Showing papers on "Random phase approximation published in 1976"
TL;DR: In this paper, it was shown that the energy of the monopole resonance is proportional to the square root of the compression modulus of finite nuclei K A, which is a regular function of K ∞ and is a possible way of reaching the compressibility of nuclear matter.
189 citations
TL;DR: In this paper, the positions and transition strengths of the giant multipole resonances of the spherical nuclei (16 O, 40 Ca, 90 Zr and 208 Pb) are calculated with large configuration spaces in the random phase approximation based on the Hartree-Fock ground states of a newly developed Skyrme interaction.
163 citations
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01 Jun 1976
TL;DR: In this article, the Hartree-Fock and particle-hole formalisms and random phase approximation are applied to the three-nucleon problem, and the authors present a theory of the structure of light nuclei.
Abstract: Introduction. I. Two- and Three Nucleon Systems . The nucleon-nucleon interaction. Phase shift analysis. Varieties of nucleon-nucleon interactions. The three-nucleon problem. II. Nuclear Matter . Formal theory of many-particle systems. Infinite nuclear matter. III. Theories of the Structure of Light Nuclei. Hartree-Fock and particle-hole formalisms and the random phase approximation. Application of the Hartree-Fock and the particle-hole formalisms. Nuclear rotation. IV. Theories of the Structure of Heavier Nuclei. Pairing and quasiparticles. Collective motion in nuclei. Appendices: A. The projection of physical states. B. Collective coordinates in a consistent microscopic theory. References. Index.
86 citations
TL;DR: In this paper, the photoionization cross sections and the oscillator strengths for helium, lithium, and beryllium atoms are calculated in the framework of the random-phase approximation with exchange.
Abstract: The photoionization cross sections and the oscillator strengths for helium, lithium, and beryllium atoms are calculated in the framework of the random-phase approximation with exchange. The energy-level shift for discrete transitions is taken into account consistently in this approximation. The results are compared with other many-body calculations and with the experimental data. The comparison shows that the random-phase approximation with exchange can even be used for systems with a small number of particles.
52 citations
TL;DR: In this paper, it was shown that a finite coherence length for the pump wave can favor the existence of absolute instability, and the conditions of validity were checked by solving exactly a particular model.
Abstract: Finite-bandwidth effects are investigated by using the random phase approximation. The conditions of validity are checked by solving exactly a particular model. It is found that a finite coherence length for the pump wave can favor the existence of absolute instability. (AIP)
43 citations
TL;DR: In this article, the s-, p-, d-and f-wave phase shifts for elastic scattering of slow positrons by He are calculated using a simplified version of the random phase approximation with exchange, with the virtual positronium formation effect taken into account.
Abstract: The s-, p-, d- and f-wave phase shifts for elastic scattering of slow positrons by He are calculated using a simplified version of the random phase approximation with exchange, with the virtual positronium formation effect taken into account.
40 citations
TL;DR: In this article, a simplified model for the scalar meson self-energy in the nuclear medium and restricting to a set of graphs which in non-relativistic normal nuclear matter reduces to the well-known random phase approximation (RPA) was used to determine whether strongly attractive multi-body forces are present or absent in the normal matter.
35 citations
34 citations
TL;DR: In this paper, the statistical mechanics of uniaxial S = 1 ferromagnets with biquadratic exchange are considered in both ferromagnetic and quadrupolar phases using the standard basis operator method proposed by Haley and Erdos (1972).
Abstract: The statistical mechanics of uniaxial S=1 ferromagnets with biquadratic exchange is considered in both ferromagnetic and quadrupolar phases using the standard basis-operator method proposed by Haley and Erdos (1972). In the random phase approximation, the collective excitation spectrum and thermodynamical properties of the system are discussed in detail, with stress laid on the role of kinematic restrictions with regard to the operators of the standard basis. The results are compared with those of molecular field theory, constant coupling approximation, and the high-temperature series expansion method. The problem of stability of the quadrupolar ordering is also considered by having recourse to the nonrelativistic analogue Goldstone theorem.
31 citations
TL;DR: In this article, the equilibrium properties of a two-dimensional plasma were examined theoretically within the framework of the random phase approximation, and an explicit form for the structure function was derived and compared with the result of a Monte Carlo calculation.
Abstract: The equilibrium properties of a two‐dimensional plasma are examined theoretically within the framework of the random phase approximation. The guiding‐center case is of most interest because of the formal equivalence to two‐dimensional discrete line vortex fluids and because of the formal admissibility of negative temperatures. Using a judicious treatment of the periodic boundary conditions, extensive thermodynamics for nonnegative temperatures and a new value for the energy at which the temperature becomes negative are found. An explicit form for the structure function is derived and compared with the result of a Monte Carlo calculation. Good agreement is found for the negative temperature threshold prediction and for the general shape of the structure function. An equilibrium energy spectrum is calculated, which for positive temperatures, is the Debye–Huckel result; for negative temperatures it predicts an enhanced excitation of the lowest mode, corresponding to macroscopic charge separation.
30 citations
TL;DR: In this paper, the Hartree-Fock Hamiltonian was used as the zeroth order Hamiltonian for the perturbation equations of the EOM corresponding to ionization processes.
Abstract: The equations of motion (EOM) which correspond to electronic excitation or ionization events are analyzed within the framework of perturbation theory. The choice of the Hartree–Fock Hamiltonian as the zeroth order Hamiltonian permits the perturbation equations to be solved in a convenient closed form. A comparison of the results for excitation processes with those given by the random phase approximation (RPA) is made. The role of two particle–two hole excitation operators, which are absent in the RPA, is discussed. Finally, connections are made between the Green’s function approach to calculating ionization energies and the perturbation theory treatment of the EOM corresponding to ionization processes.
TL;DR: In this article, the angular distribution of small-angle scattering is calculated for collisions of polar molecules, and a semiclassical treatment of the inelastic scattering amplitude is used, with a random phase approximation for the strong coupling realm at small impact parameters and the Born approximation for very large impact parameters.
Abstract: The angular distribution of small‐angle scattering is calculated for collisions of polar molecules. As found in previous calculations of the total cross section, the magnitude and form of the scattering vary drastically with the amount of inelastic energy transfer between rotation and translation. Collisions with various orientations of the increments Δj1 and Δj2 in the rotational momenta of the two molecules also give markedly different contributions. A semiclassical treatment of the inelastic scattering amplitude is used, with a random phase approximation for the strong‐coupling realm at small impact parameters and the Born approximation for the weak‐coupling realm at very large impact parameters. A classical time‐dependent perturbation calculation is also carried out using a ’’flywheel’’ approximation which averages over the unperturbed rotational motion of the molecules during the collision. These small‐angle scattering calculations give good agreement with the angular distribution measurements on CsC...
TL;DR: In this paper, the coherent potential approximation (CPA) and the random phase approximation (RPA) were extended to the case of NiFe alloys and it was shown that D is very sensitive to the assumed exchange splitting in pure nickel and that within the RPA reasonable agreement with experiment is obtained only by assuming an unusually large value for this parameter.
Abstract: Previous numerical calculations for a model of nickel alloys, employing the coherent potential approximation (CPA) and the random phase approximation (RPA), are extended to iron alloys. It is shown that often the effective scattering potentials are sufficiently weak for a rigid band calculation of the spin wave stiffness constant D to be a good guide to the more elaborate CPA calculations. The case of NiFe alloys is re-examined in the light of a recent calculation by Riedinger and Nauciel-Bloch (ibid., vol.5, p.732 (1975)). It is shown that D is very sensitive to the assumed exchange splitting in pure nickel and that within the RPA reasonable agreement with experiment is obtained only by assuming an unusually large value for this parameter.
TL;DR: In this paper, the effect of exchange interaction between electrons on the electron-phonon interaction in metals was studied within the generalized random phase approximation, and the phonon frequency of a metal was found to be closely related to the magnetic susceptibility of the metal.
Abstract: The effect of the exchange interaction between electrons on the electron-phonon interaction in metals is studied within the generalized random phase approximation. The phonon frequency of a metal is found to be closely related to the magnetic susceptibility of the metal. The sound velocity of the jellium model, for instance, is inversely proportional to the square root of the paramagnetic spin susceptibility. In particular, in the jellium model the occurrence of a charge density wave and a spin density wave is found to be simultaneous. Finally, the electron-phonon coupling constant λ is found to be enhanced significantly by the exchange interaction.
01 Jan 1976
TL;DR: In this article, it was shown that the random phase approximation with exchange (RPAE) is only one out of several possible approximations and also that the RPAE can be improved by including double excitations accounting for relaxation of the frozen core, shake off and Auger transitions.
Abstract: A suitable subtitle for these lectures would be “Many-electron theory of photoionization in atoms” in order to indicate that the random phase approximation with exchange (RPAE) is only one out of several possible approximations and also that we shall focus attention on continuum photoionization processes rather than on transitions to bound states. A continuum photoionization cross section studied over a large range of energies gives information about the dynamical behaviour of the atomic electrons and theoretical calculations have to account for the whole range between very slow and very fast photoelectrons. The purpose of these lectures is to discuss the applicability of the RPAE in relation to the type of atom, the type of transition and the photoelectron energy considered. We shall also see examples of how the RPAE can be improved by inclusion of double excitations accounting for relaxation of the frozen core, shake off and Auger transitions.
TL;DR: In this paper, the critical behavior of sound propagation above T c in ferromagnetic metals was studied from an itinerant electron model with the generalized random phase approximation, and it was shown that the phonon frequency of a metal, both above and below T c, is related to the magnetic properties of the metal.
Abstract: The critical behavior of sound propagation above T c in ferromagnetic metals in studied from an itinerant electron model with the generalized random phase approximation. First, by using the Feynman diagrammatic method, the phonon frequency of a metal, both above and below T c , is related to the magnetic properties of the metal. Then, in the jellium model the velocity s and attenuation α q of sound above T c is found to be simply related to the paramagnetic spin susceptibility, χ mm , respectively as, s ∝χ mm -1/2 and α q ∝χ mm . When the temperature is very close to T c , however, above simple behavior of s and α q breaks down owing to the increased imaginary part of the phonon frequency. At T c , s does not vanish and correspondingly α q does not diverge.
TL;DR: In this article, a relativistic generalization of the random phase approximation is used to study the response of helium-like ions to electromagnetic perturbations, and the spectrum of the response function in this relativist theory contains allowed and forbidden transitions.
Abstract: A relativistic generalization of the random phase approximation is used to study the response of helium-like ions to electromagnetic perturbations. The spectrum of the response function in this relativistic theory contains allowed and forbidden transitions. The computed E1(21,3P1-11S0), M1(23S1-11S0) and M2(23P2-11S0) transition rates agree well with those obtained by refined calculations and with experiment. Accurate values are also obtained for the excitation energies of ions with large nuclear charges, where relativistic effects are of major importance.
TL;DR: In this article, the Bloch-Hasagawa equations were used to calculate the EPR susceptibility for the s-d exchange model and an earlier RPA calculation using a new method which unlike Anderson's random phase approximation enables the calculation to be performed for the finite temperatures corresponding to current EPR practice.
Abstract: The EPR susceptibility is calculated using a new method which unlike Anderson's random phase approximation, enables the calculation to be performed for the finite temperatures corresponding to current EPR practice. The dynamic susceptibility obtained is equivalent to the Bloch-Hasagawa equations designated 'case B', i.e. relaxation towards the instantaneous equilibrium, in agreement with the results for the s-d exchange model and an earlier RPA calculation. However, the interpretation of the parameters is different to that for the s-d exchange model (i) the effective s-d exchange contains contributions from covalent mixing, atomic exchange and the conduction electron-electron interaction responsible for conduction electron enhancement (ii) the impurity g factor becomes renormalized as compared with its bare or 'ionic' value (iii) the impurity-impurity spin interaction in the Anderson model contains direct covalent mixing contributions which do not occur in the s-d exchange model.
TL;DR: Magnetic dipole states in 208 Pb were calculated in random phase approximation using a configuration space which includes also 2 h ω excitations in this article, and they found very collective 1 + -resonances around 19 MeV and 25 MeV.
TL;DR: In this paper, a tight-binding Hamiltonian in a bonding-antibonding basis is used to evaluate the optical dielectric response, within the random phase approximation, for diamond and silicon.
Abstract: A tight-binding Hamiltonian in a bonding-antibonding basis is used to evaluate the optical dielectric response, within the random phase approximation, for diamond and silicon. The authors include the effects of local microscopic fields, and compare the results with experiment. They also discuss theoretically how local fields should affect the optical response, and why the next term beyond the random phase approximation gives only a negligible contribution to the response.
TL;DR: In this article, the positions of two surface plasma resonances in a layer metal particle containing a dielectric foreign nucleus are calculated within the random phase approximation, and the results obtained give a possible explanation of a recent experimental observation by Genzel et al.
TL;DR: In this paper, a macroscopic theory of isovector states is derived from a reduction of random phase approximation using Skyrme interactions and assuming a dipole transition density of the Goldhaber-Teller shape.
Abstract: A macroscopic theory of isovector states is derived from a reduction of random phase approximation. Using Skyrme interactions and assuming a dipole transition density of the Goldhaber-Teller shape, we find reasonable agreement with experimental excitation energies for the light nucleus $sup 16$O. The theoretical excitation energies for heavy nuclei are too high by a couple of MeV. The transition density may be given a general parametric form which includes the hydrodynamic model as well as the Goldhaber-Teller model. A variational calculation of the form of the transition density gives the Goldhaber-Teller shape for light nuclei, and a shape between the hydrodynamic and Goldhaber-Teller models for $sup 208$Pb. (AIP)
TL;DR: In this article, a discontinuous change of the ultrasonic attenuation coefficient as a function of the magnetic field which is recently observed in Bi around H = 100 kG by Yoshida et al. has been interpreted as coming from the discontinuous changes in the carrier number.
TL;DR: In this paper, the perturbation expansion for the response function is examined in order to provide a useful general theory of excitation energies, oscillator strengths, dynamic polarizabilities, etc., that is more accurate than the random phase approximation.
TL;DR: In this article, the spin wave stiffness constant for itenerant electron ferromagnetic transition metal dilute alloys was calculated in the Random Phase Approximation, using the method of effective magnon Hamiltonian, and the term in the magnon energy proportional to impurity concentration was calculated by summing up exactly a perturbational series.
TL;DR: In this article, generalized oscillator strengths and their first derivatives for zero momentum transfer (i.e. in the optical limit) are calculated for the helium atom in the framework of the random phase approximation with exchange.
Abstract: Generalized oscillator strengths and their first derivatives for zero momentum transfer (i.e. in the optical limit) are calculated for the helium atom in the framework of the random phase approximation with exchange. A good agreement with the experimental data of Backx and colleagues (1975) is obtained.
TL;DR: In this article, the Tamm-Dancoff and Random Phase Approximation (RPA) method was used to estimate the energies and transition properties of the even-even N = 28, 50 isotones and Z = 28.50, 82 isotopes.
Abstract: The energies and transition properties of the even-even N = 28, 50 isotones and Z = 28, 50, 82 isotopes are calculated in the framework of the Tamm-Dancoff and Random Phase Approximation, with an effective central interaction in an extended space consisting of two quasi-particle configurations for the open shell and particle-hole configurations for the closed core. Using the results of the Inverse Gap Equation Method, practically all the necessary input data (single quasi-particle energies, force strength) are extracted from the odd-mass nuclei. The ratios of the force components are kept to fixed values for all studied nuclei and no effective charge is used. An overall excellent agreement is obtained for the energies of the vibrational states. On the other hand, while the transition properties of the 3- states are always well reproduced, those of the 2+ and 4+ states are often too small by about one order of magnitude.
TL;DR: In this article, the dielectric polarization of an electron gas in strong magnetic field was calculated in the random phase approximation for finite temperatures and finite impurity concentrations for parameter values typical for semiconductors.
TL;DR: In this article, a dynamical transverse spin susceptibility is calculated in the random phase approximation on the Hubbard model including the electron-phonon interaction for the system of d -electrons and phonons.
Abstract: A dynamical transverse spin susceptibility is calculated in the random phase approximation on the Hubbard model including the electron-phonon interaction for the system of d -electrons and phonons. The magnon energy and its life time in the long wavelength wavelength are obtained up to the second order terms with respect to the coupling constant in the electron-phonon interaction. It is shown that the shift of the exchange stiffness constant due to phonons is proportional to the fourth power of the temperature except the region of very low temperature in which the zero-point fluctuations of phonons take part in. Furthermore, the inverse of the relaxation time of a magnon with wave vector q is shown to be proportional to q 4 . The imaginary part of the dynamical transverse spin susceptibility is numerically calculated for the wave vectors near the crossing point of magnon and phonon energies.