Electron Correlations in Solids, Molecules, and Atoms

From July 20 till 31, 1981, the Advanced Study Institute on "Electron Correlations in Solids, Molecules and Atoms", sponsored by NATO, was held at the University of Antwerpen (U.I.A.), in the Conference Center Corsendonk. In the last few years, the problem of many-electron correlations has gained renewed attention, due to recent experimental and theoretic­ al developments. From the theoretical point of view, more sophisticated treatments of the homogeneous electron gas model evolved, including dynamical aspects of the electron correlation in the dielectric response. Furthermore, the homogeneous electron gas, which served as a model for simple metals, was extended to include spin- and charge-density waves and phasons. The concept of elementary excitations too was introduced not only in perfectly ordered metallic crystals, but also in magnetic alloys, in liquid metals and alloys, in semiconductors, and even in molecules and atoms. Fairly accurate quantitative calculations of these effects recently became possible, ranging from plasmon frequencies in atoms, over dielectric response of semiconduc­ tors and resistivity in magnetic alloys to electron-hole liquids and their phase separation. The recent technological evolution allowed for more accurate measurements in previously unaccessible domains, e.g. X-ray scatter­ ing and fast electron energy loss at large wavevector. Moreover, these new developments opened new perspectives in physics, accompany­ ing or even introducing the new concepts which also evolved in the theory.

Determination of S(q,?) by Inelastic Electron and X-ray Scattering.- Random phase approximation.- Static screening.- Finite frequency, small wave vector response.- Ultraviolet optical properties.- Inelastic electron scattering.- Beyond the random phase approximation.- Physical meaning of the function parameters.- High q measurements.- Stronger periodic fields.- Collective effects in atoms: a test case.- References.- Charge Density Wave Phenomena in Potassium.- I. The mysteries of the simple metals.- Charge-density-wave structure.- Mayer-El Naby optical anomaly.- Low temperature magnetoresistance.- Induced-Torque measurements.- The oil drop effect.- Other anomalous phenomena.- II. Phasons: what they are and what they do.- Phase modulation.- Relation between phasons and phonons.- The phason heat capacity.- Low temperature resistivity.- Point constant spectroscopy.- Phason thermal diffuse scattering.- III. Theory of charge density waves.- SDW-CDW instability theorem.- The correlation energy correction.- Analogy with uniform deformations.- Conclusions.- References.- Electron-Hole Liquid: Role of Correlations.- I. Introduction.- II. What is an electron-hole liquid?.- III. Is the plasma phase more stable than the excitonic phase?.- IV. Ground state energy of EHL in Ge.- (1) Band structure of Ge.- (2) Kinetic energy.- (3) Exchange-correlation energy.- (a) Self-consistent scheme for one-component system.- (b) Generalization to EHL.- (c) Ground state energy of EHL in Ge.- V. EHL in stressed Ge.- VI. Phase separation of “Hot” and “Cold” liquids.- VII. Remarks on correlations in a model e-h system.- References.- Kinetic Equations and Two-particle Correlations in the Homogeneous Electron Liquid.- 1. Basic definitions and formulas.- 2. Wigner distribution functions and the kinetic equations.- 3. Approximate decoupling procedures for the two- particles Wigner function.- 4. The kinetic equation for the two-particle Wigner function and some exact asymptotic formulas.- 5. Dynamic properties and the Mori formalism.- References.- Dynamical Exchange Effects in the Dielectric Function of the Electron Gas.- I: The jellium model: elementary concepts.- A. Ground state energy.- B. Collective and single-particle excitations.- C. Effective potential and density-functional formalism.- D. Fundamental properties of the dielectric function.- E. Dynamical exchange effects in the dielectric function.- References.- II: Dielectric function of the electron gas with dynamical exchange decoupling.- A. Introduction.- B. Derivation of G(q,?) via dynamical exchange decoupling.- §1. Dynamical exchange decoupling in the equation of motion for the Wigner distribution function.- §2. Linearization in the external field.- §3. Variational procedure.- §4. Theorem.- §5. Comparison with other dynamical approximations.- C. Analytical treatment of G(q,?).- Appendix A: Evaluation of G(q,?) by elementary methods.- References.- III: Discussion and comparison with first-order perturbation theory.- A. Introduction.- B. Consistency requirements.- C. Discussion of numerical results.- §1. Static limit.- §2. Dynamical behaviour of G(q,?).- §3. Dynamical behaviour of ?(q,?) and plasmon dispersion.- §4. Remark on spin density waves.- D. Comparison with first-order perturbation theory.- References.- Liquid Alkali Metals and Alkali-Based Alloys as Electron-Ion Plasmas.- 1. Introduction.- 2. Some results of electron screening for crystal-line metals.- 2.1. Phonon dispersion curves.- 2.2. Cohesive energy.- 3. Electron screening for liquid metals.- 3.1. Compressibility by the method of long waves.- 3.2. Cohesive properties.- 4. Structure factor of liquid alkali metals.- 4.1. Structure of the OCP at strong coupling.- 4.2. Structure of liquid alkali metals.- 5. Thermodynamic properties of liquid alkali alloys by the method of long waves.- 6. Some other alkali-based liquids.- 6.1. Solutions of molten alkali metals and molten alkali halides.- 6.2. Cesium-gold alloy.- References.- Resistance minima in Magnetic Alloys.- I. Historical survey.- II. Kondo effect.- III. Resistance minimum for impurity pairs.- IV. Superconductivity.- V. Conclusions.- References.- Theory of Exchange-Correlation Effects in the Electronic Single- and Two-Particle Excitations of Covalent Crystals.- I. Introduction.- II. Many-body description of the two-particle excitations in periodic crystals: examples diamond and silicon.- A. Many-body framework.- A1. Field-theoretical formulation.- A2. Local representation.- A3. Long wavelength or optical limit.- B. Dielectric response of diamond.- B1. Many-body effects in the optical properties.- B2. Wave-vector dependence.- C. Dielectric response of silicon.- C1. Many-body effects in the optical properties.- C2. Wave-vector dependence.- III. Dynamical correlation effects in the electronic quasi-particle states of perfect crystals: example diamond.- A. Eigenvalue equation for the quasi-particle states.- B. The self-energy? properties and approximations.- C. Local representation of the eigenvalue equation.- D. Calculation of the quasi-particle states of diamond.- D1. The Hartree Fock part of the eigen-value equation.- D2. The one-partiele Green’s function.- D3. The dynamically screened interaction (correlation part).- D4. Results for the quasi-particle states and discussion.- IV. The influence of many-body effects on the screening of impurities in perfect crystals: examples diamond and silicon.- A. Theoretical treatment of the induced potential and the induced charge density.- B. Substitutional impurities.- B1. Diamond.- B2. Silicon.- C. Interstitial impurities.- C1. Diamond.- C2. Silicon.- V. Summary and discussion.- References.- Collective Phenomena in Non-Uniform Systems.- 1. Introduction.- 2. Hydrodynamical oscillations of an inhomqgeneous electron gas.- 3. Extensions and simplifications of the hydro-dynamical model.- 4. Applications and critique of the hydrodynamical model.- 5. The response of a non-uniform system to an external field.- 6. Some many-body aspects of atomic-like systems.- 7. Linearized quantum equations for density oscillations.- 8. Density functional theory applied to photo-absorption.- References.- Dynamical Structure Factor of an Electron Liquid.- I. Introduction.- II. Formulation.- III. Numerical results.- References.- Author index.