Showing papers on "Random phase approximation published in 1986"

Fundamentals of inelastic electron scattering

Abstract: 1 Classical Scattering Theory- 11 Elastic Cross Sections- 12 The Deflection Function- 13 Scattering on a Hard Sphere- 14 The General Case- 15 Rutherford Scattering- 16 Singularities- 17 Inelastic Cross Sections- 18 The Ramsauer-Townsend Effect- 19 On the Validity of the Classical Description- 2 Quantum Mechanical Scattering Theory- 21 Absorption Edges- 22 The Differential Cross Section- 23 The Dynamic Form Factor- 24 The Generalized Oscillator Strength - 25 Rutherford Scattering- 26 The Bethe Differential Cross Section- 27 The Hydrogenic Approach- 28 The Bethe Approximation- 29 Zonal Harmonics Expansion- 210 Qualitative Interpretation- 211 The Total Elastic Cross Section- 212 The Ramsauer-Townsend Effect- 3 Practical Aspects of Absorption Edge Spectroscopy- 31 A Survey of Applications- 32 Microanalysis- 33 Electron Compton Scattering- 34 Site-specific Excitations- 35 Extended Energy Loss Fine Structure (EXELFS)- 4 Electrodynamics in Homogeneous, Isotropic Media- 41 Fourier Transform- 42 Linear Response of a Medium- 43 The Maxwell Equations- 44 The Dielectric Function- 45 The Drude Model- 46 Charge Oscillations in a Metal- 5 Some Details on Charge Oscillations- 51 Screening- 52 Plasmons- 53 Plasmon Dispersion- 54 Boundaries- 55 Surface Oscillations- 56 The ATR-Method- 57 On the Restricted Validity of the Fresnel Equations- 58 The Differential Cross Section- 59 Energy Loss Function- 6 Quantum Mechanical Preliminaries- 61 Summary of Important Facts- 62 The Lippman-Schwinger Equation- 63 The Green Operator- 64 The Dyson Equation- 65 Green Operators in the Time Domain- 66 Relation of G0 to the Time Evolution Operator- 67 Second Quantization- 68 Operators in Second Quantization- 69 The Perturbation Series in Graphical Representation- 610 An Example- 611 The Coulomb Interaction- 7 Quantum Mechanical Description of the Electron Gas- 71 The Jellium Hamiltonian- 72 Sommerfeld Non-interacting e--Gas- 73 Hartree Approximation (HA)- 74 Hartree-Fock Approximation (HFA)- 75 Why Higher Order Perturbation Theory Does not Work- 76 The Random Phase Approximation (RPA)- 77 Electron Scattering- 78 Polarization Diagrams- 8 Beyond Simple Models- 81 Solid State Effects- 82 Ion-Electron Interactions- 83 Multiple Scattering- References- Author Index

Random-phase-approximation study of the response function describing optical second-harmonic generation from a metal selvedge.

Abstract: Optical second-harmonic generation in centrosymmetric metals stems from the breaking of inversion symmetry in the selvedge and from nonlocal effects. In the present work a random-phase-approximation description of the nonlocal nonlinear conductivity tensor of an inhomogeneous jellium is given. Main emphasis is devoted to a study of the electric dipole response from the selvedge, and to the magnetic dipole and electric quadrupole responses from the profile region and the bulk. A detailed analysis of the tensor symmetry schemes associated with the p\ensuremath{\cdot}A and A\ensuremath{\cdot}A interactions is presented. Dipole and quadrupole transitions are identified, and the role of direct and indirect quantum processes is discussed. On the basis of the so-called infinite-barrier model, a few numerical results are given.

Photoionization cross section calculations of HCl by the Stieltjes technique

Abstract: Partial and total valence- and inner-shell photoionization cross sections of HCl are calculated in the random phase approximation employing an extended basis set and the Stieltjes imaging procedure. Results of independent-channel as well as multi-channel calculations in the static-exchange approximation are reported for comparison. The generally good agreement with recent experimental measurements indicates that the random phase approximation provides an efficient description of photoionization channel coupling. The calculated vertical spectra in the ‘discrete’ region of valence- and inner-shell are also reported.

Analytic dipole moment geometric derivatives from nuclear electric shielding in molecules

Abstract: We present ab initio calculations of dipole moment geometric derivatives for some first‐row atom hydrides. Dipole moment derivatives, in terms of atomic polar tensors (APT), are equivalent to nuclear electric shieldings and were determined analytically, within the random phase approximation (RPA). Polarized basis sets were used, which give accurate results with small computer effort.

Random-phase approximation and broken symmetry

Abstract: The validity of the random-phase approximation (RPA) in broken-symmetry bases is tested in an appropriate many-body system for which exact solutions are available. Initially the regions of stability of the self-consistent quasiparticle bases in this system are established and depicted in a 'phase' diagram. It is found that only stable bases can be used in an RPA calculation. This is particularly true for those RPA modes which are not associated with the onset of instability of the basis; the authors see that these modes do not describe any excited state when the basis is unstable, although from a formal point of view they remain acceptable. The RPA does well in a stable broken-symmetry basis provided one is not too close to a point where a phase transition occurs. This is true for both energies and matrix elements.

The Thermal Linear Response Theory for the Dissipative High Spin Quantum States

Abstract: The thermal linear response theory with the inclusion of the non· Markovian effect is formulated based on the thermal cranked Hartree·Fock·Bogoliubov (THFB) theory. We propose the proper strength function which is suitable to be compared with y-ray spectra from giant resonances at high spin and high temperature. A clarification is given of the relation between the stability condition of the THFB solution and the equation in the thermal random phase approximation (TRPA).

Low-energy photoionization of alkali-metal atoms: Relativistic random-phase-approximation calculations

Abstract: A complete theoretical survey of low-energy photoionization cross sections, angular asymmetry, and spin-polarization parameters for the ground states of the alkali-metal atoms Li, Na, K, Rb, and Cs, including virtual core excitations in a gauge-independent relativistic random-phase approximation (RRPA) is presented and compared with length- and velocity-form Dirac-Fock results and with available experimental data. The ab initio RRPA formulation substantially improves the agreement of cross sections with experiment at energies above the Cooper minimum.

Random Phase Approximation Spin - Isospin Nuclear Response In The Deep Inelastic Region.

Abstract: The spin-isospin volume responses of a finite nucleus are evaluated in the random phase approximation framework, utilizing a harmonic oscillator basis. Particular emphasis is given to the mixing between the longitudinal (\ensuremath{\sigma}\ensuremath{\cdot}q) and transverse (\ensuremath{\sigma}\ifmmode\times\else\texttimes\fi{}q) couplings, which arise at the nuclear surface. We show that it reduces somewhat the contrast between the two spin responses. We compare the calculated transverse response with the experimental one extracted from deep inelastic electron scattering.

Structural phase transitions in layered transition metal compounds

Abstract: Microscopic Theory of Structural Phase Transitions in Layered Transition-metal Compounds.- 1. Introduction.- 2. General theory of electron-lattice interaction and lattice dynamics based on the nonorthogonal tight-binding approximation.- 2.1. Electron-lattice interaction.- 2.2. Generalized electronic susceptibility.- 2.3. Interatomic force, phonon dispersion, and lattice instability.- 2.4. Electronic structure of the CDW state.- 2.5. Other methods of lattice dynamical calculation.- 3. 1T-type transition-metal dichalcogenides.- 3.1. TiSe2.- 3.1.1. Formation of superlattice.- 3.1.2. Electronic structure.- 3.1.3. Electron-lattice interaction and generalized electronic susceptibility.- 3.1.4. Lattice dynamics.- 3.1.5. The CDW state.- 3.2. TiS2.- 3.3. Mixed compounds.- 3.4. VSe2 and CrSe2.- 3.4.1. Summary of experimental evidence regarding structural transformation.- 3.4.2. Electronic structure.- 3.4.3. Electron-lattice interaction and lattice instability.- 3.5. TaS2 and TaSe2.- 3.5.1. Summary of successive phase transitions.- 3.5.2. Electronic structure.- 3.5.3. Lattice instability.- 4. 2H-type transition-metal dichalcogenides.- 4.1. Formation of superlattice.- 4.2. Electronic structure.- 4.3. Electron-lattice interaction and generalized electronic susceptibility.- 4.4. Lattice dynamics and phonon anomaly.- 4.5. Discussion.- 5. Transition-metal trichlorides MCl3 (M = Ti, V, Cr).- 5.1. Summary of experimental results.- 5.2. Electronic structure.- 5.2.1. Tight-binding calculation.- 5.2.2 The Wannier function.- 5.2.3 Estimation of band parameters.- 5.3. Electron-lattice interaction and lattice instability in TiC13.- 5.3.1. Generalized electronic susceptibility.- 5.3.2. Effective d-electron-lattice interaction and lattice instability.- 5.3.3. The transition temperature.- 5.3.4. Some remarks regarding VCl3 and CrCl3.- 5.4. Phase transition.- 5.4.1. Calculation of free energy.- 5.4.2. Magnetic susceptibility.- Appendix A. Perturbation theory in nonorthogonal representation.- Appendix B. Electronic free energy expansion in the adiabatic approximation and derivation of generalized electronic susceptibility.- Appendix C. Froehlich model and Bloch model.- Appendix D. Expressions for the overlap and transfer integrals and their derivatives in terms of Slater-Koster integrals.- Microscopic Theory of Effects of Lattice Fluctuation on Structural Phase Transitions.- 1. Introduction.- 2. Formulation.- 2.1. Hamiltonian and Green's functions for electron and phonon systems.- 2.1.1. Hamiltonian.- 2.1.2. Thermal Green's functions for electrons.- 2.1.3. Thermal Green's functions for phonons.- 2.1.4. Self-energy ? and polarization function ?.- 2.2. Random phase approximation.- 2.3. Mode-mode coupling.- 2.3.1. Lattice fluctuation.- 2.3.2. Transition temperature.- 2.3.3. Coherence length.- 2.3.4. Electron self-energy.- 2.4. Spin susceptibility and electrical resistivity.- 3. Effects of lattice fluctuation on CDW transition.- 3.1. Model.- 3.2. Calculated results for the 1D system.- 3.3. Calculated results for the 3D system.- 4. Effects of lattice fluctuations on the electronic density of states, spin susceptibility, and electrical resistivity.- 4.1. The 1D system.- 4.2. The 3D system.- 5. Supplementary remarks.- Appendix A. Feynman rules for ? and ?.- Appendix B. Evaluation of frequency sum with the use of contour integral in the complex plane.- Phenomenological Landau Theory of Charge Density Wave Phase Transitions in Layered Compounds.- 1. Introduction.- 2. Construction of Landau free energy.- 2.1. 2H-TaSe2.- 2.2. 1T-TaS2 and TaSe2.- 3. A simple example: single-q CDW.- 3.1. Successive phase transitions and discommensurate state.- 3.2. Fluctuation modes.- 4. 2H-TaSe2.- 4.1. Basic features of phase transitions.- 4.2. Single-layer properties.- 4.3. Commensurate phases with various symmetries.- 4.4. Discommensuration structures of two-layer stacking.- 4.5. Reentrant lock-in transition caused by pressure.- 4.6. Discommensuration diagram and dislocations.- 4.7. Fluctuation modes.- 4.8. 2H-NbSe2.- 5. 1T-TaS2 and TaSe2.- 5.1. Brief summary of observed phase transitions.- 5.1.1. 1T-TaS2.- 5.1.2. 1T-TaSe2.- 5.2. Single-layer properties.- 5.2.1. Commensurate state.- 5.2.2. Incommensurate states and discommensuration structures.- 5.3. Three-dimensional orderings of charge density waves.- 5.3.1. Commensurate states.- 5.3.2. Incommensurate and discommensurate states.- 5.4. New phase of 1T-TaS2.- 6. Concluding remarks.- Charge Density Waves in the Transition-metal Dichalcogenides: Recent Experimental Advances.- 1. Introduction.- 2. Charge density wave transformations observed in the Group Vb compounds.- 2.1. 2H structures.- 2.2. 1T structures.- 3. The 2a0 superlattice in the Group IVb compound 1T-TiSe2.- 3.1. General features.- 3.2. Infrared reflectivity-free carrier and phonon effects.- 3.3. Phonon dispersion at low temperature.- 3.4. Angle-resolved photoemission and the electronic structure of TiSe2.- 3.5. The transformed band structure of TiSe2.- 4. Recent developments.- Index of Names.- Index of Subjects.

Two photon bound-bound electronic transition calculations in molecules

Abstract: Calculations of the transition probability for the two photon excitation from the ground to some of the first excited electronic states in both NH3 and HF are presented. The transitions are taken to be vertical and a random molecular orientation is assumed. The transition moments needed to evaluate the transition amplitudes are computed by using the random phase approximation (RPA), that directly supplies the initial state-intermediate states one-electron transition density matrices and the excitation energies, while the intermediate states-final state one-electron transition density matrices are obtained from the RPA results through an equation of motion method (EMM) technique. The effect of mixing of the excitation channels is investigated. For each chosen final state enough data are supplied to give a thorough account of the dependence of the transition probability upon the polarization of the radiation and the experimental geometrical set-up. The calculations are performed using both the length and th...

Delta isobars in finite nuclei and nuclear matter.

Abstract: Random phase approximation calculations using a microscopic residual interaction (G matrix) are performed for /sup 16/O and /sup 12/C. The influence of ..delta.. isobars on isovector magnetic states is investigated and found to be small since many-body renormalization effects for the coupling of ph to ..delta..h states (g/sub NDelta//sup prime/) are considerably smaller in finite nuclei than in nuclear matter. Energies of isovector states and collective isoscalar states are described reasonably well. The electromagnetic transition strength is in general overestimated for both magnetic and electric transitions.

Impact parameter dependence of the electronic stopping in proton-solid-state atomic collisions

Abstract: In the local density approximation (LDA) the stopping power caused by the target electrons is calculated considering the response of an electron gas. Beyond the random phase approximation (RPA) the interaction of the electrons (exchange and correlation effect) is described by the dynamic local field correction. The free atom electron density is modified according to the Gertner model. Considering the interaction between the screened target nucleus and the proton as a classical two body scattering problem, the impact parameter dependence of the “friction force” is determined. The effective stopping power is calculated performing averaging over the volume of the target atom and over impact parameter.

Magnetic fluctuation spectra of very weak itinerant ferromagnets

Abstract: Neutron scattering studies have been performed in the weak ferromagnets Ni 3 Al and ZrZn 2 , and in the nearly ferromagnetic metal Ni 3 Ga. In the best studied material Ni 3 Al, the differential cross section above T c may be understood in terms of the scattering from thermal magnetic fluctuations characterised by a relaxation frequency spectrum approximately of the form Г( q ) = γ q (Χ -1 + cq 2 ), as expected in the random phase approximation, where 0.02 ≲ q ≲ 0.15 A -1 is the scattering wavevector, γ and c are constants, and χ is the measured bulk susceptibility. Below T c and at small q the cross section may be described in terms of thermal spin waves with a stiffness D = g μ B cM which in first approximation renormalises with temperature in proportion to the bulk magnetisation M . The overall scattering data may be well represented in this material solely in terms of two microscopic parameters γ and c . This description is also found to be qualitatively consistent with small angle scattering data in the paramagnetic states of ZrZn 2 and of Ni 3 Ga.

Infrared-laser excitation of the internal vibrational mode of a diatomic molecule adsorbed on a metal surface.

Abstract: : The infrared laser excitation of the internal vibrational mode of a diatomic molecule adsorbed on a metal by electron hole excitations. Simple expressions for the populations of the vibrational levels, the mean number of vibrational quanta and the rate of energy transfer between the infrared laser and the metal surface at the steady state are derived. an equation of evolution can readily be solved numerically to determine the time necessary to reach this steady state. The criteria of applicability of the Markov approximation (which leads to the golden rule) is clearly established, where it is seen that this approximation may not be used to compute the evolution of the populations of the vibrational levels. The random phase approximation is shown to give the correct kinetic equation for the populations of the vibrational levels. The excitation of carbon monoxide adsorbed on a copper surface is analyzed quantitatively.

Self-consistent relativistic band calculations and the optical conductivities of Ba and Eu

Abstract: The energy band structures for BCC metals Ba and Eu are calculated by the self-consistent symmetrised relativistic APW(SRAPW) method. A one-electron potential is constructed on the basis of the local density approximation. The correlation potential for 4f electrons of Eu is separately treated so as to give the position of the 4f level expected from XPS. Non-relativistic SAPW calculations for Ba and Eu are also carried out for the purpose of comparison. The Fermi surfaces and the extremal cross sections for Ba and Eu are calculated by the SRAPW method and the results are compared with previous theoretical and experimental results. The characteristic features on the Fermi surfaces for Ba and Eu are examined and a remarkable d-like character of the Fermi surface is indicated. The results of the SAPW band calculation is applied for calculations of the optical conductivities within the random phase approximation (RPA) for Ba and Eu in the energy range 0-10.5 eV. The theoretical results are in fairly good agreement with experimental ones. In the case of Eu, it is indicated that the transitions from the 4f states are important to reproduce the experimental results in the region around 7 eV. The effects of self-energy correction on the optical conductivities are phenomenologically considered. It is shown that the different structure observed above 4.5 eV in experiments for Ba and Eu is reasonably explained, if transitions from 4f electrons in Eu are taken into account. This result supports positively the conjecture that the 4f electron levels of Eu locate at the energy region predicted from XPS.

Ab initio polarisation potential in the random-phase approximation: application to e--H2 elastic scattering

Abstract: The interaction potential of e--molecule scattering is formulated in terms of the optical potential of many-body theory. In particular, dynamic polarisation effects directly follow from an RPA solution to the target linear response function. It is further pointed out that such a level of accuracy can most easily be obtained by simply working within the formalism of Hartree-Fock theory. An adiabatic approximation to the full optical potential is finally derived and explicitly applied to the e--H2 system, showing good agreement with alternative ab initio formulations of the literature.

Rotating transverse nuclear helimagnetism in CaF2. II. Theoretical approximations

Abstract: For pt.I see ibid., vol.19, p.2275 (1986). The authors describe two approximate methods for the study of rotating transverse helimagnetism in high field in CaF2: the random phase approximation (RPA) and a physical model based on the fact that the Weiss field at any nuclear site is produced by distant spins. Both methods predict the helical structure to be stable in zero effective field, and the physical model predicts the occurrence of a mixed longitudinal and transverse phase in non-zero effective field. The rate of thermal mixing upon irradiation of the rare 43Ca spins with the 19F spins is analysed through RPA, and the shape of the NMR line of the ordered 19F spins is analysed through the physical model.

Random-phase-approximation calculations and residual interactions in the sigma tau channel.

Abstract: We compare numerical results for renormalized spin-isospin matrix elements within the random phase approximation. Extended calculations are carried out for a pionlike excitation in a finite nucleus; the effects of contact versus momentum-dependent residual interactions, and of \ensuremath{\Delta}-h configurations, are demonstrated. We point out the implications of our results on nuclear structure calculations, where such effects are sometimes neglected. The role of the finite geometry of the system is crucial in determining the features of the spin-isospin responses. We emphasize that a crucial test of the theory can only be achieved through a direct comparison of the longitudinal and transverse channels.

Coincident electrofission of 238U at q

Abstract: We have measured the coincidence cross sections /sup 238/U(e,e'f) at three values of momentum transfer (qroughly-equal0.26, 0.40, and 0.55 fm/sup -1/) over the range from 5 to 23 MeV in excitation energy; these values of q correspond approximately to the first maxima of the electric dipole, quadrupole/monopole, and octupole form factors, respectively. The angular distribution of fission fragments is peaked along the direction of q near fission threshold, indicating the dominance of K -- 0 states, but becomes isotropic above 10 MeV. We have integrated our cross sections over fission angle and compared them to recent calculations of multipole strength derived in the quasiparticle random phase approximation. Using model-dependent form factors generated from the Tassie model and the quasiparticle random phase approximation, we have extracted strength functions for the lowest electric multipoles. The deduced E1 strength agrees well with photofission results for reasonable choices of the model form factors. The E2/E0 distribution displays resonant structures at 10 and 13 MeV which agree in position with the collective E2 and E0 strength, respectively, predicted in the quasiparticle random phase approximation. If we make such an assignment for the multipolarity of these two structures, the observed E0 strength agrees with the theoreticalmore » prediction, whereas the E2 strength is low by a factor of 2-3. Higher order multipoles also contribute substantially to the cross section at our highest value of q.« less

Two-photon transition probability calculations: electronic transitions in methane

Abstract: Results obtained in the calculation of the transition probabilities for the two-photon excitation from the ground to some low-lying excited electronic states in methane, under the hypothesis of vertical transitions of randomly oriented molecules, are accounted for. The one-electron transition density matrices of interest in the computation are obtained by a non-standard application of the random phase approximation (RPA). A comparison between the results obtained both by allowing and by suppressing the coupling of the excitation channels is presented. For each final state the transition rate for a particular choice of the photon polarisation parameters is displayed. This supplies all information needed to compute the transition rates at each photon energy for every possible combination of geometrical arrangement and polarisation choice. Both length and velocity forms of the perturbing operator are employed in the calculations.