex}}{(\text{GeV}∕c)}^{2}$.

Separated spectral functions for the quasifree12C(e,e′p)reaction

A separation of the longitudinal and transverse 12 C(e, e8p) cross sections in the quasifree region has been performed in parallel kinematics at Q 2 of 0.64 and 1.8 GeV 2 for initial proton momentum ,80 MeV. The separated transverse and longitudinal spectral functions at Q 2 50.64 GeV 2 show significant differences for missing energy between 25 and 60 MeV indicating a breakdown in the single nucleon knockout picture. The transverse spectral functions exhibit definite momentum transfer dependence.

Anomaly in the transverse longitudinal ratio for3He(e,e′p)Xreaction at 260 MeV/crecoil momentum

${}^{3}$He${(e,e}^{\ensuremath{'}}p)X$ cross sections were measured in parallel kinematics for recoil momenta around 260 MeV/$c$. A Rosenbluth decomposition of the cross section was made and transverse and longitudinal spectral functions were extracted. The longitudinal spectral function is strongly quenched relative to the transverse one, the ratio of the integral of the longitudinal to transverse spectral functions over the continuum channel being $0.175\ifmmode\pm\else\textpm\fi{}0.046\ifmmode\pm\else\textpm\fi{}0.049$. A model which takes into account final state interactions and meson exchange currents predicts a ratio of 0.43, it can therefore explain only part ot the quenching.

The longitudinal and transverse structure functions of the 4H(e, e'p) 3H reaction

4He(e, e'p) 3H cross sections were measured in parallel kinematics for recoil momenta of 30, 90 and 190 MeV/ c. For 30 and 90 MeV/ c, the cross sections were also measured as a function of the momentum transfer between 0.30 and 0.83 GeV/ c. A Rosenbluth decomposition of the cross sections was made, and experimental longitudinal and transverse spectral functions were derived. The longitudinal spectral function is quenched by about 40% relative to the transverse. After model-dependent corrections for final-state interactions, mesonic currents, and charge exchange scattering, the quenching remains at the level of ≌20%. The spectral functions are compared to calculations employing realistic 4He wave functions. The longitudinal function is below the theoretical value; the transverse function is in agreement. The spectral function data reveal no significant q-dependence and imply an r.m.s. proton magnetic radius in 4He within a few percent of the free value.

Final-state-interaction effects in the (e,e'p) reaction.

Particle emission after electroexcitation of a nucleus is studied in the quasielastic region of the $^{4}\mathrm{He}$(e,e'p${)}^{3}$H reaction. The calculations are performed using a meson-exchange potential. The displacement observed in the experimental spectral functions appears to be due to the mean-field scattering mainly. The rescattering processes lead to the splitting between the longitudinal and transverse spectral functions in agreement with the trend of the Saclay data. The related damping of the longitudinal spectral function originates from the coupling between (e,e'p) and (e,e'n) channels.

Spectral functions in QCD

The longitudinal and transverse spectral functions for arbitrary conserved or non-conserved vector or axial vector currents of massive quarks are calculated to first order in α s and exact analytical expressions are given. As an intermediate step the (in general three) form factors to the same order in α s are determined. We derive a remarkably simple result for the combination of spectral functions corresponding to the first Weinberg sum rule. It behaves asymptotically like α s/ s 2 thus ensuring the rapid convergence of the sum rule.

Space-Time Correlations in Anisotropic Heisenberg Paramagnets at Elevated Temperatures

The structure of the space-time-dependent spin-correlation functions for an anisotropic Heisenberg paramagnet with cylindrical symmetry at elevated temperature is analyzed in terms of a two-parameter Gaussian representation representation of the generalized diffusivity. The parameters are chosen so as to exactly preserve the frequency moments, i.e., ${{〈{\ensuremath{\omega}}^{2n}〉}_{\mathrm{K}}}^{\ensuremath{\alpha}\ensuremath{\alpha}}$ ($\ensuremath{\alpha}=z, x, or y$; $n=0, 1, 2$) of the longitudinal and the transverse spectral functions. These moments are calculated for arbitrary spin $S$, arbitrary range of the exchange interactions, and arbitrary dimensionality. The results for the correlation functions are worked out for one, two, and three dimensions. In the extreme transverse limit, the results are compared with the exactly soluble $\mathrm{XY}$ model for a one-dimensional spin-\textonehalf{} system with only nearest-neighbor (transverse) exchange. The agreement of the results is found to be satisfactory.