Simple model of the static exchange-correlation kernel of a uniform electron gas with long-range electron-electron interaction

A simple approximate expression in real and reciprocal spaces is given for the static exchange-correlation kernel of a uniform electron gas interacting with the long-range part only of the Coulomb interaction. This expression interpolates between the exact asymptotic behaviors of this kernel at small and large wave vectors which in turn requires, among other thing, information from the momentum distribution of the uniform electron gas with the same interaction that have been calculated in the G0W0 approximation. This exchange-correlation kernel as well as its complement analogue associated to the short-range part of the Coulomb interaction are more local than the Coulombic exchange-correlation kernel and constitute potential ingredients in approximations for recent adiabatic connection fluctuation-dissipation and/or density functional theory approaches of the electronic correlation problem based on a separate treatment of long-range and short-range interaction effects.Comment: 14 pages, 14 figures, to be published in Phys. Rev.

The influence of local field corrections on Thomson scattering in non-ideal two-component plasmas

Thomson scattering in non-ideal (collision-dominated) two-component plasmas is calculated accounting for electron-ion collisions as well as electron-electron correlations. This is achieved by using a novel interpolation scheme for the electron-electron response function generalizing the traditional Mermin approach. Also, ions are treated as randomly distributed inert scattering centers. The collision frequency is taken as a dynamic and complex quantity and is calculated from a microscopic quantum-statistical approach. Implications due to different approximations for the electron-electron correlation, i.e. different forms of the OCP local field correction, are discussed

Structure of the Local-field factor of the 2-D electron fluid. Possible evidence for correlated scattering of electron pairs

The static local-field factor (LFF) of the 2-D electron fluid is calculated {\it nonperturbatively} using a mapping to a classical Coulomb fluid $\lbrack$Phys. Rev. Lett., {\bf 87}, 206$\rbrack$. The LFF for the paramagnetic fluid {\it differs markedly} from perturbation theory where a maximum near 2$k_F$ is expected. Our LFF has a quasi-linear small-k region leading to a maximum close to 3$k_F$, in agreent with currently available quantum Monte Carlo data. The structure in the LFF and its dependence on the density and temperature are interpretted as a signature of correlated scattering of electron pairs of opposite spin.The lack of structure at $2k_F$ implies weakened Friedel oscillations, Kohn anomalies etc.Comment: 4 pages, 3 figures, version 2 of condmat/0304034, see http://nrcphy1.phy.nrc.ca/ims/qp/chandre/chnc/ Changs in the text, figure 2 and updated reference

Kirzhnits gradient expansion for a D-dimensional Fermi gas

For an ideal D-dimensional Fermi gas under generic external confinement we derive the correcting coefficient $(D-2)/3D$ of the von Weizsacker term in the kinetic energy density. To obtain this coefficient we use the Kirzhnits semiclassical expansion of the number operator up to the second order in the Planck constant $\hbar$. Within this simple and direct approach we determine the differential equation of the density profile and the density functional of the Fermi gas. In the case D=2 we find that the Kirzhnits gradient corrections vanish to all order in $\hbar$.Comment: 6 pages, 0 figures, accepted for publication in J. Phys. A: Math. Theo

Faint calcium-rich transient from the double-detonation of a 0.6 M⊙0.6\,M_\odot carbon-oxygen white dwarf star

We have computed a three-dimensional hydrodynamic simulation of the merger between a massive ($0.4\,M_\odot$) helium white dwarf (He WD) and a low-mass ($0.6\,M_\odot$) carbon-oxygen white dwarf (CO WD). Despite the low mass of the primary, the merger triggers a thermonuclear explosion as a result of a double detonation, producing a faint transient and leaving no remnant behind. This type of event could also take place during common-envelope mergers whenever the companion is a CO WD and the core of the giant star has a sufficiently large He mass. The spectra show strong Ca lines throughout the first few weeks after the explosion. The explosion only yields $<0.01\,M_\odot$ of $^{56}$Ni, resulting in a low-luminosity SN Ia-like lightcurve that resembles the Ca-rich transients within this broad class of objects, with a peak magnitude of $M_\mathrm{bol} \approx -15.7\,$mag and a rather slow decline rate of $\Delta m_{15}^\mathrm{bol}\approx 1.5\,$mag. Both, its lightcurve-shape and spectral appearance, resemble the appearance of Ca-rich transients, suggesting such mergers as a possible progenitor scenario for this class of events.Comment: Submitted to A&A letters, posted on ArXiv after positive referee report. 7 pages, 4 figure

Nonlocal density functionals and the linear response of the homogeneous electron gas

The known and usable truly nonlocal functionals for exchange-correlation energy of the inhomogeneous electron gas are the ADA (average density approximation) and the WDA (weighted density approximation). ADA, by design, yields the correct linear response function of the uniform electron gas. WDA is constructed so that it is exact in the limit of one-electron systems. We derive an expression for the linear response of the uniform gas in the WDA, and calculate it for several flavors of WDA. We then compare the results with the Monte-Carlo data on the exchange-correlation local field correction, and identify the weak points of conventional WDA in the homogeneous limit. We suggest how the WDA can be modified to improve the response function. The resulting approximation is a good one in both opposite limits, and should be useful for practical nonlocal density functional calculations.Comment: 4 pages, two eps figures embedde

Polarizational stopping power of heavy-ion diclusters in two-dimensional electron liquids

The in-plane polarizational stopping power of heavy-ion diclusters in a two-dimensional strongly coupled electron liquid is studied. Analytical expressions for the stopping power of both fast and slow projectiles are derived. To go beyond the random-phase approximation we make use of the inverse dielectric function obtained by means of the method of moments and some recent analytical expressions for the static local-field correction factor.Comment: 9 pages, 5 figures. Published in Physical Review B http://link.aps.org/abstract/PRB/v75/e11510

Dynamic Many-Body Theory. II. Dynamics of Strongly Correlated Fermi Fluids

We develop a systematic theory of multi-particle excitations in strongly interacting Fermi systems. Our work is the generalization of the time-honored work by Jackson, Feenberg, and Campbell for bosons, that provides, in its most advanced implementation, quantitative predictions for the dynamic structure function in the whole experimentally accessible energy/momentum regime. Our view is that the same physical effects -- namely fluctuations of the wave function at an atomic length scale -- are responsible for the correct energetics of the excitations in both Bose and Fermi fluids. Besides a comprehensive derivation of the fermion version of the theory and discussion of the approximations made, we present results for homogeneous He-3 and electrons in three dimensions. We find indeed a significant lowering of the zero sound mode in He-3 and a broadening of the collective mode due to the coupling to particle-hole excitations in good agreement with experiments. The most visible effect in electronic systems is the appearance of a ``double-plasmon'' excitation.Comment: submitted to Phys. Rev.

Exact exchange potential evaluated solely from occupied Kohn-Sham and Hartree-Fock solutions

The reported new algorithm determines the exact exchange potential v_x in a iterative way using energy and orbital shifts (ES, OS) obtained - with finite-difference formulas - from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to v_x and the latter - for increments of ES and OS due to subsequent changes of v_x. Thus, solution of the differential equations for OS, used by Kummel and Perdew (KP) [Phys. Rev. Lett. 90, 043004 (2003)], is avoided. The iterated exchange potential, expressed in terms of ES and OS, is improved by modifying ES at odd iteration steps and OS at even steps. The modification formulas are related to the OEP equation (satisfied at convergence) written as the condition of vanishing density shift (DS) - they are obtained, respectively, by enforcing its satisfaction through corrections to approximate OS and by determining optimal ES that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the DFT exchange-only approximation, proves highly efficient. The calculations using pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact v_x so that, for Ne, Ar and Zn, the corresponding DS norm becomes less than 10^{-6} after 13, 13 and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10^{-4} Hartree accuracy are obtained for these atoms after, respectively, 9, 12 and 12 density iteration steps, each involving just 2 steps of v_x iteration, while the accuracy limit of 10^{-6}--10^{-7} Hartree is reached after 20 density iterations.Comment: 21 pages, 5 figures, 3 table

Density-Functional Theory of Quantum Freezing: Sensitivity to Liquid-State Structure and Statistics

Density-functional theory is applied to compute the ground-state energies of quantum hard-sphere solids. The modified weighted-density approximation is used to map both the Bose and the Fermi solid onto a corresponding uniform Bose liquid, assuming negligible exchange for the Fermi solid. The required liquid-state input data are obtained from a paired phonon analysis and the Feynman approximation, connecting the static structure factor and the linear response function. The Fermi liquid is treated by the Wu-Feenberg cluster expansion, which approximately accounts for the effects of antisymmetry. Liquid-solid transitions for both systems are obtained with no adjustment of input data. Limited quantitative agreement with simulation indicates a need for further improvement of the liquid-state input through practical alternatives to the Feynman approximation.Comment: IOP-TeX, 21 pages + 7 figures, to appear, J. Phys.: Condens. Matte