Showing papers on "Random phase approximation published in 1972"
TL;DR: In this paper, an optimized random phase approximation (ORPA) was applied to the calculation of the thermodynamic properties and pair correlation function of simple liquids, together with results for the Lennard Jones fluid, which are compared with Monte Carlo and molecular dynamic results.
Abstract: The optimized random phase approximation (ORPA) is applied to the calculation of the thermodynamic properties and pair correlation function of simple liquids. General formulas are presented, together with results for the Lennard‐Jones fluid, which are compared with Monte Carlo and molecular dynamic results. Excellent agreement is obtained for the entire single phase fluid region of the phase diagram, except for the critical region and the very low temperature vapor. The theory converges especially rapidly at high densities or at high temperatures. The importance of separating the intermolecular potential in the proper way to obtain most rapid convergence of perturbation theories is discussed. It is concluded that the structure of simple liquids is determined mostly by the rapidly varying parts of the potential. Further, the ORPA provides an accurate theory for calculating the contributions from different forces to the structure and thermodynamics of liquids.
196 citations
TL;DR: In this paper, the specific heat of NaNO 2 was measured as a function of temperature near its antiferroelectric-to-paraelectric phase transition point (T N ).
76 citations
TL;DR: The angular distribution of electrons in the noble gas photoionization was calculated with many-electron correlations taken into account in the random phase approximation with exchange in this article, where the correlation between the electron correlations was considered.
63 citations
TL;DR: The use of London's gauge-invariant orbitals in the calculation of magnetic rotational strengths is investigated in this article, where the results are origin-independent and compare well with experimental values.
Abstract: The use of London's gauge-invariant orbitals in the calculation of magnetic rotational strengths is investigated. Self-consistent molecular orbitals at non-zero magnetic field strengths have been determined in the Pariser-Parr-Pople model and these have been employed in the calculation of excitation energies and transition moments according to the mono-excited configuration interaction and the random phase approximations. Applications to the magneto-optical activity of aniline, phenol, and benzonitrile are reported. The results are origin-independent and compare well with experimental values.
50 citations
TL;DR: In this paper, the phase transition of NaNO 3 crystal associated with the ordering of the orientation of NO 3 ion has been investigated by X-ray scattering and the experimental results have been analyzed on a microscopic basis to obtain pair interactions between NO 3 - ions.
Abstract: The phase transition of NaNO 3 crystal associated with the ordering of the orientation of NO 3 - ion has been investigated by X-ray scattering. The experimental results have been analyzed on a microscopic basis to obtain pair interactions between NO 3 - ions. The results are summarized as follows. (i) The ellipsoidal distribution of critical diffuse scattering in the reciprocal space is explained by taking the pair interactions up to second nearest neighbours. (ii) The temperature dependence of critical scattering gives a reasonable agreement with theoretical values in random phase approximation in the temperature range of T > T c +4.5 K. (iii) Both the temperature dependence of long range order parameter and of anomalous lattice expansion can be satisfactorily explained by taking the strain dependence of pair interaction energy into account.
33 citations
TL;DR: In this article, a many-body optical potential, which has been demonstrated to give excellent electron-helium elastic scattering cross sections, is analyzed and a partial semi-empirical form of this potential is achieved.
Abstract: A many-body optical potential $\ensuremath{\Sigma}$ which has been demonstrated to give excellent electron-helium elastic scattering cross sections is analyzed. It is shown to encompass, yet be more general than, almost all previous model potentials used in electron scattering and Rydberg-state calculations. A partial semiempirical form of this potential is achieved. It is shown how $\ensuremath{\Sigma}$ can be computed by methods of variation-perturbation theory.
33 citations
32 citations
28 citations
TL;DR: In this paper, the random phase approximation (RPA) and the singly excited configurations-interaction (SECI) methods were compared for H2O, HCHO, CH2N2, and HCOOH molecules.
Abstract: Selected excitation energies, potential surfaces of excited states, and oscillator strengths are computed using three methods: (1) the random‐phase approximation (RPA), (2) the singly excited configurations‐interaction (SECI) method based upon the ground‐state restricted Hartree‐Fock (RHF) determinant, (3) a variational or quasivariational method which is essentially an excited‐state Hartree‐Fock (HF) method and which is applied to each state of the system. The simplification of the intermediate neglect of differential overlap (INDO) method is used throughout and it seems not to affect the validity of the comparison of the different methods. The advantages and the disadvantages of respective methods are discussed. The molecules chosen for study are H2O, HCHO, CH2N2, and HCOOH. Conclusions are drawn on the basis of what are the most extensive set of semiempirical RPA calculations to date. The RPA method, within the approximations used and in the given examples, is found to have no advantages and to have se...
20 citations
TL;DR: The theory of localized spin fluctuations in the renormalized random phase approximation of Anderson's model has been used to obtain theoretical expressions for the resistivity rho (T) and the density of states of localized electrons Nd(T) which are valid at high temperatures as discussed by the authors.
Abstract: Previous experimental data (see abstr. A73604 of 1971) for the resistivity rho (T) dilute AlMn show that rho (T) exhibits a linear decrease above 150 K. The theory of localized spin fluctuations in the renormalized random phase approximation of Anderson's model has been used to obtain theoretical expressions for the resistivity rho (T) and the density of states of localized electrons Nd(T) which are valid at high temperatures. The theoretical and experimental values for rho (T) are in good agreement, whereas the agreement for Nd(T) is poor.
16 citations
TL;DR: In this article, the authors investigated the field penetration into a metal surface by including both short range and long range interactions and showed that the work function increases when a high electrostatic field is applied to the metal.
Abstract: The field penetration into a metal surface is investigated in this paper. By including both short range and long range interactions it is shown that the work function increases when a high electrostatic field is applied to the metal. The nonlinearity of the response to the external field is shown and results qualitatively different from those of the random phase approximation are obtained.
TL;DR: Using a Hartree-Fock basis the diagrams of the Tamm-Dancoff and random-phase approximations have been summed to calculate the effective charge in the (1s 0d) shell.
TL;DR: In this paper, the Dyson equation for the polarization (particlehole) propagator was derived with the diagrammatic technique and the secular equation which gives poles of the polarization propagator is solved.
Abstract: The Green's function method for the calculation of orbital energies which was discussed in a preceding paper is applied to the calculation of the lower excited states of the benzene molecule. The Dyson equation for the polarization (particle—hole) propagator is derived with the diagrammatic technique and the secular equation which gives poles of the polarization propagator is solved. The random phase approximation is not used in our calculation. Theoretical results are discussed in comparison with experimental data. Using a model system of two π-electrons, our method is compared with the equations-of-motion method.
TL;DR: In this article, the time-dependent Hartree-Fock theory of molecular dynamic polarizabilities is reviewed in the context of the Dirac density operator approach and the energy denominators are shown to vanish for external field frequencies which are solutions of an eigenvalue-equation which is the same as that arising under the random phase approximation assumptions.
Abstract: The time-dependent Hartree-Fock theory of molecular dynamic polarizabilities is reviewed in the context of the Dirac density operator approach. The energy ‘denominators’ are shown to vanish for external field frequencies which are solutions of an eigenvalue-equation which is the same as that arising under the random phase approximation assumptions. A perturbative approach to its solution is presented which gives good results at its lowest-order when applied to the prediction of the lowest excited singlet state of the ethylene molecule.
TL;DR: In this paper, the dielectric tensor pertaining to static perturbations of an electron gas in a dc magnetic field is calculated in the random phase approximation for the weak field and de Haas-van Alphen regimes.
TL;DR: In this article, a new model potential is adopted to represent the effective electron-ion interaction in metals, and a calculation has been carried out to obtain the form factor, binding energy and the monovacancy resistivity.
Abstract: A new model potential is adopted to represent the effective electron-ion interaction in metals. An application is made in the case of lead. A calculation has been carried out to obtain the form factor, binding energy and the monovacancy resistivity. It is also applied to evaluate some liquid state properties, namely, resistivity, temperature coefficient of resistivity at constant volume and the thermoelectric power. The temperature dependence of the Knight shift at constant volume is also examined in solid and liquid phases. In all these calculations the dielectric function is introduced on two methods, in random phase approximation and on Sham's theory. The two sets of theoretical results are not significantly different and present a tolerable agreement with the experimental data.
TL;DR: In this article, the generalized oscillator strengths for Ar are presented both in single-particle Hartree-Fock approximation and with correlations included in the random phase approximation with exchange.
TL;DR: In this article, the eigenvalue matrix of impurity modes is reduced to (z +1)×( z + 1) from 2 N ×2 N by introducing an appropriate approximation.
Abstract: Within the random phase approximation, the Green functions are obtained in Heisenberg antiferromagnets doped with impurities. In order to understand the temperature dependence of spin-wave impurity modes intuitively, the local energy renormalization factors are introduced which play a role of an effective field for individual spin. Dimension of the eigenvalue matrix of impurity modes is reduced to ( z +1)×( z +1) from 2 N ×2 N by introducing an appropriate approximation. Here, z and N represent the coordination number and the number of ions in one sublattice, respectively, Numerical calculations of the Green functions and spin correlations are carried out self-consistently. Magnetizations of impurity and its nearest neighbor ions, energy eigenvalues of the localized modes and energy spectra of the resonant modes are calculated as functions of temperature for various values of the impurity-host exchange coupling J ' and the impurity spin S ' in a simple cubic antiferromagnet with S =5/2.
TL;DR: In this paper, the effects induced by applying the schematic model, within the framework of the quasiparticle random phase approximation, to the description of collective vibrational states in deformed heavy nuclei are discussed.
TL;DR: In this paper, the quasi-particle random-phase approximation of rare-earth nuclei is tested by determining the quasiparticle occupation numbers in the ground state of rare earth nuclei.
TL;DR: In this paper, microscopic expressions for the coefficients in the angular momentum expansion were obtained for the energies of quasirotational members of quadrupole vibrational bands, and limitations on the applicability of perturbation treatments of anharmonic corrections to the random-phase approximation were noted.
Abstract: Microscopic expressions are obtained for the coefficients in the angular momentum expansion ${E}_{I}={a}_{2}(\frac{1}{2}I)+{a}_{4}{(\frac{1}{2}I)}^{2}+\ensuremath{\cdots}$ of the energies of quasirotational members of quadrupole vibrational bands. Some limitations on the applicability of perturbation treatments of anharmonic corrections to the random-phase approximation are noted.
TL;DR: In this article, the authors developed a model based on the Ziman formula for understanding the dc conductivity of liquid metals at high temperature, in the immediate vicinity of the critical point.
Abstract: In this work we try to develop a model calculation based on the Ziman formula for understanding the dc conductivity of liquid metals at high temperature, in the immediate vicinity of the critical point. We start with a correlation function S ( k , ω ) and a local electron-ion interaction weighted with the dielectric function e ( k , ω ) taken in the random phase approximation. These quantities are considered in the hydrodynamic limit ω → 0, k → 0. Then, it appears that near the critical point, the forward scattering and the resistivity become strongly enhanced by the long range ion-ion correlations. This result remains valid when multiple ionic correlations are taken into account.
TL;DR: In this paper, the effect of magnon interaction on the magnon energies of haematite by using a random phase approximation was studied and the conclusion of the present theory was contrary to that of Herbert.
Abstract: Herbert (1969) suggested that the Morin transition temperature of haematite is not given by the temperature at which the acoustic mode magnon energy vanishes but is given by the temperature at which the optic mode energy vanishes. In his expression of the optic mode energy E0, the correction term due to the magnon interaction is proportional to the inverse of the free optic mode energy Ef0, and therefore E0 is large if the Ef0 is small. Then, the free spin wave theory may not be used in the analysis of the experimental value on E0 even at low temperature. The present authors studied the effect of magnon interaction on the magnon energies of haematite by use of the random phase approximation. According to the theory, the optic mode energy becomes small if the free optic mode energy is small. Thus, the conclusion of the present theory is contrary to that of Herbert. On the other hand, if one uses the conventional random phase approximation adopted by, for example, Oguchi and Honma (1961), the optic mode energy is found to become large when Ef0 is small.
01 Jan 1972
TL;DR: A short review of the microscopic theory of phonons, its achievements and its present difficulties is given in this paper, where the authors also present a short survey of the current state of the art.
Abstract: This paper is a short review of the microscopic theory of phonons, its achievements and its present difficulties.
TL;DR: In this paper, the Anderson model for dilute magnetic alloys is re-examined in the magnetic limit U/J~1 (U and J are the Coulomb energy and the level width at the impurity site, respectively) in the renormalized random phase approximation, which has recently been studied by Hamann and the present author.
Abstract: The Anderson model for dilute magnetic alloys is re-examined in the magnetic limit U/J~1 (U and J are the Coulomb energy and the level width at the impurity site, respectively) in the renormalized random phase approximation, which has recently been studied by Hamann and the present author. The result is rather different from previous works and proves that the characteristic te~perature T,o in our model is given by T,o.._J. (J/U) 2•683, which is too large in comparison with the corresponding Kondo temperature, and that the magnetic susceptibility X does not show the Curie law but x---1/T· (T/U)O.S43 at high tem· perature (T~ T,o).
TL;DR: In this article, the effect of using various correlated ground states on the energies of excited collective RPA states was examined and it was shown that if the exact correlated state given by Lipkin, Meshkov and Glick is used as a variational correlated ground state, then the energy of the excited states are closer to their exact values than the ones given by the exact particle-hole model.
TL;DR: In this article, the existence of a collective excitation with vanishing excitation energy and momentum was shown to correspond to the creation of a Cooper pair and the creation operator satisfies a nonlinear operator equation which dose not depend on the magnitude of order parameter.
Abstract: In the generalized random-phase approximation, introduced by Anderson and applied to the theory of superconductivity, existence of a collective excitation with vanishing excitation energy and momentum was known. It is shown to correspond to the creation of a Cooper pair. The creation operator satisfies a nonlinear operator equation which dose not depend on the magnitude of order parameter. It is, therefore, independent of dynamics, that is, of the strength of the pairing interactions. Nevertheless it has the assumed matrix elements between a given state in an N-particle system and the corresponding state in the N+2 par ticle system. Discussions are confined to the BCS superconductor at absolute zero temperature.
TL;DR: In this paper, it was shown that the method used by Lukes and Morgan to calculate the resolvent operator of a perfect lattice can be used to obtain the one electron Green function and hence the dielectric constant in random phase approximation provided the matrix elements of the pseudopotential are known.