Electrostatic and electromagnetic surface shape resonances

The homogeneous integral equations that give the electromagnetic field in the vicinity of a protuberance or a depression on the otherwise planar interface with vacuum of a semi-infinite dielectric medium or a thin dielectric film on a semi-infinite substrate have been obtained. The Rayleigh hypothesis, the vectorial equivalent of the Kirchhoff integral, and the extinction theorem have been used for this purpose. The assumption that the perturbation of the vacuum dielectric interface has cylindrical symmetry about the normal to the nominal surface allows a significant simplification of these integral equations to be carried out. We have used Gaussian quadrature schemes to convert the resulting integral equations into matrix equations, and have obtained the frequencies of the shape resonances by equating to zero the determinants of the matrices obtained. Calculations have been carried out for Gaussian (x ₃=Aexp(–x ² /R ²)) and exponential (x ₃=Aexp(–x /R)) surface profiles, and convergent results obtained for values ofA/R of the order of unity.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Theory of the line shape of gamma-photon transitions

There is a discussion of the line shape for the nuclear two-quantum transition due to the simultaneous absorption of a Mossbauer quantum and a quantum from a classical photon source. The problem is solved through the use of density-matrix equations, and an equation is derived for the intensity of absorbed gamma rays. In contrast with the case of the ordinary probabilistic approach, the equation for the intensity of gamma absorption reveals a dependence on the relaxation times within the ground and excited states. The line shape for gamma-photon transitions for low intensities of the incident radiation usually differs little from the shape of the Mossbauer line. However, at large irradiation intensities, a shift and a broadening of the resonant lines occur, proportional to the radiation power. These corrections must be taken into account in, e.g., gamma-magnetic resonance.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 12, No. 7, pp. 24–30, July, 1969.     

On ηc line shape in charmonium transitions

The line shapes to observe ηc in charmonium transitions, I.e.,ψ(2S), J/ψ→γηc, are investigated. The ηc line shapes in exclusive decays or by observing the inclusive photon spectrum are given. The sensitivities to measure the ηc resonance parameters are also evaluated. With more than two thousand ηc events observed, the precision of the ηc decay width measurement will be improved by better than 3%. However, the uncertainties associated with the ηc modified line shapes will dominate the systematic errors and this will prohibit precision mass and width measurements.     

Electrostatic surface shape resonances of a finite number of ridges

The resonance properties of localized electrostatic surface modes associated with a finite number of ridges on an otherwise planar surface are investigated. Numerical solutions of the homogeneous integral equations that describe the electromagnetic fields in the vicinity of the ridges are used to obtain the dispersion relation of surface plasmons. The frequencies of the electrostatic surface shape resonances are calculated for ridges with Gaussian, Lorentzian, sinusoidal, exponential, and triangular profiles. We show the existence of splittings of the plasmon frequencies, which depends on the surface profile function and on the distance between the ridges. Considering the ridge with a sinusoidal profile, we obtain the limit on the number of ridges which generates a frequency splitting of the electrostatic surface shape resonances, whose frequency values converge to those of the dispersion relation of surface plasmons on one-dimensional sinusoidal grating. Received: 24 June 1997 / Received in final form: 5 September 1997 / Accepted: 15 September 1997     

The shape of saturated-absorption polarimetric resonances caused by transitions between degenerate states of the neon atom

We have studied experimentally and theoretically the shapes of spectropolarimetric resonances of a linearly polarized probe wave for the transitions 1s ₅-2p ₂ and 1s ₅-2p ₄ in the neon atom in the presence of a strong counterpropagating circularly polarized wave of the same frequency. Physical processes that lead to a change in the shape of polarimetric resonances under the action of a longitudinal magnetic field have been determined.     

Spreading of analog resonances in inelastic proton channels

The reaction⁹⁰Zr(p, p′) leading to the 1.76 MeV excited state was studied at the 6.22 MeV 5/2⁺ analog resonance. Excitation functions taken at 150° and 170° were analyzed in terms of Weidenmüller's theory, in order to deduce the spectroscopic factor, external spreading width and level shift in the inelastic channel. An upper limit of 3.2 keV for the internal spreading width of this resonance was set.     

Influence of the thermal motion on the line shape and position of resonances in collinear fast beam laser spectroscopy

We derive the spectral line shape for collinear fast beam laser spectroscopy. As initial condition we take a thermally distributed ensemble into account. While the thermal velocity distribution of the fast ensemble has an asymmetric structure due to the acceleration by the electrostatic field, under typical experimental conditions the convolution with the natural line shape preserves the Lorentz profile with negligible broadening. However, the spectral line as a whole experiences a small shift depending on the temperature of the source and the acceleration . PACS 32.70.Jz     

The neverending story of shape resonances

Shape resonances, their definition, their nature, their use and supposedly almost miraculous capabilities, have been a rather controversial topic in the scientific literature for quite a long time. There was an upsurge of papers and heated discussions at conferences about these issues more than 10 years ago, the main point of which was whether the shape resonance position in energy above a core level ionization threshold in molecules, either isolated or adsorbed on surfaces, bears some information on bond lengths, with two opposite schools of thought, one maintaining that such connection, if existent at all, is rather loose, the other one ready to use some linear dependence of the shape resonance energy upon bond lengths to actually derive unknown bond distances in adsorbed molecules (the so-called ‘bond-lengths-with-a-ruler’ party). The latest technical and instrumental developments have given rise to another wave of shape resonance papers in the last 3 years. Criteria to assign shape resonances have been reconsidered under the light of new experimental results, and some molecules which were categorized as textbook examples for shape resonances have been shown not to exhibit such continuum phenomena at all. Therefore it is time for a historical survey which hopefully will straighten up some misconceptions still floating around in the literature.     

Theoretical investigation of giant resonances by inelastic proton scattering

A fully microscopic, antisymmetrized DWBA analysis of (p, p') spectra in the giant resonance region of ¹⁶O, ⁴⁰Ca and ²⁰⁸Pb is presented. The nuclear structure information is derived from RPA wave functions calculated in large configuration spaces. The theoretical spectra are in general in agreement with the experimental results. A new interpretation follows from our. investigation for the spectrum of the giant dipole region in the heavy nuclei: This resonance structure is mainly due to the breathing mode, whereas the electric dipole contribution is much smaller.     

Parametrizing the line shapes of near-threshold resonances

A parametrization is proposed for the line shapes of near-threshold resonances, which is based on the model of coupled channels and can include an arbitrary number of elastic and inelastic channels and bare poles. The proposed parametrization satisfies the requirements imposed by unitarity and analyticity, and is convenient for the data analysis embracing all available experimental information. The model parameters are physically meaningful, and their values can be found using different theoretical schemes.     

Surface shape resonances of ridges on a thin film

The spectrum of surface shape resonances associated with a finite number of ridges on one interface of an otherwise plane film is calculated. The frequencies are obtained numerically by solving the homogeneous integral equations which describe the electrostatic field in the vicinity of a surface defect. The calculations are performed for a surface with ridges with Gaussian, Lorentzian and sinusoidal profiles. The results show a strong dependence of the localized plasmon frequencies on the surface profile, on the distance between the ridges, and on the thickness of the film. Received 5 April 1999 and Received in final form 6 July 1999     

Extracting the width of giant resonances from the analysis of heavy ion inelastic scattering

The energy and percentage of the energy-weighted sum rule associated with low-lying collective modes and with the giant resonances, are input parameters of the coherent surface excitation model of heavy ion reactions of Broglia, Dasso and Winther. In the present letter we study how the magnitude of structures in the energy spectra associated with the excitation of giant resonances depend on the spreading widths of these modes.     

Effect of contact line curvature on solid-fluid surface tensions without line tension

For sessile droplets partially wetting a solid surface, it has been observed experimentally that the value of the contact angle depends on the contact line curvature and this dependence has been attributed to tension in the contact line. But previous analyses of these observations have neglected adsorption at the solid-liquid interface and its effect on the surface tension of this interface. We show that if this adsorption is taken into account the relation between the contact angle and contact line curvature is completely accounted for without introducing line tension. Further, from the observed relation between the contact angle and contact line curvature, the adsorption at the solid-liquid interface can be determined, as can the surface tensions of the solid-liquid and solid-vapor interfaces.     

Effect of phase transitions on thermal desorption from a solid surface

Thermal desorption from the surfaces of films and polycrystals undergoing semiconductor-metal (VO₂), ferroelectric-paraelectric (Ba_0.9Sr_0.1TiO₃ and TsTS-19), ferromagnet-paramagnet (Ni) phase transitions has been investigated. A sharp increase in the desorption activity of a surface was observed near a phase transition. The increase in the thermal desorption signal is caused by local deformations which arise in a solid at a phase transition. Fiz. Tverd. Tela (St. Petersburg) 39, 573–576 (March 1997)     

On the shape of cross resonances in counterpropagating wave spectroscopy

Physical processes that generate cross resonances are studied. It is revealed that not only populational, but also coherent, effects can make a contribution to formation of cross resonances. The effects of coherent processes, lifetimes of levels, the parameter of radiation branching from the upper level, and light fields?? characteristics are shown to be qualitatively different for the ??-, V-, and J = 1 ? J = 1 types of transition. Conditions for the change in the sign of cross resonances are found and a situation wherein the cross resonance has a purely coherent nature is shown.     

Effect of a weak dimer-dimer interaction on the EPR line shape of polycrystalline samples

The spectroscopic manifestations of a weak interaction between dimers in the EPR spectra of polycrystalline samples are analyzed. It is shown that, under specific conditions, the weak interaction between dimers can be responsible for the additional lines in the EPR spectrum. The appearance of these features is associated with the collapse of the spectral lines in orientations satisfying the condition of exchange narrowing for the components of the fine structure in the spectrum of the dimer.     

Collisional interference in the infrared spectrum of HD: calculation of the line shape of vibrorotational transitions for HD-He

The line shape parameters for the collision-induced vibration-rotation spectrum of HD-He are calculated with the formalism of Gao et al. The total intensity interference parameters and line asymmetry parameters are found to be larger than those for pure rotational transitions. The results depend on collisional propagation among rotational levels in both vibrational states and can be sensitive to vibrational-state dependence of the intermolecular potential.