Strong Short-range Correlations Research Articles

On the theory of the interactions and phase transitions of hydrogen in the transition metals

Analytical methods based on the cluster approximation described previously are proposed for calculating the thermodynamic properties and phase diagrams of hydrogen in transition metals (Me). In contrast with the mean field approaches usually adopted, these methods allow quantitatively for the strong short-range correlation effects, including blocking and competitive interaction, which are characteristic of Me-H systems. Detailed calculations of the stress-induced and screened Coulomb H-H interactions for the NbH x and PdH x systems have also been performed. They reveal that the blocking effects in b.c.c. Me-H systems are apparently due to the anharmonicity of the stress-induced interactions at small H-H distances. Applications of the methods developed to the description of the incoherent α-α′ phase transitions in NbH x and PdH x and α⊂α)-β phase transitions in NbH x have shown that the methods have a high accuracy and are well suited to the theory of the Me-H systems. In particular, results have been obtained which suggest that many-body interactions of hydrogen atoms have a noticeable effect on the phase diagrams of b.c.c. MeH x alloys.

Exchange and correlation potentials in the one-electron equation

The self-energy operator of an electron liquid is examined by including the particle-hole and particle-particle ladder types of vertex corrections to the simplest approximation discussed by Hedin and Lundqvist. It is found that the real part of the self-energy correction ∑( p, ε p ) is much more independent of the wavenumber p than that in the simplest approximation because of the strong short-range correlations at metallic densities. The quasi-particle mass ratio m ∗/ m in the present approximation gives values smaller than 1 in the whole metallic density region.

Correlated P-wave pairing theory for Fermi systems. Application to liquid3He

A variational theory is presented for the isotropic triplet pair-condensed state of liquid 3He. Using a correlated pairing wavefunction the authors express the expectation values of the required quantities in terms of the diagonal and off-diagonal matrix elements of the Hamiltonian and unit operators with respect to a correlated basis of normal wavefunctions. The correlated basis consists of Slater determinants modified by a Jastrow correlation factor which incorporates the strong short-range correlations induced by the interparticle potential. The formalism has been developed within the weak-coupling approximation. The study of the instability of the normal state with respect to the triplet pair-condensed state is achieved via an exact criterion. This criterion has been expressed in terms of normal-state quantities which have been evaluated within the correlated basis functions scheme with the accuracy of the Fermi hypernetted chain approximation. The numerical calculations indicate an instability of the normal ground state with respect to the 3P0 superfluid state but at too low a density.

Spin dynamics of an amorphous Y0.33Fe0.67alloy

The authors report neutron inelastic scattering measurements of the amorphous spin-glass alloy Y0.33Fe0.67. A broad inelastic (quasi-elastic) spectral response, centred about zero energy transfer and a resolution-limited central 'elastic' peak, is observed at all temperatures down to 5K, the lowest temperature in the study. Both the 'elastic' scattering and the integrated inelastic scattering are strongly peaked in the forward direction at all temperatures (5<T<200K). This suggests strong ferromagnetic short-range correlations with a wide distribution of correlation sizes, evolving continuously with decreasing temperature. The energy width of the scattering, obtained by force-fitting a single Lorentzian spectral function to the broad quasi-elastic spectrum, is found to increase with q over the q range investigated (below 1 AA-1). Additionally, the spectral width initially decreases with decreasing temperature, goes through a minimum at a temperature somewhere above the temperature of the maximum in the susceptibility and increases again at lower temperatures. As the temperature decreases, however, the spectral intensity of the broad quasi-elastic response decreases steadily below a reasonably high temperature around 3 Tsg while the resolution-limited 'elastic' scattering intensity increases. Overall, the spin dynamics of the system bear strong resemblance to those of the CuMn spin glasses investigated earlier.

Dynamical structure factor of an electron liquid. II

The dynamical structure factor $S(q,\ensuremath{\omega})$ of an electron liquid at metallic densities is studied numerically on the basis of the quasi-one-pair excitation approximation obtained in the preceding paper. The spin-averaged local field correction $G(q)$ is estimated numerically; the local field correction $C(q)$ arising from only spin-antiparallel correlation is also estimated. It is pointed out that inclusion of short-range correlations is important for the quantitative estimation of the energy width of the quasiparticle $\ensuremath{\Gamma}(p)$ at metallic densities. Owing to the local field corrections and the energy width of the quasiparticle, the cutoff wave number ${q}_{c}$ estimated by the present theory is considerably reduced, compared with the random-phase approximation case. The spectral structure in $S(q,\ensuremath{\omega})$ is numerically estimated from the wave number much smaller than ${q}_{c}$ up to the wave number twice as large as the Fermi wave number. The calculated plasmon dispersion around ${q}_{c}$ is in excellent agreement with the observed one for A1 in electron scattering experiments. In the intermediate wave-number region the calculated spectra of $S(q,\ensuremath{\omega})$ reproduce distinctly a plasmonlike peak and a broad peak in good agreement with experimental observations. These characteristic features of $S(q,\ensuremath{\omega})$ are ascribed to the striking damping effect of one-electron states originating from virtual plasmon emission under the influence of strong short-range correlations at metallic densities.

Dynamical structure factor of an electron liquid. I

Electron correlations of an electron liquid at metallic densities are studied by means of a diagrammatic method, the primary aim being the interpretation of the spectral structure observed for several metals in recent inelastic electron and x-ray scattering experiments. Several sum rules and requirements such as the positivity of the pair distribution function, the compressibility sum rule, the frequency moment sum rules, and the conservation law of the local electron number which have hitherto been regarded as guiding principles in theoretical formulation are first examined and discussed in a critical manner. Detailed examinations are made of the proper polarization function within the Hartree-Fock approximation. The lowest-order perturbation expressions giving two-pair excitations and one-pair---one-plasmon excitations are next examined. It is pointed out that these expressions are indeed divergent in the usual one-pair excitation region; the renormalization of the one-particle Green's function is indispensable there. From the above considerations and further discussions, the quasi-one-pair excitation approximation is presented for the purpose of describing the spectral shape in the dynamical structure factor $S(q,\ensuremath{\omega})$ in the intermediate wave-number and intermediate frequency regions. In the quasi-one-pair excitation approximation the proper polarization function is constructed from a coherent part of the renormalized one-particle Green's function and a static part of the irreducible particle-hole interaction including strong short-range correlations.

Elementary excitations in quantum liquids

By 1931 it was already clear that condensed matter was to be a marvelous proving ground for the then newly developed quantum mechanics. The Sommerfeld free electron gas model for a metal; Bloch's theorem; the description of energy bands in solids; the theoretical explanation of why some solids are metals, some insulators, some semiconductors; all these provide eloquent testimony to the ingenuity of the theorist in developing a quantum description of independent electron motion that explained or illuminated experiment. During the succeeding decade, theorists began to examine some consequences of electron–electron interactions. Thus in 1934, when Frederick Seitz and Eugene Wigner developed the first theory of energy bands and cohesion in the alkali metals, they drew upon the pioneering study by Wigner of Coulomb correlations in a quantum plasma (interacting electrons moving in a uniform background of positive charge). In 1937, John Bardeen took into account the screening of ion motions by electrons in his seminal investigation of electron–phonon interactions in metals, while the concept of a pseudopotential to describe the way in which strong short-range electron correlations influence the electron–ion interaction in solids was put forward by H. Hellman in 1936 and independently by Conyers Herring in 1939.

Dynamical structure factor of an electron liquid

Inelastic X-ray scattering experiments of the dynamical structure factor carried out at Bell Laboratories for various metals are interpreted. The existence of a plasmon-like peak and a broad peal in the intermediate momentum region is ascribed to the striking damping effect of one-electron states originating from virtual plasmon emission under the influence of strong short-range correlations at metallic densities. An anomalous dispersion of the plasmon around the cut-off wave-number observed in electron scattering experiments is also interpreted.

Studies in the method of correlated basis functions: (III). Pair condensation in strongly interacting Fermi systems

A variatonal theory of pairing phenomena is presented for systems like neutron matter and liquid 3He. The strong short-range correlations among the particles in these systems are incorporated into the trial states describing normal and pair-condensed phases, via a correlation operator F ̂ . The resulting theory has the same basic structure as that ordinarily applied for weak two-body interactions; in place of the pairing matrix elements of the bare interaction one finds certain effective pairing matrix elements ℘ kl and modified single particle energies ϵ( k) appear. Detailed prescriptions are given for the construction of the ℘ kl and ϵ( k) in terms of off-diagonal and diagonal matrix elements of the Hamiltonian and unit operators in a correlated basis of normal states. An exact criterion for instability of the assumed normal phase with respect to pair condensation is derived for general F ̂ . This criterion is investigated numerically for the special case of Jastrow correlations, the required normal-state quantities being evaluated by integral equation techniques which extend the Fermi hypernetted-chain scheme. In neutron matter, an instability with respect to 1S 0 pairing is found in the low-density region, in concert with the predictions of Yang and Clark. In liquid 3He, there is some indication of a 3P 0 pairing instability in the vicinity of the experimental equilibrium density.

Charge structure and correlation features inpnmultiparticle final states at 195 GeV/c

We have investigated the charge distribution and the correlation between charged particles in $\mathrm{pn}$ collisions at 195 GeV/c. The experiment was carried out at Fermilab with the 30-in. hybrid system. The charge and rapidity structures of the events were studied and the data manifest, among other things, a tendency toward local charge conservation. A strong short-range correlation feature has been observed in rapidity space for like and unlike charged pairs. Some correlation effects between transverse momenta have also been seen. An interpretation of our data in terms of cluster models is discussed.

Charge symmetry breaking nuclear forces and the properties of nuclear matter

The charge symmetry breaking (CSB) component of the nuclear forces yields the charge asymmetric term Ea(N-Z)/A in the nuclear binding energy of nuclear matter. Calculations performed with several models of CSB nuclear forces, and accounting for the strong short-range two-body correlations, give Ea approximately=-0.2 MeV at the normal nuclear density. The charge asymmetry of the effective nucleon-nucleon interaction is determined primarily by the CSB nuclear forces at the neutron excess, observed in finite nuclei. The exclusion principle and dispersion (self-consistency) effects of the nuclear medium decrease this charge asymmetry.

Two-pion correlations in 9.1 GeV/c antiproton-proton reactions

We present a study of two-pion correlations in 9.1 GeV/ c antiproton-proton reactions where both annihilation channels and non-annihilation channels are investigated. We find an asymmetry in the distribution of the azimuthal angle between the pions for different charge combinations. The variation of the asymmetry parameter B with the rapidity difference between the two pions indicates a strong short range correlation. A marked forward-backward asymmetry of the charge distribution in the c.m. system is found in the rapidity classification of the pions. The asymmetry is also found in the local ordering of the charges. In the space angle distribution there is a pronounced accumulation of event the region 0.3 < cos θ π + π − <0.8 in the 5π and 7π final states. This effect is partly explained by ϱ(770) production.

Angular correlations between the charged particles produced in pp collisions at ISR energies

We present an analysis of rapidity and azimuthal correlations between the charged products of pp collisions at ISR energies. The use of streamer chambers as detectors permits a study of the correlation mechanism at fixed multiplicities. The analysis is restricted to the central rapidity region to suppress diffractive production. A strong short-range correlation is observed, which can be described by independent emission of low-multiplicity clusters, suggestive of abundant resonance production.

Spatial correlations and sum rules for a Fermi liquid

The effect of strong short-range spatial correlations in a Fermi liquid is discussed in connection with various sum rules. It is found that all mean-field theories with a frequency-independent localfield factor will necessarily violate either the susceptibility sum rule or the third frequency moment sum rule, and the physics behind this is discussed. The necessary modifications in the available theories are briefly discussed and the situation one is facing is demonstrated on the simpler system of a harmonic lattice.

Lattice Dynamics of Transition-Metal Carbides

The phonon dispersion relations of ZrC, NbC, HfC, TaC, and UC are investigated using a phenomenological-model theory. For the transition-metal carbides, a shell with a free-electron screening is used to describe the over-all shape of the phonon curves. The results strongly support the model, where the extreme physical properties of these compounds are attributed mainly to strong covalent metal-nonmetal bonding. In contrast, for UC the interstitial-alloy picture seems to be more appropriate. The pronounced anomalies in the acoustic branches of TaC and NbC occur at certain $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}$ values which are directly related to definite lattice vectors. We interprete the anomalies as originating from a resonancelike increase of the electronic polarizability due to strong short-range correlations of the $d$ conduction electrons. In a theory, we represent this $d$ charge density by a further electronic degree of freedom at the metal-ion sites, i.e., a second shell. Calculations with this double-shell model show very good agreement with experimental data. It is strongly indicated that the anomalies are caused by $d$ electrons of ${T}_{2g}$ symmetry. The connections to structural phase transitions are discussed.

Superfluid condensation energy of neutron matter

The detailed energetics of pure neutron matter, an ideal form of neutron-star matter, are investigated at low density. The energy shift associated with the normal-to-superfluid-state transition induced by S-wave pairing is estimated by a variational method, with trial superfluid-state and reference normal-state wave functions incorporating strong short-range correlations. The neutron system remains unbound, and indeed there is no indication of a relative minimum of the ground state energy of the (assumed uniform) system as a function of density. However, the transition energy is not entirely negligible compared to the other characteristic energies of the problem - it may be somewhat greater than one-tenth the normal-state energy at densities typical of the inner crust of a neutron star.

Density-functional theory of magnetic instabilities in metals

A density-functional formulation of magnetic states in metals is set up in which, initially, a spin-dependent external potential is switched on to the metal. The usual Hartree-Fock treatment of strong short-range correlations in an s-band is shown to follow very simply from the theory. Building up this Hartree-Fock theory for the lattice by switching on the interactions one site at a time suggests an approximate way of incorporating correlation effects into the density-functional theory. This is consistent with the philosophy that electron correlation effects are best treated via a picture in which the electron density, and, in magnetic metals, the spin density distributions are thought of as localized round atomic sites. In keeping with this philosophy, a new general magnetic instability condition for the lattice is proposed, which is essentially that for the one-site model and involves the density of states through the band, and not simply at the Fermi level, as with the Hartree-Fock condition. The properties of the Green function associated with this new instability condition are considered. While it is not possible, within the present framework, to resolve completely some ambiguity in higher-order terms of the Green function, nevertheless it is possible to set up a Green function which includes the band and the atomic limits correctly, has required symmetry properties, and exactly conserves states in the band. The density of states in this model does not show simple exchange in the magnetic metal but corresponds to deformation of the magnetic sub-bands by the electron interactions. It seems possible still that the inclusion of the long-range Coulomb correlations may, even in the non-magnetic case, after the basic character of the bands from that of a “cell” model.

Dipolsummenregel bei nichtlokalen Potentialen

The integrated cross section of photonuclear reactions is considered in the electricdipole approximation. The nucleon-nucleon potential used is well-behaved and nonlocal. We use the Tabakin potential, which matchesS-, P- andD-wave phase shifts up to 320 MeV without generating strong short-range correlations.

Cluster Development Method in the Quantum Mechanics of Many Particle System, I

In order to investigate the many particle system by the variational principle, the cluster develop­ ment method propcsed by Jastrow is sys~cmatically formulated. It is a dircct generalization of the Hartree method, in which two particle functions are included in the trial function to represent the correlations between particlcs. The cnergyxpectation value is expar..ded in a series, each term of which is expressed in cluster integra's. It is found that the series convergcs rapidly when the cor· relations are marked only fot· small particle separations, so that this method is expected to be useful especially for the system of particles interacting through short range potentials with repulsive cores. § I. Introduction The Hartree method ·for a many particle system, in which each particle is supposed to move independently 2.nd to be influenced by other p2.rticles only through their average field of force, has been an importa.nt approximation a.nd successful in various problems. However, in some cases where the correlations between particles play an important role, this simple approximation is no longer valid. In one case, when the range of the interaction between particles is long compared with the mean distance between them, many particles may be coupled togeth:::r to move in some organized mode of motion as a whole, as is seen in the typical example of the plasma oscillation in- a dense electron gas. The recent study by Tomonaga 1l made the mechanism of this so-called collective motion quite clear_ In :>.nothe: case, when the interaction is strong but of short range, the actual potential determi11cd by the instantaneous configuration of the other . particles fluctuates from the average one considerably, and the image of the independent particle motion becomes far from the truth. Such a situation occurs especially when the interaction potential has a repulsive core at short distance as in liquid helium .or in the atomic nucleus. (In the latter case the existence of the repulsive core seems very likely from the analysis of the nucleon-nucleon scattering/) the binding energy differ~nce between H'l and He3, 3l and so forth.) In fact, if .we apply the Hartree method to these systems, the rc3ulting average potential diverges to infinity. Actually, the wave function of the system must vanish in the region of the configuration space where at least two particles arc fotmd. within the hard core range. In such cases we have to take into· account this strong short range correlation in some way.