Third-order Contributions Research Articles

Interplay of disorder and anharmonicity in heat conduction: Molecular-dynamics study.

The main purpose of the present paper is to study the effect of third- and fourth-order anharmonicity on the heat conductivity in the high-temperature (i.e., classical or saturation) regime of disordered systems. We show that the fourth- and third-order contributions, respectively, enhance and lower the conductivity, which can be understood by a strengthening or weakening of the stiffness of the bonds in the system. On comparing the heat conductivity in percolating and compositionally disordered systems, we find that disorder loosening the structure (percolating systems) favors the effect of anharmonicity.

Many-body perturbation theory calculations of two-photon absorption in lanthanide compounds.

Third-order spin-orbit contributions to two-photon absorption rates were introduced by Judd and Pooler when the second-order theory was found to be inadequate to explain the experimental data for ${\mathrm{Gd}}^{3+}$ ions in ${\mathrm{LaF}}_{3}$. However, only one of the two perturbation terms that arise in thrid order was considered. When the omitted term is added, ``unlinked'' parts are canceled and the good agreement with experiment is lost. Inclusion of previously overlooked scalar two-electron contributions can restore the agreement between theory and experiment.

Intramolecular coupling effect in the refractive index for a simple three-level model of molecules diluted in water

We have calculated the first-, second-, and third-order contribution to the refractive index of a dilute aqueous solution of three-level molecules irradiated by an intense one-frequency external field. Each solute molecule is described by two coupled harmonic curves of electronic energies with the same force constant and with minima displaced in energy and nuclear coordinate. We assume that the intramolecular coupling mixes only the states corresponding to two near degenerate of the three levels considered. Important linear and nonlinear contributions of the solute molecules to the refractive index have been found, mostly in the so-called weak and intermediate coupling regions. © 1993 John Wiley & Sons, Inc.

Theoretical reproduction of the electronic Raman spectra of cerium ions. II. Hierarchy of the effective operators based on ab initio calculations.

The results of ab initio calculations performed for the ${\mathrm{Ce}}^{+3}$ ion doped in ${\mathrm{LuPO}}_{4}$ are presented. The numerical analysis is based on the third-order crystal-field approach introduced in the first paper of this series. In this approach the third-order effective operators originate from the intershell and intrashell interactions via the crystal-field potential. The relative importance of various effective operators is discussed in terms of the contributions evaluated within the perturbed-function approach. This means that the results presented here have been obtained for the complete radial basis sets. Thus, the second- and third-order contributions to the scattering amplitude contain the perturbing influence of the excited configurations n'd,n'f,n'g for all n', including the continuum states.

Density-functional-based linear and nonlinear polarizabilities of fullerene and benzene molecules.

To address recent experiments showing a relatively large off-resonant nonlinear optical response of the fullerene molecule, we have calculated the static electronic response of fullerene molecules. While our linear polarizability is in good agreement with experimental measurements, we find that the third-order contribution is approximately one or two orders of magnitude lower than the experimental measurements. Using the same theoretical method, we have calculated the first- and third-order polarizabilities of benzene and find good agreement between our results and other experimental and theoretical results.

Intensity of forbidden hyperfine ( Delta m=2) transitions in the electron paramagnetic resonance spectra of transition ions

Expressions are derived for determining the angular variation in the intensity of the forbidden hyperfine transitions ( Delta M=1, Delta m=+or-2) in the EPR spectra of transition ions. The intensities calculated using these expressions are compared with the predictions of Bleaney and Rubins and of Bir. It is found that third-order contributions arising from the nuclear spin operator as well as the quadrupole term are important in interpreting the intensity of forbidden hyperfine lines.

Impact of Drag‐Force Approximations on Spectral Wave‐Force Predictions

This article explores the issue of drag-force approximation through the examination of dimensionless spectral wave-force ratios. These dimensionless ratios were developed in an attempt to clarify when third-order approximations to the spectral drag force could be expected to significantly contribute to the predicted wave force. They represent ratios of the spectral wave force per unit length for rigid cylindrical elements. It was found that for low period values, those around the natural period of fixed offshore platforms, the magnitude of the third-order correction to the drag-force spectrum can be a significant percent of the first-order approximation. At higher periods, those in the range of deepwater or compliant platforms, the drag force dominates the total wave force and the magnitude of the third-order force contribution is significant. This finding is consistent with studies addressing the analysis of offshore platforms presented in the current open literature. Finally, changing the Keulegan-Carpenter number strongly influences the magnitude and the location of the low-period peak associated with the third-order drag-force term. Thus, for high NKC and low Hs, the third-order drag force could become an important consideration in wave-force computations.

Analysis of the 8S7/2 to 6P7/2 two-photon absorption transitions of Gd3+ in Gd(OH)3 in an applied magnetic field

The authors report a detailed analysis of the intensity and polarisation dependence of the 8S7/2 to 6P7/2 two-photon transition Stark components of Gd3+ in the concentrated magnetic insulator Gd(OH)3 under an applied magnetic field (up to 3.5 T) at very low temperature (2 K). The experimental technique consisted of detecting the ultraviolet 6P7/2 to 8S7/2 one-photon fluorescent emission resulting from two-photon excitation in the 6P7/2 states, using a single pulsed dye-laser beam. The standard second-order theory of Axe is shown to fail in explaining the relative intensities of the Stark components. This is especially true in the case of the Delta M=0 transitions for which strong disagreements are observed. It is shown that the introduction of the third-order contribution involving the spin-orbit interaction within the 4f65d states allows the experimental spectra to be reproduced in a correct way. Finally the effects of ion-ion interactions on the two-photon line profiles are discussed.

Third-order correlation theory of electronic Raman scattering for rare-earth ions in crystals. II. Numerical analysis for ions across the lanthanide series.

The importance of electron correlation effects in the theoretical description of electronic Raman scattering is demonstrated. The values of second- and third-order contributions to the scattering amplitude evaluated within the perturbed-function approach are analyzed. The discussion is based on the numerical results of exact ab initio calculations performed for ${\mathrm{Pr}}^{3+}$, ${\mathrm{Nd}}^{3+}$, ${\mathrm{Eu}}^{3+}$, ${\mathrm{Gd}}^{3+}$, ${\mathrm{Tb}}^{3+}$, and ${\mathrm{Tm}}^{3+}$ ions.

The structure of the Glauber third-order optical potential

The author considers the second-order and third-order contributions, V2 and V3, to a local optical potential for the scattering of electrons by an S-state atom, which is constructed so that the corresponding scattering amplitude reproduces the three first terms of the Born series in lowest order. It is shown that the structure of the third-order Glauber optical potential, introduced by Byron and Joachain (1981) to represent V3, reflects the local nature of V2.

Third order a b i n i t i o calculations of amplitudes of two-photon absorption for ions across the lanthanide series

The third-order electron-correlation theory of two-photon absorption in rare earth ions in crystals has been extended by the effective operators arising from doubly excited configurations. The approach defined in terms of one-particle effective operators has been applied to the Pr+3, Nd+3, Eu+3, Gd+3, Tb+3, and Tm+3 ions. The relative importance of third-order contributions and their properties across the lanthanide series are presented. The discussion is based on the numerical results of exact ab initio calculations performed within the perturbed-function approach.

Calculations combining the multiconfiguration Hartree-Fock method and many-body perturbation theory. III. Higher-order effects involving the correlation of the core

The multiconfiguration Hartree-Fock theory and many-body perturbation theory are combined in a calculation of the third-order contribution to the inner-shell correlation energy of the neutral beryllium atom. For this purpose, the contributions to the energy due to pair excitations from a MCHF reference state are expressed in terms of two-electron functions, and these functions are determined by solving numerically a pair equation. Good agreement is obtained with other accurate beryllium calculations.

Third order a b i n i t i o calculations of the f↔f transition amplitudes for ions across the lanthanide series

The behavior of various contributions to the f↔f transition amplitude defined up to the third order in perturbation theory is analyzed. Main attention is paid to the third-order contributions which are due to electron correlation inside the rare earth ion and arise from the static and dynamic models. The discussion is based on the numerical results of exact ab initio calculations performed for Pr+3, Nd+3, Eu+3, Gd+3, Tb+3, and Tm+3 ions.

Freezing in the density functional approach: Effect of third-order contributions

The widely used Ramakrishnan–Youssouff density functional theory of freezing (a functional expansion, usually truncated at second order, of the excess Helmholtz free energy Fex of the solid about Fex of the coexisting liquid) is extended in a straightforward manner to third order to study the convergence of the theory. The required three-particle direct correlation function of the liquid c(3) is obtained by using the weighted-density functional approximation to Fex as a generating functional. A freezing transition in the hard sphere system is obtained but the predicted coexistence conditions are much worse than those of the second-order theory and in poor agreement with simulations. The magnitude of the third-order contribution to the solid grand potential is typically about one-half of the second-order contribution. Expanding about the equal density liquid rather than the coexisting liquid includes a subset of terms exactly to all orders but fails to predict freezing at either second or third order. These results indicate that the convergence of the functional expansion is not sufficiently rapid to justify truncation at low orders. The generally good agreement predicted by the usual second-order theory is thus apparently fortuitous.

Problem of asymmetry in electronic Raman scattering of lanthanide (III) systems

In this work the influence of surrounding ligands on the asymmetric features of electronic Raman scattering (ERS) in lanthanide ions has been investigated. Within the independent systems model we have developed the theory, which takes into account both the static and dynamic coupling between the lanthanide ion and the ligands. The third-order contributions arising from these mechanisms have been carefully analysed. It is demonstrated that they are able to introduce noticeable corrections to the asymmetry resulting from the theory of Mortensen and Koningstein (ref. 1).

Hadronic production of gluinonium in three-jet events

The third-order supersymmetric QCD contribution to the high-energy hadronic production of gluino-gluino bound states is calculated. Several experimental cuts are proposed in order to increase the signal-to-background ratio. This ratio is shown to be 2 to 3 times larger in three-jet events than in two-jet events, reaching 5–7%. This gain in efficiency could be crucial in the case of limited statistics and an experimental two-jet mass resolution of a few GeV.

Third-order a b i n i t i o calculations of the intensity parameters for the Pr+3 ion in LaAlO3, NdAlO3, and LaCl3 hosts

The values of intensity parameters for the Pr+3 ion in LaAlO3, NdAlO3, and LaCl3 hosts evaluated with complete ab initio calculations based on the third-order f↔f transition theory are reported. In this theory, the intensity parameters, in addition to the standard second-order contributions, contain the static and dynamic third-order contributions which arise from electron correlation within the central ion. In the numerical procedure performed, all the one-particle effective operators which originate from singly excited intermediate configurations were included and the radial factors were evaluated within the perturbed-function approach. For the first time the discussion of the influence of electron correlation upon the values of intensity parameters is presented, and a comparison with experiment is made.

Third-order optical model analysis of e+or-H(2s), e+or-He(21S) and e+or-He(23S) elastic scattering at intermediate energies

The authors study the elastic scattering of electrons by the metastable states H(2s), He(21S) and He(23S) at intermediate energies within the framework of the third-order optical potential theory. The first-, second- and third-order contributions to the optical potential are analysed separately, and are compared with the corresponding quantities for e-H(1s) and e-He(11S) elastic scattering. Results for positron impact scattering are also presented.

Electron correlation third-order contributions to the electric dipole transition amplitudes of rare earth ions in crystals

A complete expression for the f↔f transition amplitude defined up to the third order in perturbation theory is presented. The third-order contributions are due to electron correlation inside the rare earth ion and arise from the static and dynamic models. The approach is formulated by means of double perturbation theory and in terms of effective tensor operators expressed by unit tensor operators. The discussion of the relative importance of various kinds of effective operators is based on the numerical results of test ab initio calculations performed within the perturbed function approach for the Pr+3 ion.

Electron-correlation third-order contributions to the electric dipole transition amplitudes of rare earth ions in crystals

Electron-correlation third-order contributions to the electric dipole transition amplitudes of rare earth ions in crystals