Two electron problem and the nonlocal equations of electrodynamics

Gadomskiǐ, O. N.

doi:10.3367/ufnr.0170.200011a.1145

Cited by 38 publications

(10 citation statements)

References 37 publications

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“…3 it can be seen that the range of action of the third element is long enough, that is, significant at distances of about 10 particle diameters. In addition, in contrast to the optical dimensional resonances whose position on the frequency scale depends on particle spacing as was repeatedly indicated in a number of works [2,14,15,17,20], the wavelength of the peaks caused by the presence of the distant neighbor does not change as it approaches to or moves away from the system; however, this affects the peak amplitudes.…”

Section: Optical Properties Of the Examined Structurementioning

confidence: 90%

“…This method was tested in [14,15,17,20] by solving various boundary optics problems. According to this method, the electric field strength ( , ) t E r for the examined system at arbitrary observation point r at the moment of time t is expressed as follows: (n is the number of particles in the system), j ′ r is the coordinate over which integration is carried out, j p are the quantum-mechanical averages of the induced dipole moments of the two-level impurity atoms: (2) and the quantities j X obey the equations for the coupled quantum dipoles [2,14]:…”

Section: Electric Field Equationsmentioning

confidence: 99%

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Electrodynamic response of a colloid ensemble with allowance for the influence of distant nanoparticles

Shalin

2006

Russ Phys J

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A. S. ShalinUDC 537.876The optical properties of a colloid consisting of nanoparticles are investigated on the example of interaction of three dielectric particles consisting of nonresonant atoms (whose natural transition frequencies are far from the radiation frequency) with interstitial barium atoms in the field of external optical radiation. On the basis of integrodifferential equations, expressions for the electric and magnetic fields in the wave zone are derived. The influence of distant neighbors in the ensemble on the light-scattering properties of a nanoparticle is considered, and the condition of applicability of the frequently used two-particle approximation is obtained. The spectrum of the system is investigated, and an additional resonant peak at the natural frequency of the isolated particle caused by the distant neighbor is established. Under some specific conditions, the additional peak intensity may exceed the main peak intensity of the optical near-field resonance in the two-particle system.

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Section: Optical Properties Of the Examined Structurementioning

confidence: 90%

Section: Electric Field Equationsmentioning

confidence: 99%

Electrodynamic response of a colloid ensemble with allowance for the influence of distant nanoparticles

Shalin

2006

Russ Phys J

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“…As far back as in the early seventies of the last century, the interest in the given problem arose in the connection with the intensive study of multiatomic systems placed into a field of radiation. The credit for the realization and development of new ideas in this direction goes to the authors of papers [18][19][20][21], where the problem of interaction of two bound electrons belonging to two hydrogen-like atoms was considered by using methods of quantum electrodynamics without any restrictions on interatomic distances. However, the generalized Breit operator constructed in the above quoted papers does not manifest the symmetry with respect to the interacting particles and therefore, cannot be utilized in the consistent relativistic quantum theory.…”

Section: Introductionmentioning

confidence: 99%

The generalized Breit operator of the interaction between two quasimolecular electrons in the framework of the third-order effects of quantum electrodynamics

Lazur¹,

Reity²,

Pavlyk³

2010

J. Phys. A: Math. Theor.

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The problem of the interaction of two quasimolecular electrons located at an arbitrary distance from each other and near different atoms (nuclei) is solved. Effects of the third order of quantum electrodynamics, which include the exchange of a virtual photon between the electrons and emission (absorption) of a real photon, are considered. The general expression for the matrix elements of the operator of the effective interaction energy of the two quasimolecular electrons with the external radiation field, which allows us to calculate the probabilities of inelastic processes with rearrangement in slow collisions of multiply-charged ions with relativistic atoms, is obtained. Carrying out consistently the procedure of symmetrization of the retardation factor with respect to both the electrons results in the appearance of additional terms in the relativistic operator of the interaction of two quasimolecular electrons in comparison with both the standard and generalized Breit operators known previously.

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“…plicated form [13,[16][17][18]. In the case under consideration, for some colloid made up of dielectric (glass) nanoparticles activated by impurity atoms, we can write the simplified expression [16,17]:…”

mentioning

confidence: 99%

Light scattering by nanosized systems with different spatial organizations

Shalin

2006

J Appl Spectrosc

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The integrodifferential equation method is used to study the spectrum of a nanoparticle colloid for the example of interaction of three arbitrarily arranged dielectric particles made up of nonresonant atoms (the eigenfrequency of the transition is far from the emission frequency) with incorporated barium atoms in an external optical radiation field. The effect on the light-scattering properties of a nanosphere in the ensemble of its distant "neighbors" is studied; an additional peak associated with them is observed as a frequency close to the resonance for an isolated nanosphere, which under certain conditions has higher intensity than the main peak corresponding to optical near-field resonance in a two-particle system. The dependence of the spectrum of the nanosized system on the geometric structure is studied, and it is shown that very precise tuning of the resonance frequency is possible by varying the angular distribution of the particles.Introduction. In many optical problems connected with emission by microsized and nanosized structures, the problem arises of studying their scattering spectrum, and also identifying the resonance frequencies corresponding to the considered system. In [1], such a problem was solved for the case of metastructural coatings composed of dimers of alkali metals. In [2, 3], clusters were studied that included several tens of interacting atoms. Considerable attention has also been paid to application of such structures in medicine [4-7] (DNA-bound nanoparticles, biomarkers). For this purpose, mainly spherical nanoparticles on the order of 10-30 nm in size have been used, the optical properties of which [8,9] are determined by resonance at the wavelength ≈550 nm. Papers are available that study the light-scattering characteristics of particles of arbitrary shape [10].A large number of papers have also been devoted to study of the interaction between nanoparticles in systems of two or more components. Thus the papers [11,12] study the interaction of a metallic nanosphere with the smooth surface of a semi-infinite medium, which is of significant interest, for example, for optical near-field microscopy. The papers [13,14] study the interaction of a spherical nanoparticle with the surface of an optical medium when island films are present on the surface. This has made it possible to satisfactorily explain the spectral properties of objects observed in [15].We should note that in practically all the indicated papers, the studied structures were considered in the nearest "neighbor" approximation, i.e., neglecting the effect of more distant particles (considering that effect as negligibly small compared with the effect of the surrounding environment). Nevertheless, under certain conditions, we cannot neglect the distant "neighbors", and taking them into account leads to the appearance of additional peaks in the spectrum of the interacting nanoparticles.In this paper, a successive solution of the boundary-value problem of optics for light scattering from some colloid is proposed, taking into...

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Two electron problem and the nonlocal equations of electrodynamics

Cited by 38 publications

References 37 publications

Electrodynamic response of a colloid ensemble with allowance for the influence of distant nanoparticles

Electrodynamic response of a colloid ensemble with allowance for the influence of distant nanoparticles

The generalized Breit operator of the interaction between two quasimolecular electrons in the framework of the third-order effects of quantum electrodynamics

Light scattering by nanosized systems with different spatial organizations

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