Resonance Approximation Research Articles

Interaction of non-monochromatic laser field with two-level atom

Abstract The problem of a two-level atom interacting with a non-monochromatic radiation pulse is studied in the resonant approximation for arbitrary detunings, and without the resonant approximation. By using the time-dependent theory of perturbation the analytical expressions for the transition probability and induced dipole moment of the atom are obtained. It is shown that the upper level population of the atom exhibits oscillations that are absent in the resonant approximation. The temporal shape of the pulse is shown to affect significantly the atomic transition probability. The behaviour of the transition probability and dipole moment spectrum for arbitrary pulse shapes, phases and detunings is investigated. The interference between the spectral components arising in nonlinear processes is shown to play a considerable role in the formation of a dipole moment spectrum.

Interaction of non-monochromatic laser field with two-level atom

The problem of a two-level atom interacting with a non-monochromatic radiation pulse is studied in the resonant approximation for arbitrary detunings, and without the resonant approximation. By using the time-dependent theory of perturbation the analytical expressions for the transition probability and induced dipole moment of the atom are obtained. It is shown that the upper level population of the atom exhibits oscillations that are absent in the resonant approximation. The temporal shape of the pulse is shown to affect significantly the atomic transition probability. The behaviour of the transition probability and dipole moment spectrum for arbitrary pulse shapes, phases and detunings is investigated. The interference between the spectral components arising in nonlinear processes is shown to play a considerable role in the formation of a dipole moment spectrum.

Particle–hole interaction effect on a core-level XPS spectrum II

Abstract X-ray photoelectron spectroscopy (XPS) spectral behavior of an initial discrete core-hole state embedded or nearly embedded in a continuum is studied by a Green’s function model calculation. The particle–hole interaction U in the final two-hole one-particle state is included in the initial core-hole self-energy by the ladder and ring approximation. With an increase of U, the transition to an unoccupied (particle) state near the double-ionization threshold increases in the final state. With a further increase of U, the transition to an empty bound level below the Fermi level dominates. It is shown that even when the coupling between the initial discrete core-hole state and the final continuum state is strong there can be a sharp resonant state. When the coupling is weak, there is a possibility of the breakdown of the quasi-particle approximation for the initial core-hole state. U can substantially affect the initial core-hole spectral function.

Theoretical calculation of the cross sections of dielectronic recombination onHe+

The relativistic multichannel theory has been applied to calculations of cross sections of dielectronic recombination on ${\mathrm{He}}^{+}.$ A first-order approximation is adopted for the radiative process. A correction based on isolated resonance approximation is used for the very narrow resonances among the ${2lnl}^{\ensuremath{'}}$ states to include the radiation width. Twelve partial cross sections are calculated for both the ${2lnl}^{\ensuremath{'}}$ and ${3lnl}^{\ensuremath{'}}$ resonance states with $nl~5.$ The convolved cross sections for the $nl~3$ states are in good agreement with those of the observations. A quantitative discrepancy for the $n=4$ and $n=5$ states may be attributed to the l dependence of the field ionization and the radiative decay during the time of flight.

Electron resonance dynamics in a double quantum well

We consider the two-level electron dynamics in a double quantum well in a periodic, anharmonic external electric field. We propose a method for solving the Schrodinger equation, which is based on the generalization of conventional resonance approximation for a system with an arbitrary number of resonances. The method is used for the case of both weak and strong fields. We obtain expressions for the quasi-energy wave functions and the electron dipole moment. It is shown that the dependence of the dipole moment on the constant component of external field is quasi-periodic, and the dipole moment changes sign at different half-periods.

The effect of nonpair atomic interactions on the short-range order in disordered alloys

The high numerical accuracy of the recently developed (Chepulskii R V 1999 J. Phys.: Condens. Matter 11 8645-60) generalized ring approximation for analytical description of the short-range order (SRO) in disordered alloys with many-body atomic interactions of arbitrary orders is revealed through comparison with the corresponding data of the Monte Carlo simulation. It is shown that this accuracy rises with an increase of the characteristic radius of atomic interactions. By the example of both the simplest model systems and Ni-V alloy, we demonstrate that, within the generalized ring approximation, it is possible to describe the phenomenon of the temperature dependence of a position in reciprocal space of the SRO Fourier transform's maximum at temperature independent atomic interactions. The analytical description of the effect of nonpair atomic interactions on the Fourier transform of the SRO parameters is performed in case of Ni-V alloy.

Acoustic attenuation in very shallow water due to the presence of bubbles in rip currents

An experiment was performed just off the research pier at the Scripps Institute of Oceanography to determine the acoustic effects of small bubbles in very shallow water (∼6 m depth). The distance offshore was ∼300 m. The propagation lengths were 2–10 m, and the frequency range was from 39 to 244 kHz. During the experiment, rip currents passed through the field of measurement instruments. These rip currents were laden with bubbles created in the surf between the instruments and the shore. The effects of these rip currents on the spatial distributions of the resulting acoustic attenuation are discussed. From the attenuation data, the bubble distributions are calculated using a new iterative approach [Caruthers et al., in press, J. Acoust. Soc. Am.] that is based on the well-known resonant bubble approximation. Calculated bubble distributions varied from an essentially uniform lack of bubbles during quiescent periods to highly inhomogeneous and dense bubbly regions within rip events. Such observed distributions were consistent with measurements made by other investigators during the experiment.

The static pressure and temperature coefficients of laboratory standard microphones

The sensitivity of condenser measurement microphones depends on the environmental conditions, which affect the acoustic properties of the air enclosed between the diaphragm and the back electrode and in the cavity behind the back electrode. A theoretical investigation has been performed based on an extended lumped parameter representation of the mechanical and acoustic elements of the microphone. The extension involves the frequency dependency of the dynamic diaphragm mass and stiffness as well as a first-order approximation of resonances in the back cavity. It was found that each coefficient, for a given type of microphone, can be described by a single function when the coefficients are normalized using their low-frequency value and the frequency is normalized with respect to the individual resonance frequency of the microphone. The theoretical results are supported by experimentally determined coefficients for about twenty samples of microphone types B&K 4160 and B&K 4180.

Diffusion in lattice Lorentz gases with a percolation threshold.

A mean-field approximation for the diffusion coefficient in lattice Lorentz gases with an arbitrary mixture of pointlike stochastic scatterers in the low-density limit is proposed. In this approximation, the diffusion coefficient is directly related to the first return probability of the moving particle in the corresponding Cayley tree through an effective ring operator. A renormalization scheme for the approximate determination of the first return probability is constructed. The predictions of this mean-field theory and those of the repeated ring approximation (RRA) are compared with computer simulation results for models in which a fraction x(B) of the scatterers are deterministic backscatterers, so that the diffusion coefficient vanishes beyond a certain percolation threshold x(c)(B). The approximation proposed in this paper is seen to be in good agreement with the simulation results, in contrast to the RRA, which already fails to give the correct percolation threshold.

An iterative approach for approximating bubble distributions from attenuation measurements

A precise theory exists, based on an integral equation, by which acoustic signal attenuation versus frequency, due to a known bubble-density distribution versus bubble radius, may be calculated. Lacking a simple inversion scheme for the integral equation, an approximation which accounts only for attenuation due to resonant bubbles is available (and often applied) to calculate a bubble distribution. An iterative approach for improving on that resonant bubble approximation is presented here. That new approach is based on alternating calculations and corrections between attenuation data and the bubble distribution presumed to have produced it. This iterative technique is tested, first, on two simulated data sets of bubble distributions. It is then applied to attenuation data measured as a function of frequency from 39 to 244 kHz during the Scripps Pier Experiment [Caruthers et al., Proc. 16th Int. Cong. on Acoust., pp. 697–698 (1998)]. The results of the simulations demonstrate the validity of the method by faithfully reproducing the initial distributions for the simulated attenuation data. When applied to the real data, the method leads to a bubble distribution whose use in a direct solution of the integral equation reproduces the measured data with greater accuracy than does the resonant bubble approximation alone.

Quasielastic electron scattering from nuclei: Random-phase vs ring approximations

We investigate the extent to which the nuclear transverse response to electron scattering in the quasielastic region, evaluated in the random-phase approximation, can be described by ring approximation calculations. Different effective interactions based on a standard model of the type ${g}^{\ensuremath{'}}{+V}_{\ensuremath{\pi}}{+V}_{\ensuremath{\rho}}$ are employed. For each momentum transfer, we have obtained the value of ${g}_{0}^{\ensuremath{'}}$ permitting the ring response to match the position of the peak and/or the non-energy-weighted sum rule provided by the random-phase approach. It is found that, in general, it is not possible to reproduce both magnitudes simultaneously for a given ${g}_{0}^{\ensuremath{'}}$ value.

Donor states in tunnel-coupled quantum wells

We study the energy spectrum of the impurity states in tunnel-coupled double quantum wells for Coulomb and short-range donor potentials. We calculate the impurity contribution and the density of states and detect the transformation of a localized donor state into a resonant state when the binding energy of the donor in an isolated quantum well is less than the separation of the energy levels of the double quantum wells. In the opposite case, where the binding energy is greater than the level separation, there is tunneling repulsion between adjacent impurity levels, with the degree of degeneracy of the levels changing when there is tunneling mixing of the ground and excited impurity states from different wells. Resonant states emerge in an asymmetric double quantum well, while in a symmetric double quantum well the impurity level at the barrier’s center proves to be localized even against the background of the continuum. The calculations are based on a general expression for the impurity contribution to the density of states in terms of a 2-by-2 matrix Green’s function, i.e., only a pair of tunnel-coupled levels of the double quantum wells is taken into account. For an impurity with a short-range potential, we derive a matrix generalization of the Koster-Slater solution, while the impurity with a Coulomb potential is analyzed by using the approximation of a narrow resonance and close arrangement of the repulsive levels.

Theory of the backscattering of sound by phase-matched nonlinear interaction

The nonlinear interaction of noncollinear acoustical waves is considered. Conditions of the resonant backscattering of one wave from the lattice produced by the other two are formulated in analogy with the four-wave mixing known in optics. The efficiency of the phase-matched interaction of acoustical waves is calculated in the resonant approximation for a gas media. Such approximation is constructed on the basis of the expansion of the sound equations preserving up to cubic terms. The amplitude of the backscattered wave is expressed as the product of the efficiency, the amplitudes of three waves, the wave number of the backscattered wave, and the size of the region of interaction. Such backscattering is proposed as an acoustical remote probe. The distance to the interaction region and the amplitude of initial waves are limited by nonlinear degradation of waves due to the second-order nonlinearity. For acoustical waves with wave number 10 m−1, sources of size 1 m, and about 100 m to the interaction region, the amplitude of the backscattered wave can be about 10−10 of the atmospheric pressure. At the detection with a signal-to-noise ratio about of 10, the resolution of such method on the wind velocity may be about 1 m/s.

Enhancement of dielectronic recombination by an electric field

Dielectronic recombination from a continuum of finite bandwidth has been examined down to very low electric fields, 60 mV/cm, with very high resolution. A tunable laser is used to excite atoms to the continuum of finite bandwidth, the broad $\mathrm{Ba} {6p}_{3/2}11d$ autoionizing state, which straddles the ${\mathrm{Ba}}^{+} {6p}_{1/2}$ limit. Atoms which make transitions into the high-lying $\mathrm{Ba} {6p}_{1/2}\mathrm{nd}$ states and radiatively decay to the bound $6snd$ states are detected by field ionization. The recombination, integrated over energy, has been measured for fields from 60 mV/cm to 28 V/cm, showing a peak at 0.5 V/cm, in agreement with expectation based on calculations done for other systems. The final-state distribution has been measured, showing that the outer electron remains a spectator in the radiative decay. At fields below 1.0 V/cm and binding energies less than 12 ${\mathrm{cm}}^{\ensuremath{-}1}$ below the ${\mathrm{Ba}}^{+} {6p}_{1/2}$ limit we find a deviation of our experimental results from the isolated resonance approximation.

Improving the wide resonance approximation

A resonance is considered wide if its practical width, in energy, exceeds the average energy loss per collision, E(1- α A )/2, of the absorbing material. When the mass number, A, is taken infinite, the scattering produces only a change in the direction of motion of the neutron and not in its energy. Based on this assumption, the integral in the slowing-down equation describing the contribution of the resonant absorber is evaluated by taking its limit when α A→1. This work questions the necessity to take such a limit and shows that it is still possible to obtain a simple and more accurate expression for the integral without taking such limit.

A Multiband Method with Resonance Interference Effect

The multiband method has been extended to treat the resonance interference effect between two nuclides based on the intermediate resonance approximation. The integral equation of the flux belonging to different bands of the two nuclides is derived for a heterogeneous cell system. In the equation, a new band parameter is introduced. The new parameter denotes the conditional probability that a nuclide takes a certain band under the condition that the other nuclide takes another band. The calculational procedure of band parameters is described in a homogeneous medium. This method has been applied to a homogeneous medium and a thermal reactor cell containing 235U and 238U. The effective cross sections calculated by this method and the conventional multiband method without considering the interference effect are compared with the results by a reference continuous-energy Monte Carlo method. It is seen that the conventional multiband method greatly overestimates the fission and capture cross sections of 235U for energy groups where there are both resonances of 235U and 238U, and the present method remarkably improves the overestimation.

Restoring good high energy behaviour in Higgs production via W fusion at the LHC

The W-fusion scattering process W+W- --> ZZ for off-shell W bosons is studied, focusing on the issue of its high-energy behaviour which is known to be anomalous. It is shown that the unitarity violating terms can be isolated and extracted in a well-defined and efficient way using the pinch-technique. This restores the good high energy behaviour of the cross section and, in particular, makes possible the identification of the Higgs resonance in the invariant mass distribution M(ZZ) of the Z pair. The discarded terms, which are proportional to the off-shellness of the W bosons, cancel against similar terms originating from the remaining diagrams for the full physical process f1 f2 --> f1' f2' Z Z. This cancellation ensures the gauge invariance of our result, which therefore constitutes a meaningful separation between signal and background when they both contribute coherently. Equipped with this result, we are able to define a resonant approximation for the process p p --> Z Z + 2 jets + X, which circumvents the problem of good high energy behaviour without having to resort to the lengthy calculation of the complete set of diagrams. In this approximation only the W and Z fusion signal graphs are included, i.e. the ones which contain the Higgs resonance. We have verified that the approximate resonant cross section describes very well the full result not only close to the resonance but also beyond it.

Analytical methods for calculation of interatomic potentials through the data on the short-range order in alloys

Within the framework of the high-accuracy ring approximation elaborated by the authors (Chepulskii R V and Bugaev V N 1998a, b 10 7309-26, 7327-48) in the context of the modified thermodynamic perturbation theory as applied to the lattice gas model, two methods are developed for calculation of the atomic interaction parameters in binary disordered alloys with Bravais crystal lattices through the data on the atomic short-range order (SRO) - the iteration method resulting in explicit analytical relationships and the variational method. Within both methods, the Fourier components of SRO parameters are used as initial data, thus, the most complete information on SRO in the alloy is taken into account. Both the iteration and variational methods permit us to calculate the atomic interaction parameters for an arbitrary number of the coordination shells as well as the Fourier components of the atomic interaction potentials. It is demonstrated that both methods have wide temperature-concentration intervals of applicability. The methods can be used under investigation not only of alloys, but also of other lattice systems (including low-dimensional ones, semiconductors and magnetics).

Measurement of the modulus and phase of the linear coupling coefficient by analysis of the transverse beam profile

We study the dynamics of transverse oscillations near the linear coupling resonance excited by a pair of skew quadrupoles at the Laborat\'orio Nacional de Luz S\'{\i}ncrotron UVX electron storage ring through the analysis of the beam profile. Transverse coherent oscillations were excited with a fast kicker and the profile of the oscillating beam was observed by focusing visible synchrotron radiation from a bending magnet onto a fast charge-coupled device camera. Using a single resonance approximation, we calculated the border of the time-averaged transverse beam profile as a function of the complex coupling coefficient $\ensuremath{\kappa}$, which characterizes the distribution of coupling fields along the storage ring. A least-squares fit of the calculated beam profile border to the experimentally obtained isointensity contours provided a new method to determine both the modulus and the phase of $\ensuremath{\kappa}$. The values obtained for the modulus are in good agreement with those from the conventional normal mode tune separation technique, and the values obtained for the phase of $\ensuremath{\kappa}$ agree with calculations based on the model lattice and the known skew quadrupole distribution.

Broad sub-continuum resonances and the case for finite-energy sum-rules

There is a need to go beyond the narrow resonance approximation for QCD sum-rule channels which are likely to exhibit sensitivity to broad resonance structures. We discuss how the first two Laplace sum rules are altered when one goes beyond the narrow resonance approximation to include possible subcontinuum resonances with nonzero widths. We show that the corresponding first two finite energy sum rules are insensitive to the widths of such resonances, provided their peaks are symmetric and entirely below the continuum threshold. We also discuss the reduced sensitivity of the first two finite energy sum rules to higher dimensional condensates, and show these sum rules to be insensitive to dimension $> 6$ condensates containing at least one $\bar{q}q$ pair. We extract the direct single-instanton contribution to the $F_1$ sum rule for the longitudinal component of the axial-vector correlation function from the known single-instanton contribution to the lowest Laplace sum rule for the pseudoscalar channel. Finally, we demonstrate how inclusion of this instanton contribution to the finite-energy sum rule leads to both a lighter quark mass and to more phenomenologically reasonable higher-mass-resonance contributions within the pseudoscalar channel.