Showing papers on "Random phase approximation published in 1973"
TL;DR: In this paper, the effect of spin fluctuations on itinerant electron ferromagnetism was extended to include the ferromagnetic phase and the correction to the Hartree-Fock free energy as a function of magnetization was expressed in terms of the transversal dynamical susceptibilities.
Abstract: The theory of the effect of spin fluctuations on itinerant electron ferromagnetism, which we have developed previously, is extended to include the ferromagnetic phase. The correction to the Hartree-Fock free energy as a function of magnetization is expressed in terms of the transversal dynamical susceptibilities and is actually calculated by using a modified random phase approximation for the dynamical susceptibilities; the random phase approximation is modified so as to give a consistent static limit throughout the whole temperature range covering both below and above the Curie point. As a result, the magnetization at low temperatures shows a T 3/2 dependence due to the spin wave excitations, the Curie temperature is generally lowered from the Stoner (Hartree-Fock) value and the magnetic susceptibility above the Curie temperature shows an approximate Curie-Weiss behavior.
307 citations
TL;DR: In this paper, the authors considered the vibrational relaxation of a guest molecule in a host matrix and derived explicit solutions for the Wigner-Weisskopf approximation for both single phonon and multiphonon processes, which was applied for the study of the time evolution of the distribution, the cooling and heating processes of the oscillator by a thermal field and for the coupling between vibrati...
Abstract: In this paper we consider some features of vibrational relaxation of a guest molecule in a host matrix. The model system involves a harmonic molecule interacting with a harmonic medium. The molecule-medium coupling was handled by the rotating wave approximation considering linear terms in the intramolecular displacements and high terms in the medium displacements. Three specific models for the molecule-medium coupling were considered, which involve single phonon decay, vibron-phonon decay and multiphonon decay. Within the framework of the random phase approximation the Heisenberg equations of motion for the system could be expressed in terms of a unified scheme which is valid for both single phonon and multiphonon processes. Explicit solutions were derived utilizing the Wigner-Weisskopf approximation. This generalized formalism was applied for the study of the time evolution of the distribution, the cooling and the heating processes of the oscillator by a thermal field and for the coupling between vibrati...
168 citations
TL;DR: In this article, the properties of a one-dimensional model of the electron-phonon system which exhibits the Peierls instability were investigated, and it was shown that the instability tends to suppress BCS pairing, and the resulting PEierls state below the structural transformation is semiconducting.
Abstract: We investigate the properties of a one-dimensional model of the electron-phonon system which exhibits the Peierls instability. The instability tends to suppress BCS pairing, and the resulting Peierls state below the structural transformation is semiconducting. Results of the conductivity calculation compare favorably with recent measurements on most samples of tetrathiofulvalinium tetracyanoquinodimethane but cannot explain the extraordinary conductivity peaks found in a few samples.
74 citations
TL;DR: In this paper, the low lying states of 208 Pb were calculated within the theory of Finite Fermi System (FFS) using a density dependent residual interaction, and a strong M2-transition at 751 MeV was predicted.
74 citations
TL;DR: In this paper, an energy-dependent transition potential was introduced for electron-atom (molecule) inelastic scattering, which constitutes a higher order approximation than the GRPA elastic theory.
Abstract: Using the Martin-Schwinger variational technique (1959), a new theory is obtained for electron-atom (molecule) inelastic scattering. This theory constitutes a higher order approximation than the GRPA elastic theory. In analogy with elastic scattering, an equivalent optical potential, named, the transition potential, is introduced for inelastic scattering. In the GRPA this transition potential is of the first-order static-exchange type. The present theory adds three new effects to the GRPA transition potential. One of them represents the screening of the first-order exchange term, another one the transition polarization effect and the third the effect of the final state field. In contrast to close-coupled or Kohn-type variational theories, the present theory has the advantage of decoupling the scattering channels through the use of the energy-dependent transition potential.
37 citations
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TL;DR: In this article, the consequences of the existence of pairing correlations in nuclei are discussed and the dynamical aspects of the pairing degree of freedom, as revealed by two-nucleon transfer reactions.
33 citations
TL;DR: In this article, the excitation of the lowest 3− and 5− levels in 40Ca was studied using a microscopic description and the long-range part of the Hamada-Johnston potential was shown to be a good effective interaction especially when supplemented by a phenomenological imaginary term.
Abstract: The excitation of the lowest 3− and 5− levels in40Ca is studied using a microscopic description. The long-range part of the Hamada-Johnston potential is shown to be a good effective interaction especially when supplemented by a phenomenological imaginary term. Transition densities are constructed from holeparticle RPA wave functions normalized to give the correct electric transition rates. Various wave functions and other interactions are studied. Other features of the calculations are discussed.
28 citations
26 citations
25 citations
TL;DR: In this article, the average energy per an electron-hole pair and the pair correlation functions are calculated beyond the random phase approximation by taking into account the effects of the exchange and the electronhole scattering corrections.
Abstract: For the metallic state of an electron-hole gas, the average energy per an electron-hole pair and the pair correlation functions are calculated beyond the random phase approximation by taking into account the effects of the exchange and the electron-hole scattering corrections. Here we introduce a variational method, in which the Fourier components of the correlations between any kinds of particles are chosen as the variational parameters for each value of the wave vector. These parameters are determined by minimizing the total energy calculated in r.p.a. On the basis of the results in r.p.a., exchange and scattering corrections are evaluated by perturbational method. As a result, the applicability of our results is extended to the concentration region as low as r s ≃2. The results of our calculation show that the minimum of the average energy amounts to E g -1.00 E ex b at r s ≃2 and that the effects of the scattering correction between electrons and holes are fairly large even in the metallic system.
22 citations
TL;DR: In this paper, the Tamm-Dancoff and random-phase approximations have been summed to calculate the effective charge in the 1s0d and 1p0f shells.
TL;DR: In this article, an expression for the spin wave stiffness constant D in a ferromagnetic alloy using essentially the random phase approximation was derived for NiFe and NiCo alloys.
Abstract: An expression is derived for the spin wave stiffness constant D in a ferromagnetic alloy using essentially the random phase approximation. On applying the coherent potential approximation a result previously derived by Fukuyama (1973) is obtained. Numerical calculations are made for NiFe and NiCo alloys.
TL;DR: In this paper, it was shown that the singlet excited states of the water molecule cannot be adequately represented by an ab initio calculation (no semi-empirical elements) using a valence-like basis set (either minimum basis or double zeta) of Slater-type orbitals.
Abstract: By performing calculations on H2 O similar to the calculations of Dunning and McKoy on C2H4 and HCHO [1a], it is shown that the singlet excited states of the water molecule cannot be adequately represented by an ab initio calculation (no semiempirical elements) using a valence-like basis set (either minimum basis or double zeta) of Slater-type orbitals. The triplets which are the lowest states of their symmetry appear to be described more accurately than the other states, and the lowest four triplet excitation energies are calculated to be 8.1, 8.4, 9.5, and 10.3 eV. The implications for the applicability of simple molecular orbital theory of the type commonly applied are discussed.
TL;DR: In this article, the analytical and numerical procedures used in calculation of e − -He elastic scattering phase shifts in the Generalized Random Phase Approximation (GRPA) and e − −He inelastic cross sections in the RPA are presented.
TL;DR: In this article, the effect of many-electron correlations in the inelastic electron-atom scattering at high energies is investigated and the importance of these correlations is shown by comparison of the results of calculations with the best possible independent particle model and the experimental data.
Abstract: The effect of many-electron correlations in the inelastic electron-atom scattering at high energies is investigated The importance of these correlations is shown by comparison of the results of calculations with the best possible independent particle model and the experimental data Many-electron correlations are included in the random phase approximation with exchange (RPAE) and the corresponding integral equation for the effective interaction is displayed This equation has been solved numerically for argon, and generalized oscillator strength densities as well as the differential cross section were calculated The results agree with the experiment quite well, showing thus the very important role the many-electron correlations play in the inelastic electron-atom scattering The calculations confirm the relative importance of the monopole and the quadrupole transitions in the process under consideration
TL;DR: In this article, a generalisation of the dispersion equation is given for the study of E2 and E0 properties of excited 0 + states in even-even deformed nuclei.
TL;DR: In this paper, a new theory is presented on the excited states of molecular crystals by using the random phase approximation (RPA) method applied to the analysis of the absorption spectrum of anthracene crystal.
Abstract: A new theory is presented on the excited states of molecular crystals by using the random phase approximation (RPA). The method is applied to the analysis of the absorption spectrum of anthracene crystal. The Davydov splitting for the long axis polarized band is calculated as about 9200 cm−1 while the observed value is 9000 ∼ 12000 cm−1. In the earlier theories, much larger values are reported and a simple dipole-dipole approximation gives the value of 32000 cm−1. The general feature of the crystalline spectra is well predicted.
TL;DR: In this article, the effects of the geometry of the cubic lattices on the properties of a Heisenberg antiferromagnet with first-and second-nearest-neighbour interactions are investigated.
Abstract: The effects of the geometry of the cubic lattices on the properties of a Heisenberg antiferromagnet with first- and second-nearest-neighbour interactions are investigated. Both the Neel temperature and the quantum defect are calculated using temperature-dependent Green function theory and the random phase approximation (RPA) for all values of the exchange constants leading to antiferromagnetic order. Special attention is given to the properties of the phase transitions which occur when the exchange constraints are varied. Graphs of the Neel temperature and the quantum defect are presented to aid comparison between theory and experiment.
TL;DR: In this article, the transverse dynamic susceptibility for the modified Zener model of ferromagnetism is calculated in order to examine the behavior of neutron scattering resonances at low temperatures and at the Curie temperature.
Abstract: The transverse dynamic susceptibility for the modified Zener model of ferromagnetism is calculated in order to examine the behavior of neutron scattering resonances at low temperatures and at the Curie temperature ${T}_{C}$. The relationship of these calculations to those for a pure itinerant-electron ferromagnet is discussed. The inadequacy of the random-phase approximation in describing the behavior of the spin waves for Ni near ${T}_{C}$ is also discussed.
TL;DR: The generator coordinate method based on states derived from the random phase approximation, together with a strong assumption, leads to a differential equation for collective motion similar to the Bohr Hamiltonian with inertial parameters given by a formula related to the cranking model as mentioned in this paper.
TL;DR: In this article, the spin wave modes of a metallic ferromagnet were studied using a short range interaction between the electrons, in the random phase approximation (RPA), and it was shown that the amplitude of the spin waves relative to the non-spin wave contribution to the transverse spin correlation function is a monotonic decreasing function of the wavenumber.
Abstract: The spin wave modes of a metallic ferromagnet are studied using a short range interaction between the electrons, in the random phase approximation (RPA). Besides confirming known properties of the undamped spin waves found for momentum less than a certain value p1 (such as the existence of negative velocity spin waves) the authors find that the amplitude of the spin waves, relative to the non-spin wave contribution to the transverse spin correlation function, is a monotonic decreasing function of the wavenumber going from unity at p=0 to zero at p=p1. For p>p1, decay of spin waves into Stoner excitations becomes possible and the spin waves are damped. The dynamical transverse susceptibility was studied by analytic continuation. Two branches of complex poles are found for relative magnetization xi <1. (one branch for xi =1).
TL;DR: In this paper, a method for calculating the d electron generalized susceptibility for a transition metal which takes full account of the multiplicity of the band structure is described, and a magnetic instability criterion is derived.
Abstract: Describes a method for calculating the d electron generalized susceptibility for a transition metal which takes full account of the multiplicity of the band structure. It is assumed that the band structure can be represented by a model Hamiltonian and that electrons interact only when occupying the same atomic cell and then only when in d orbitals. The random phase approximation is used. A magnetic instability criterion is derived. This criterion is applied to a discussion of the magnetic instability in gamma manganese.
TL;DR: In this paper, the dispersion curves of the d.h.c.p. praseodymium single crystal were used to obtain the low-lying collective excitation spectra at zero and finite temperatures.
Abstract: The Hamiltonian constructed in a previous work in pseudo-spin space to explain the crystal-field effects in certain magnetic systems with various crystal-field level schemes has been studied in the random phase approximation of the double-time Green function method. By using the molecular field results obtained before as a second approximation, we obtain the low-lying collective excitation spectra at zero and finite temperatures. As an application, we have extended our calculations to look at the dispersion curves of the d.h.c.p. praseodymium single crystal. Comparison with the experimental measurements is discussed. Suggestions on further studies and possible improvements of the present calculations are also provided.
TL;DR: In this paper, the ground-state correlations are treated in the random-phase approximation of low-energy nuclear reactions in which the matrix elements of two weakly energy-dependent effective interactions describing particle-hole pair scattering and pair creation or annnihilation in a correlated system are introduced.
Abstract: We present a practical formalism of low-energy nuclear reactions in which the ground-state correlations are treated in the random-phase approximation. The building blocks of the method are the matrix elements of two weakly energy- dependent effective interactions describing particle-hole pair scattering and pair creation or annnihilation in a correlated system. The corresponding transition operator, which give complete information on any nuclear reaction, are then introduced. We apply the method to a study of nucleon scattering, photonuclear, muonuclear reactions proceeding through the 1- states of /sup 16/O. The single-particle basis states are generated by a local, real Woods-Saxon potential, while the residual interuction has a zero range. In the relatively high excitation energy being studied, the correlations retained in the random- phase approximation affect very little nucleon scattering but reduce transition rates in photonuclear reactions and muon capture by about 8%. (auth)
TL;DR: In this paper, the dependence of the energy of the lowest pairing-vibrational state on the quadrupole-pairing strength was investigated in the Pt isotopes using the Random Phase Approximation.
Abstract: The dependence of the energy of the lowest pairing-vibrational state on the quadrupole-pairing strengthG2 is investigated in the Pt isotopes. The calculation are made using the Random Phase Approximation for the collective states with the pairing forces treated in the BCS approximation.
TL;DR: In this article, the form factor, binding energy and the monovacancy resistivity in the solid state were calculated, and the work was extended to include some liquid state properties, namely, resistivity, temperature coefficient of resistivity at constant volume and the thermoelectric power.
Abstract: A calculation is made, concerning the form factor, binding energy and the monovacancy resistivity in the solid state. The work is also extended to include 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 the liquid and the solid phase. In all these calculations the screening due to the electron gas is accounted through two standard techniques: one in random phase approximation and the other based on selfconsistent theory. A fairly good agreement with the available experimental data is obtained in both cases. It has been found that the two sets of results are significantly different in most of the cases.
TL;DR: A selfconsistent version of the static random phase approximation leads to a quasi-particle energy satisfying ϵ(k)=Akv for small k, where v ≈ 1.8.
TL;DR: In this article, a model potential of the form omega b(q)=(1/ Omega 0)(-(4 pi Ze2/q2)+ beta (sin qrc-qrccos qrc)exp(-q gamma c)) is employed to study some electronic properties of aluminium.
Abstract: A model potential of the form omega b(q)=(1/ Omega 0)(-(4 pi Ze2/q2)+ beta (sin qrc-qrccos qrc)exp(-q gamma c)) is employed to study some electronic properties of aluminium, by considering electron gas screening with and without the inclusion of exchange and correlation effects as in the self-consistent theory of Singwi et al and in the random phase approximation respectively. A calculation is carried out to obtain form factor, binding energy, monovacancy resistivity and also the resistivity, temperature coefficient of resistivity and the thermoelectric power in the liquid state. The temperature coefficient of the Knight shift at constant volume is also calculated in both solid and liquid phases. The results show a fairly good agreement with the available experimental data. It has also been found that the two sets of results obtained using either form of the dielectric function are significantly different.