High temperature equation of state of metallic hydrogen

The equation of state of liquid metallic hydrogen is solved numerically. Investigations are carried out at temperatures from 3000 to 20 000 K and densities from 0.2 to 3 mol/cm³, which correspond both to the experimental conditions under which metallic hydrogen is produced on earth and the conditions in the cores of giant planets of the solar system such as Jupiter and Saturn. It is assumed that hydrogen is in an atomic state and all its electrons are collectivized. Perturbation theory in the electron-proton interaction is applied to determine the thermodynamic potentials of metallic hydrogen. The electron subsystem is considered in the randomphase approximation with regard to the exchange interaction and the correlation of electrons in the local-field approximation. The proton-proton interaction is taken into account in the hard-spheres approximation. The thermodynamic characteristics of metallic hydrogen are calculated with regard to the zero-, second-, and third-order perturbation theory terms. The third-order term proves to be rather essential at moderately high temperatures and densities, although it is much smaller than the second-order term. The thermodynamic potentials of metallic hydrogen are monotonically increasing functions of density and temperature. The values of pressure for the temperatures and pressures that are characteristic of the conditions under which metallic hydrogen is produced on earth coincide with the corresponding values reported by the discoverers of metallic hydrogen to a high degree of accuracy. The temperature and density ranges are found in which there exists a liquid phase of metallic hydrogen.     

Equation of state of metallic helium

The effective ion-ion interaction, free energy, pressure, and electric resistance of metallic liquid helium have been calculated in wide density and temperature ranges using perturbation theory in the electron-ion interaction potential. In the case of conduction electrons, the exchange interaction has been taken into account in the random-phase approximation and correlations have been taken into account in the local-field approximation. The solid-sphere model has been used for the nuclear subsystem. The diameter of these spheres is the only parameter of this theory. The diameter and density of the system at which the transition of helium from the singly ionized to doubly ionized state occurs have been estimated by analyzing the pair effective interaction between helium atoms. The case of doubly ionized helium atoms has been considered. Terms up to the third order of perturbation theory have been taken into account in the numerical calculations. The contribution of the third-order term is significant in all cases. The electric resistance and its temperature dependence for metallic helium are characteristic of simple divalent metals in the liquid state. The thermodynamic parameters—temperature and pressure densities-are within the ranges characteristic of the central regions of giant planets. This makes it possible to assume the existence of helium in the metallic state within the solar system.     

Metallization degree of hydrogen at a pressure of 1.4 Mbar and a temperature a 3000 K

The electrical resistivity of liquid metallic hydrogen at a temperature of 3000 K and a density of 0.35 mol/cm³ is calculated. Hydrogen is considered as a three-component system consisting of electrons, protons, and neutral hydrogen atoms. The second order of perturbation theory in electron-proton and electron-atom interactions is used to determine the inverse relaxation time for electric conductivity. The Coulomb electron-electron interaction is taken into account in the random phase approximation and the exchange interaction and correlation of conductivity electrons are included in the local-field approximation. The model of hard spheres is used for the proton and atomic subsystems. The concentration of the electrically neutral atomic component proved to be significantly lower than the value assumed by the discoverers of metallic hydrogen.     

Electrical conductivity and thermopower of metallic helium

The pair effective interionic interaction, electrical resistance, and thermopower of liquid metallic helium have been calculated over wide temperature and density ranges using the perturbation theory for the potential of electron-ion interaction. For conduction electrons, the random-phase approximation has been used taking into account the exchange interaction and correlations in the local-field approximation. The nuclear subsystem has been described by the hard-sphere model. The sphere diameter is the only parameter of the theory. The diameter and the system density at which helium is transformed from the singly ionized to doubly ionized state have been estimated based on an analysis of the pair effective interaction between helium nuclei. The case of doubly ionized helium atoms has been considered. The numerical calculations have been performed taking into account the perturbation theory in terms up to the third order. In all cases, the role of the third-order correction is significant. In the case of metallic helium, the values of the electrical resistance and its temperature dependence are characteristic of divalent simple liquid metals, as well as the dependences of the thermopower on the density and temperature.     

Rotating nuclear matter

Rotating nuclear matter is defined as the system of infinitely many nucleons in a rotating frame neglecting the electrostatic interaction and centrifugal single-nucleon potential. We study the ground state of this system as a function of the densities of neutrons and protons. In the limit where the angular velocity is much smaller than the Fermi energy, the structure of the single-nucleon density corresponds to anisotropic spin distributions at the surfaces of local neutron and proton Fermi spheres. The anisotropy results from the non-central terms in the effective two-nucleon interaction. Contrary to the situation in a system of non-interacting nucleons, the spin asymmetry induced by rotation is a strongly non-linear function of the Fermi momentum. In symmetric nuclear matter at normal density it equals roughly that of the non-interacting system due to mutually cancelling contributions from the spin-orbit and central parts of the effective two-nucleon interaction. The volume contributions to the moments of inertia and single-nucleon Routhian of finite nuclei are calculated, and estimates obtained of certain surface contributions to the moment of inertia.     

High energy proton scattering by medium and heavy nuclei

The recent data on both elastic and inelastic scattering of 1 GeV protons by ⁴⁰Ca and ²⁰⁸Pb are analyzed by means of the first term of the multiple scattering series for the optical potential and the DWIA. Theory and experiment agree quite well. Coulomb effects are taken into account. Neutron and proton ground state densities given by Hartree-Fock calculations employing a density-dependent Hamiltonian and which provide a good fit to elastic electron scattering are used. The Tassie form factors, normalized by comparison with inelastic electron scattering, are employed in the DWIA.     

Small mass enhancement near the metal–insulator transition in gated silicon inversion layers

The strong resistivity changes in the metallic state of two-dimensional electron systems have recently been assigned to quantum interaction corrections in the ballistic regime. We have performed analysis of Shubnikov–de Haas oscillations on high-mobility silicon inversion layers where we have explicitly taken into account that the back scattering angle has different influence on momentum relaxation and quantum life time. The consistent analysis under the assumption of the ballistic interaction corrections leads to smaller increase of the effective mass with decreasing electron density as usually reported.     

Density and thermodynamics of hydrogen adsorbed inside narrow carbon nanotubes

A model is proposed for calculating the thermodynamic functions and the equilibrium density of a one-dimensional chain of molecules (atoms) adsorbed inside a narrow nanotube. The model considers both the interaction between introduced atoms (molecules) and their interaction with the nanotube walls. The quantum-mechanical effects resulting in discrete energy levels of a particle and in its smeared position between neighbors are taken into account. In calculating the free energy at a nonzero temperature, the phonon contribution and the particle transitions to excited levels are considered. The model is applied to calculate the thermodynamic parameters of adsorbed hydrogen molecules inside extremely narrow single-wall carbon nanotubes of the (3,3) and (6,0) type. It is shown that external pressure gives rise to a sequence of first-order phase transitions, which change the density of adsorbed hydrogen molecules.     

Observation of a metallic superfluid in a numerical experiment

We report the observation, in Monte Carlo simulations, of a novel type of quantum ordered state: the metallic superfluid. The metallic superfluid features Ohmic resistance to counterflows of protons and electrons, while featuring dissipationless coflows of electrons and protons. One of the candidates for a physical realization of this remarkable state of matter is hydrogen or its isotopes under high compression. This adds another potential candidate to the presently known quantum dissipationless states, namely, superconductors, superfluid liquids and vapors, and supersolids.     

An iterative fitting procedure for the determination of longitudinal NMR cross-correlation rates

We present a method to measure (15)N-(1)H dipolar/(15)N CSA longitudinal cross-correlation rates in protonated proteins. The method depends on the measurement of four observables: the cumulative proton-proton cross relaxation rates, the (15)N R(1) relaxation rate, the multiexponential decay of 2N(Z)H(N)(Z) spin-order, and multiexponential buildup of 2N(Z)H(N)(Z) spin-order. The (15)N-(1)H dipolar/(15)N CSA longitudinal cross-correlation rate is extracted from these measurements by an iterative fitting procedure to the solution of differential equations describing the coupled relaxation dynamics of the z-magnetization of the (15)N nucleus, the two-spin-order 2N(Z)H(N)(Z), and a two-spin-order term 2N(Z)H(Q)(Z) describing the interaction with remote protons. The method is applied to the microbial ribonuclease binase. The method can also extract longitudinal cross-correlation rates for those amide protons that are involved in rapid solvent exchange. The experiment that serves for extracting proton-proton cross-relaxation rates is a modification of 3D (15)N-resolved NOESY-HSQC. The experiment restores the solvent magnetization to its equilibrium state during data detection for all phase cycling steps and all values of NOE mixing times and is recommended for use in standard applications as well.     

Calculation of the equation of state of a dense hydrogen plasma by the Feynman path integral method

A method is developed for calculating the equation of state of a system of quantum particles at a finite temperature, based on the Feynman formulation of quantum statistics. A general analytical expression is found for the virial estimator for the kinetic energy of a system with rigid boundaries at a finite pressure. An effective method is developed for eliminating the unphysical singularity in the electrostatic potential between a discretized Feynman path of an electron and a proton. It is shown that the “refinement” of an expansion of a quantum-mechanical propagator by addition of high powers of time exacerbates, rather than eliminates, the divergence of a Feynman path integral. A brief summary of the current status of the problem is presented. The proposed new approaches are presented in relation to progress made in this field. Path integral Monte Carlo simulations are performed for nonideal hydrogen plasmas in which both indistinguishability and spin of electrons are taken into account under conditions preceding the formation of the electron shells of atoms. The electron permutation symmetry is represented in terms of Young operators. It is shown that, owing to the singularity of the Coulomb potential, quantum effects on the behavior of the electron component cannot be reduced to small corrections even if the system must be treated as a classical system according to the formal de Broglie criterion. Quantum-mechanical delocalization of electrons substantially weakens the repulsion between electrons as compared to protons. In relatively cold plasmas, many-body correlations lead to complex behavior of the potential of the average force between particles and give rise to repulsive forces acting between protons and electrons at distances of about 5 angstroms. Plasma pressure drops with decreasing plasma temperature as the electron shells of atoms begin to form, and the electron kinetic energy reaches a minimum at a temperature of about 31000 K. The minimum point weakly depends on plasma density. Owing to quantum effects, the electron component is “heated” well before electrons are completely bound in the field of protons.     

Charge-changing transitions in an extended Lipkin-type model

Charge-changing transitions are considered in an extended Lipkin-Meshkov-Glick (LMG) model taking into account explicitly the proton and neutron degrees of freedom. The proton and neutron Hamiltonians are taken to be of the LMG form and, in addition, a residual proton-neutron interaction is included. Model charge-changing operators and their action on eigenfunctions of the model Hamiltonian are defined. Transition amplitudes of these operators are calculated using exact eigenfunctions and then the RPA approximation. The best agreement between the two kinds of calculation is obtained when the correlated RPA ground state, instead of the uncorrelated HF ground state, is employed and when the proton-neutron residual interaction, besides the proton-proton and neutron-neutron residual interactions, is taken into account in the model Hamiltonian. Received: 4 May 1998     

Atomic band structure effects on resonant scattering of atoms from solid surfaces

Bound state resonances related to the band structure of adsorbed atoms and their usefulness for determining the periodic components of atom-solid interaction potential are theoretically investigated. A variety of specular intensity patterns associated with bound state resonances near the Brillouin zone boundaries are exhibited. The (10) and (11̄) bound state resonances give rise to two split specular minima with the splitting depending essentially on v₁₀ for a fixed beam energy; however, the detailed features are dependent on other periodic components. For incidence along a crystal symmetry direction, symmetrization of basis states not only makes numerical computation very efficient, but also implies that there is only one specular minimum for a pair of bound states which are equivalent by symmetry. The (01) and (10) resonances along and near the x = y direction are presented to illustrate the symmetrization principle. The depth of one of the specular minima decreases and finally vanishes as the symmetry direction is approached. The single specular minimum corresponds to a resonance with the bound state which is a symmetric linear combination of (01) and (10) states in a potential well of v₀ + V₁₁. As expected, the shift in positions of specular minima caused by the periodic surface potential increases with decreasing beam energy.     

A study of proton-12C inelastic scattering at 1 GeV

The inelastic scattering of protons on ¹²C is investigated on the basis of the first order term of the multiple scattering expansion of Kerman, McManus, and Thaler. The spin degrees of freedom are taken into account. The inelastic transitions to the three lowest excited states of the target are studied within the distorted wave impulse approximation, the distortion being evaluated using an eikonal approximation. The elementary nuleon-nucleon high-energy interaction employed contains a simplified but realistic spin dependence. Special emphasis is placed on the influence of the small-angle approximation, the effect of spin, and the sensitivity to different nuclear transition densities.     

Quantum-chemical interpretation of spectral and photochemical properties of complexes of metalloporphyrins with pyridine anions

A quantum-chemical study is made of the energy minima and profiles of the potential surface of complexes of Zn-porphyrin with dilithiumpyridine in different energy states. It is shown that the axial distribution of dilithiumpyridine relative to the porphyrin ring corresponds to the energy minimum pertaining to the lower singlet state. A radically different geometry is obtained for the lower triplet state of charge transfer, and at this energy minimum the latter state represents, according to calculation data, the ground state. Based on an investigation of the profiles of potential surfaces between the energy minima, an explanation is given for the photochemical behavior of the complex. “S. I. Vavilov Institute of Optics” All-Russia Scientific Center, 12, Birzhevaya Liniya, St. Petersburg, 199034. Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 1, pp. 38–41, January–February, 1997.     

Further studies of density-dependent interactions for the excitation of collective states

The density-dependent DDM3Y effective nucleon-nucleon interaction was used in a double-folding model with macroscopic transition densities to explore further density-dependent effects on the inelastic scattering of α-particles and protons. In particular, we investigate whether transition densities with a node near the nuclear surface, such as occurs for the giant monopole (breathing mode) resonance, are particularly sensitive to density dependence in the interaction. We also study the imposition of a consistency condition on the use of density dependence for inelastic scattering. In both situations, the effects are small (≲20%) for α-particles but large for protons. The consistency condition is discussed further in an appendix.     

Out of equilibrium dynamics of supersymmetry at high energy density

We investigate the out of equilibrium dynamics of global chiral supersymmetry at finite energy density. We concentrate on two specific models. The first is the massive Wess–Zumino model which we study in a self-consistent one-loop approximation. We find that for energy densities above a certain threshold, the fields are driven dynamically to a point in field space at which the fermionic component of the superfield is massless. The state, however, is found to be unstable, indicating a breakdown of the one-loop approximation. To investigate further, we consider an O(N) massive chiral model which is solved exactly in the large N limit. For sufficiently high energy densities, we find that for late times the fields reach a nonperturbative minimum of the effective potential degenerate with the perturbative minimum. This minimum is a true attractor for O(N) invariant states at high energy densities, and this provides a mechanism for determining which of the otherwise degenerate vacua is chosen by the dynamics. The final state for large energy density is a cloud of massless particles (both bosons and fermions) around this new nonperturbative supersymmetric minimum. By introducing boson masses which softly break the supersymmetry, we demonstrate a see-saw mechanism for generating small fermion masses. We discuss some of the cosmological implications of our results.     

On the validity of the triple-dipole interaction as a representation of non-additive intermolecular forces

A complete partial wave analysis of the non-expanded non-additive coulomb interaction energy for three non-degenerate S-state atoms is given through third-order in the interatomic potential energy function. Pseudo state techniques are used to evaluate various partial wave components of the non-expanded second and third-order non-additive interaction energies for various isosceles triangular configurations of three interacting ground-state hydrogen atoms. These second and third-order non-expanded coulomb results are used, in conjunction with Heitler-London results for the first-order non-additive energies for the quartet spin state of the H(1s)-H(1s)-H(1s) interaction, to discuss the relative importance of various parts of the non-additive energy as a function of the geometrical configuration of the atoms, and the validity of both the non-expanded triple-dipole energy and the expanded Axilrod-Teller-Muto triple-dipole result as a representation of non-additive coulomb energies. For example, in the non-bonded interaction of three S-state atoms it appears that representing the non-additive energy by the non-additive coulomb energy is not reliable until the interatomic separations are somewhat larger than R*, the interatomic distance associated with the van der Waals minimum in the corresponding non-bonded dimer interaction. Further, the use of the triple-dipole interaction energy, with or without charge overlap corrections, to represent the non-additive coulomb energy is of doubtful validity until the interatomic separations are considerably greater than R*.