Resonance Approximation Research Articles

Parameterisation of symmetrical peaks in capillary electrophoresis using [3/2]-type rational approximants

The peaks in data from electrophoresis are parameterised in terms of a resonance model. The method we describe is based on forming a rational interpolant to the data. The interpolant is converted to a resonance approximation for symmetrical peaks; the method is found to discriminate successfully against formation of a resonance approximations to asymmetrical peaks. The method would also apply to equally good quality data from GC, LC and NMR.

Monte Carlo simulation of equilibrium L1 ordering in FePt nanoparticles

First, second, and third nearest-neighbor mixing potentials for FePt alloys were calculated from first principles using the Connolly–Williams approach. Using the mixing potentials obtained in this manner, the dependency of equilibrium L10 ordering on temperature was studied for bulk and for a spherical nanoparticle with a 3.5-nm diameter at equiatomic composition by use of Monte Carlo simulation and the analytical ring approximation. The calculated order-disorder temperature for bulk (1495–1514K) was in relatively good agreement (4% error) with the experimental value (1572K). For nanoparticles of finite size, the (long-range) order parameter changed continuously from unity to zero with increasing temperature. Rather than a discontinuity indicative of a phase-transition we obtained an inflection point in the order as a function of temperature. This inflection point occurred at a temperature below the bulk phase-transition temperature and which decreased as the particle size decreased. Our calculations predict that 3.5-nm diameter particles in configurational equilibrium at 600°C (a typical annealing temperature for promoting L10 ordering) have an L10 order parameter of 0.83 (compared to a maximum possible value equal to unity). According to our investigations, the experimental absence of a (relatively) high L10 order in 3.5-nm diameter nanoparticles annealed at 600°C or below is primarily a problem of kinetics rather than equilibrium.

The longitudinal and transverse nuclear responses within the RPA framework

The longitudinal and transverse nuclear responses to inclusive electron scattering reactions are analysed within the random phase approximation (RPA) framework. Several residual interactions are considered and it is shown that the exchange terms in the RPA make it very difficult to find an effective residual interaction capable of reproducing simultaneously the quasielastic peak of both the longitudinal and transverse responses. By means of a simplified model it is illustrated that the residual interaction used in a ring approximation must fulfil some restrictions in order to qualitatively reproduce the full RPA results.

Quantum unified theory applied to Ly$\mathsf{\beta}$, Lyγ and Lyδ electronic Stark broadening

New quantum calculations for the Ly β , Ly γ , Ly δ profiles perturbed by electron collisions are obtained from the unified one-perturber theory in the exact resonance approximation (Tran-Minh et al. 1975, J. Phys. B: Atom. Molec. Phys., 8, 1810; Feautrier et al. [CITE], J. Phys. B: Atom. Molec. Phys., 9, 1871). This accounts for the-long range dipole interaction. The profiles are obtained by summing the partial contributions of each total angular momentum L T . It appears that there is a threshold $L_{\min}$ below which some eigenchannels become complex and are not well described by the exact resonance method. To overcome this problem, the contribution of the first angular momenta is estimated by taking into account the real eigenvalues and by neglecting the complex ones. Estimation of the error due to this systematic underestimation of the profile is given. Density effects due to the Debye screening are found in the near wings.

Mixed-Potential Volume Integral-Equation Approach for Circular Spiral Inductors

The electromagnetic behavior of circular spiral inductors on layered substrates is analyzed by using the concentric ring approximation. The problem is formulated in terms of mixed-potential volume integral equations. The latter are semianalytically solved within the quasi-one-dimensional approximation. The result is a fast computationally efficient model, which takes into account substrate RF loss, as well as nonuniform current density distribution across inductor windings. The results are in good agreement with experimental data from various inductors on both low- and high-resistivity silicon substrates.

The influence of orientation and strength of external magnetic field on the time dependences of populations of atomic levels for Lamda systems

AbstractThe theory of interaction of intense laser fields with multilevel atoms in external constant magnetic fields is applied to analysis of the dependences of the populations on time, on detuning of laser frequency, on magnetic field orientation, and strength for spontaneous decay on the levels of thermostat. Solving the Schrödinger equation for the “atom in magnetic field + radiation field” system in resonant approximation we have obtained the probability of the population of common level for a generalized Λ system (e.g., 6P1/2‐7S1/2‐6P3/2 levels of Tl atoms). The results of computer simulations permit the investigation of the peculiarities of coherent population trapping in such system. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Intersubband gain in a biased superlattice

Intersubband transitions in a superlattice under homogeneous electric field is studied within the tight-binding approximation. Since the levels are equi-populated, the non-zero response appears beyond the Born approximation. Calculations are performed in the resonant approximation with scattering processes exactly taken into account. The absorption coefficient is equal zero for the resonant excitation while a negative absorption (gain without inversion) takes place below the resonance. A detectable gain in the THz spectral region is obtained for the low-doped $GaAs$-based superlattice and spectral dependencies are analyzed taking into account the interplay between homogeneous and inhomogeneous mechanisms of broadening.

Resonance approximation and charge loading and unloading in adiabatic quantum pumping

Quantum pumping through mesoscopic quantum dots is known to be enhanced by resonant transmission. The pumped charge is close to an integer number of electrons when the pumping contour surrounds a resonance, but the transmission remains small on the contour. For noninteracting electrons, we give a quantitative account of the detailed exchange of electrons between the dot and the leads (to the electron reservoirs) during a pumping cycle. Near isolated distinct resonances, we use approximate Breit-Wigner expressions for the dot's Green function to discuss the loading/unloading picture of the pumping: the fractional charge exchanged between the dot and each lead through a single resonance point is related to the relative couplings of the dot and the leads at this resonance. If each resonance point along the pumping contour is dominated by the coupling to a single lead (which also implies a very small transmission), then the crossing of each such resonance results in a single electron exchange between the dot and that lead, ending up with a net quantized charge. When the resonance approximation is valid, the fractional charges can also be extracted from the peaks of the transmissions between the various leads.

Statistical-thermodynamic description within the ring approximation. I. Lattice-gas model

The general method is elaborated for the statistical-thermodynamic description within the ring approximation of the lattice gas with a complex crystal lattice and with nonpair atomic interactions of any order and effective radii of action. The ring approximation corresponds to the first order of a modified thermodynamic perturbation theory under the choice of the inverse effective number of atoms interacting with one fixed atom as a small parameter of expansion. By the elaborated method one can calculate the complete phase diagram of the lattice gas as well as the correlation effects in both disordered and long-range ordered states of it. The elaborated method is general and analytically simple. The corresponding analytical expressions do not change their form at an increase of the effective radius of atomic interactions and are valid in case of any superstructure. The number of the ``variational'' parameters for minimization of the free energy is considerably fewer than that within the cluster-variation method and are determined by the type of the superstructure rather than by the value of the effective radius of atomic interactions. Due to the analytical nature of the ring approximation, the time for calculations within it is much less than that of the Monte Carlo simulation. By a comparison with the results of the Monte Carlo simulation the high numerical accuracy of the ring approximation is demonstrated in wide temperature-concentration intervals. The tendency of increase of the numerical accuracy of the ring approximation with increase of the effective radius of atomic interactions is shown. The applicability of the ring approximation is discussed. The obtained results may be useful for a description of solid solutions, alloys, magnetics, fluids, and amorphous materials.

Statistical-thermodynamic description within the ring approximation. II. Ising model

The results obtained previously [R. V. Chepulskii, Phys. Rev. B 69, 134431 (2004)] within the ring approximation in the case of the lattice gas model are generalized to the case of the Ising model with a complex crystal lattice and arbitrary magnetic order. The nonpair spin interactions of any order and effective radii of action are taken into account. The verification of the numerical accuracy of the ring approximation in the cases that are typical at consideration of the Ising model is performed.

Z-scaledK-shell dielectronic recombination rate coefficients

State-specific dielectronic recombination (DR) rate coefficients from ground states of H- and He-like Al, Ti, Ni, Kr, and Mo ions have been calculated in the isolated resonance and intermediate coupling approximation. The data generated for these calculations consists of energies of singly and doubly excited states, radiative rates, autoionization rates, and dielectronic recombination branching ratios. A Hartree-Fock method that includes relativistic corrections was employed in order to carry out the calculations. Three parameter fits to the data were then made using the Al, Ti, and Kr data to obtain scaling relations that enable one to calculate similar data for other ions by interpolation in the range between Al and Kr and somewhat beyond by extrapolation. The scaling accuracy was verified by comparing the scaling relation predictions to detailed data obtained for Ni and Mo calculations. The results obtained also compared well with other published work in which total ground state to ground state dielectronic recombination rates were calculated. The DR rate coefficients that are calculated from the scaled DR data are generally most accurate for intermediate to high-temperature collisional plasmas. However, in low-temperature photoionized plasmas, significant DR contributions come from the $\ensuremath{\Delta}n=0$ core excitations that are not present for K-shell recombination and thus one should expect the Z scaled DR rates to be accurate for any range of temperatures of interest.

A Heuristic Description of Internal Wave Dynamics

The oceanic internal wave spectrum has long been interpreted as being shaped by nonlinear processes. The empirical Garrett and Munk synthesis of oceanic observations is E(m, v) } Nm22v 22 at high wavenumber and frequency. Results of both approximate analytic and numerical estimates of weak nonlinear interactions under the resonant interaction approximation have previously been interpreted as implying the dominance of scaleseparated interactions and that the Garrett and Munk spectrum is stationary with respect to the nonlinear interactions. However, dimensional analysis cobbled together with several basic observational constraints requires a stationary spectrum of E(m, v) } Nm22v 23/2 at high vertical wavenumber and frequency. Given this stationary spectrum, dimensional analysis and extant data are used to infer a flux representation for the spectral transports. The resulting semiempirical flux laws can be described as a relaxation to the stationary power laws. The stationary spectrum is consistent with energy sources at low frequencies and dissipation at higher frequencies and vertical wavenumber. The analysis is then extended to include vertically asymmetric wave fields. Vertical wavenumber spectra of horizontal velocity that exhibit a difference between rotary (clockwise and counterclockwise phase rotation of the velocity vector with depth) spectra at large wavelengths tend to be symmetric at smaller scales. This pattern is hypothesized to be a result of nonlinearity within the wave field. In particular, vertical symmetry is linked here to the issue of momentum conservation. A backscattering process is invoked to achieve momentum conservation. This representation of nonlinearity is used in a numerical scheme to assess the spatial evolution of a bottom-generated wave field. The predicted patterns of relaxation and vertical symmetry are in reasonable agreement with finescale observations above rough bathymetry in the Brazil Basin.

Variational perturbation approach to the Coulomb electron gas

The efficiency of the variational perturbation theory [Phys. Rev. C {\bf 62}, 045503 (2000)] formulated recently for many-particle systems is examined by calculating the ground state correlation energy of the 3D electron gas with the Coulomb interaction. The perturbation beyond a variational result can be carried out systematically by the modified Wick's theorem which defines a contraction rule about the renormalized perturbation. Utilizing the theorem, variational ring diagrams of the electron gas are summed up. As a result, the correlation energy is found to be much closer to the result of the Green's function Monte Carlo calculation than that of the conventional ring approximation is.

Higher order corrections to an iterative approach for approximating bubble distributions from attenuation measurements

A formal theory exists for determining sound attenuation from a known distribution of bubble sizes in the ocean; however, an integral equation must be inverted if attenuation is given and the distribution of bubbles is not. An approximate distribution can be determined based on the resonant bubble approximation (RBA). An iterative approach, for which the RBA represents the zeroth iteration, was proposed and carried out to the first iteration in a previous paper . It was suggested that additional iterations would improve the bubble-distribution results. Here we formulate the procedure to carry the results to a higher order and demonstrate, based on a theoretical distribution of a multiple power law form, the improvements in successive approximations of the bubble distribution to the fourth iteration level. A recursion relation is developed that allows one to carry the iteration out to an arbitrary order. It is shown that regions of the distribution that change in the power-law exponent are places where the higher order corrections improve the results the most.

Approximating multileg processes: Higgs production via W-fusion

Meaningful approximations for multileg processes at tree level are constructed which circumvent the problems of unitarity violation and gauge invariance. In this article we study the LHC: pp → ZZ + 2 jets + X and the Linear Collider: e+e− → ZZνeν̄e processes both of which contain the W-fusion scattering process for off-shell Ws. Using the pinch technique the signal and background, which contribute coherently, are separated in a well defined and gauge invariant way thus defining a resonant approximation which behaves well at high energies. The speed of the numerical calculation is greatly reduced compared to the lengthy calculation of the complete set of diagrams while at the same time the approximations describe very well the full result not only close to the resonance but also beyond it, as shown in various differential distributions of the cross section. The problem of regulating the resonant Higgs diagram is treated both with the naïve approach of adding a constant width to the Higgs propagator and with the minimal field theoretic approach of dressing both the Higgs propagator and the ZZH vertex with their one loop imaginary parts, both fermionic and bosonic, as calculated by the pinch technique. No significant numerical differences were observed between the two approaches in this particular example.

Dielectronic recombination for oxygenlike ions relevant to astrophysical applications

In the modeling of the astrophysical plasmas, the relative elemental abundance inferred from solar and stellar upper atmosphere can be affected by as much as a factor of 5 due to the uncertainties in the current dielectronic recombination (DR) rate coefficients used to analyze the spectra [Savin and Laming, Astrophys. J. 566, 1166 (2002)]. DR rate coefficients for oxygenlike ions have been identified as the most urgent needs for the astrophysical applications. In this work, we report on the calculations of DR rate coefficients for Mg V, Si VII, S IX, and Fe XIX ions which are important for the modeling of the astrophysical plasmas. The calculations are carried out in isolated resonance and distorted-wave approximations. The relevant atomic data are calculated using the multiconfigurational Dirac-Fock method. We include 2s-2p, 2p{sub 1/2}-2p{sub 3/2}, 2l-3l{sup '}, and 1s-2p excitations and cover temperatures ranging from 0.001 eV to 10 000 eV. For low temperatures, it is essential to have accurate DR resonance energies and to include fine-structure excitations in order to obtain reliable DR rate coefficients. Good agreement with experiment has been found for Fe XIX. For Mg V, Si VII, and S IX, significant discrepancies are noted between this work andmore » recommended rate coefficients.« less

Nuclear correlation effects in neutrino-nucleus interactions

We present a model of neutrino-nucleus cross-sections computations taking into account nuclear effects such as short range correlations — through the ring approximation of the RPA, Delta resonance excitation with a medium modified decay width and ( np-nh) excitations ( n=2,3) relevant in the region between the quasi-elastic peak and the Delta peak. The inclusive reaction cross-section is split into exclusive channels classified according to the number of final state pions. This model was originally developped for the water Čerenkov experiments in which the pions in the final state often lead to Čerenkov ring(s) and are therefore crucial for the analysis.

The line shape of linear optical Ramsey resonance

In this work we suggest a way of describing the Ramsey resonance for arbitrary saturation and arbitrary transverse laser field shape, which takes into account the first order term correction to resonance approximation (zero pulse width) of the order of a/ L ( a is the width of the laser beam, L is a distance between laser beams). It permits to take correctly into account the transverse velocity distribution and real (Gaussian) shape of laser fields. An additional rather interesting phenomenon consists in non-trivial performance of the recoil effect in case of the linear optical Ramsey resonance (in two standing waves separated by λ/2 grating), where we have a few (more than 2) recoil components of the same shape but with different intensities.

The influence of the orientation and strength of a magnetic field on the coherent population trapping in the Λ system

The influence of the orientation and strength of a magnetic field on the dynamics and dispersion of the populations of the multilevel Λ system upon spontaneous decay into thermostat levels is considered. The radiation field consists of two components and is specified by the vector-potential in the electric dipole approximation. From the solution of the Schodinger equation for a system consisting of an atom in a magnetic field + radiation field, the probability of populating a common level for the generalized Λ system is determined in the resonance approximation. The calculation of the dynamics and dispersion of the populations demonstrates their dependence on the orientation of the magnetic field vector with respect to the light field polarization vector and on the relationship between the magnetic field strength and radiation field intensities. The coherent population trapping occurs only in the case when Rabi frequencies either exceed or are comparable to the Zeeman splitting of magnetic sublevels. By varying the orientation of the magnetic field, it is possible to change the dynamics and dispersion of the populations, thus affecting the coherent population trapping.

Electron-positron pair production in the field of superstrong oppositely directed laser beams.

The multiphoton electron-positron pair production through nonlinear channels by superintense opposed laser pulses of the same frequencies in vacuum is considered. On the basis of the Dirac model the resonance approximation for vacuum induced transitions is developed. The analytic formulas for energetic and angular distributions and total number of created particles in the limit of a short interaction time are obtained.