Optical Theorem Research Articles

Multi-reaction-channel fitting calculations in a coupled-channel model: Photoinduced strangeness production

To describe photo- and meson-induced reactions on the nucleon, one is faced with a rather extensive coupled-channel problem. Ignoring the effects of channel coupling, as one would do in describing a certain reaction at the tree level, invariably creates a large inconsistency between the different reactions that are described. In addition, the imaginary parts of the amplitude, which are related through the optical theorem, to total cross-sections, are directly reflected in certain polarization observables. Performing a full coupled-channel calculation thus offers the possibility to implement the maximum number of constraints. The drawback one is faced with is to arrive at a simultaneous fit of a large number of reaction channels. While some of the parameters are common to many reactions, one is still faced with the challenge to optimize a large number of parameters in a highly non-linear calculation. Here we show that such an approach is possible and present some results for photoinduced strangeness production.

Top quark mass effects in NNLO Higgs boson production at LHC

QCD corrections to Higgs boson production at the LHC are evaluated to NNLO. Taking advantage of the optical theorem and exact master integrals, we perform asymptotic expansions of the QCD cross-sections near the limit of infinitely heavy top quark and present a few first terms of the series.

Phase space matching and finite lifetime effects for top-pair production close to threshold

The top-pair $t\bar t$ production cross section close to threshold in $e^+e^-$ collisions is strongly affected by the small lifetime of the top quark. Since the cross section is defined through final states containing the top decay products, a consistent definition of the cross section depends on prescriptions how these final states are accounted for the cross section. Experimentally, these prescriptions are implemented for example through cuts on kinematic quantities such as the reconstructed top quark invariant masses. As long as these cuts do not reject final states that can arise from the decay of a top and an anti-top quark with a small off-shellness compatible with the nonrelativistic power-counting, they can be implemented through imaginary phase space matching conditions in NRQCD. The prescription-dependent cross section can then be determined from the optical theorem using the $e^+e^-$ forward scattering amplitude. We compute the phase space matching conditions associated to cuts on the top and anti-top invariant masses at next-to-next-to-leading logarithmic (NNLL) order and partially at next-to-next-to-next-to-leading logarithmic (N${}^3$LL) order in the nonrelativistic expansion and, together with finite lifetime and electroweak effects known from previous work, analyze their numerical impact on the $t\bar t$ cross section. We show that the phase space matching contributions are essential to make reliable NRQCD predictions, particularly for energies below the peak region, where the cross section is small. We find that irreducible background contributions associated to final states that do not come from top decays are strongly suppressed and can be neglected for the theoretical predictions.

The effect of gravitational tidal forces on vacuum polarization: How to undress a photon

The effect of gravitational tidal forces on photon propagation in curved spacetime is investigated. It is found that the imaginary part of the local refractive index Imn(u;ω) may be negative as well as positive, corresponding to a local amplification as well as attenuation of the amplitude of the renormalized photon field. This is interpreted in terms of the effect of tidal forces on the virtual e+e− cloud surrounding the bare photon field—a positive/negative Imn(u;ω) corresponds to an increased dressing/undressing of the bare photon. Below threshold decays of the photon to e+e− pairs can occur. Photon undressing in the vicinity of a black hole singularity is described as an example. These results are shown to be consistent with unitarity and the optical theorem in curved spacetime, which is derived here both in a local form and integrated over the photon trajectory.

General laws of X-ray reflection from rough surfaces: I. Optical theorem and energy conservation law

The optical theorem is generalized for the general case of X-ray wave reflection from an arbitrary layered rough medium. It is proven strictly that in the absence of absorption the energy conservation law is exactly satisfied within the distorted wave Born approximation if the angular scattering distribution is calculated taking into account only the single wave scattering from the inhomogeneities of the medium and if the specular reflectance and transmittance are calculated with allowance for both single and double scattering.

Optical forces on small magnetodielectric particle

We present a study of the optical force on a small particle with both electric and magnetic response, immersed in an arbitrary non-absorbing medium, due to a generic incident electromagnetic field. Expressions for the gradient force, radiation pressure and curl components are obtained for the force due to both the electric and magnetic dipoles excited in the particle. In particular, for the magnetic force we tentatively introduce the concept of curl of the spin angular momentum density of the magnetic field, also expressed in terms of 3D generalizations of the Stokes parameters. From the formal analogy between the conservation of momentum and the optical theorem, we discuss the origin and significance of the self-interaction force between both dipoles; this is done in connection with that of the angular distribution of scattered light and of the extinction cross section.

How does zero forward-scattering in magnetodielectric nanoparticles comply with the optical theorem?

A few decades ago, Kerker et al. [J. Opt. Soc. Am. 73, 765-767 (1983)] theoretically pointed out the interesting possibility of conceiving small magnetodielectric spheres that may provide zero scattering in the forward direction, despite significantly larger scattering in any other direction. Recent experimental and theoretical papers on the topic have further discussed this possibility in more realistic scenarios. Inspecting some of their analyses, it seems indeed possible to conceive nanoparticles characterized by a scattering pattern with a sharp minimum, although not zero, in the forward direction. From a theoretical standpoint, however, it is well known that the total scattered power from any object has to be proportional to a portion of the scattered field in the forward direction, implying that very small or zero forward scattering should be synonymous to even smaller or zero total scattering, regardless of the nature of the object and of its design. Using analytical theory and an accurate scattering formulation, we clarify the nature of this apparent paradox and the limitations of this anomalous phenomenon in terms of particle size. In this way, we shed some new light on theoretical and experimental papers on the topic, identifying relevant missteps in some of their physical interpretation, and considering the general possibility of verifying these effects. This discussion may also be relevant to some cloaking applications using exotic artificial materials.

On seismic interferometry, the generalized optical theorem, and the scattering matrix of a point scatterer

We have analyzed the far-field approximation of the Green’s function representation for seismic interferometry. By writing each of the Green’s functions involved in the correlation process as a superposition of a direct wave and a scattered wave, the Green’s function representation is rewritten as a superposition of four terms. When the scattered waves are modeled with the Born approximation, it appears that a three-term approximation of the Green’s function representation (omitting the term containing the crosscorrelation of the scattered waves) yields a nearly exact retrieval, whereas the full four-term expression leads to a significant nonphysical event. This is because the Born approximation does not conserve energy and therefore is an insufficient model to explain all aspects of seismic interferometry. We use the full four-term expression of the Green’s function representation to derive the generalized optical theorem. Unlike other recent derivations, which use stationary phase analysis, our derivation uses reciprocity theory. From the generalized optical theorem, we derive the nonlinear scattering matrix of a point scatterer. This nonlinear model accounts for primary and multiple scattering at the point scatterer and conforms with well-established scattering theory of classical waves. The model is essential to explain fully the results of seismic interferometry, even when it is applied to the response of a single point scatterer. The nonlinear scattering matrix also has implications for modeling, inversion, and migration.

Coupled channels optical theorem and non-elastic cross section sum rule

Within a coupled channels framework a theorem, similar to the optical theorem, is proved which provides a new formula for total non-elastic (inelastic, rearrangement and absorption) cross sections. An approximate cross section energy sum rule is also developed in terms of the trace of the imaginary part of an energy independent, but non-local optical potential. Corrections to sum rule are found small indicating that the result is a good approximation. The theorem and sum rule are applied to the Lane model describing charge exchange reactions.

Calculation of tip enhanced Raman scattering caused by nanoparticle plasmons acting on a molecule placed near a metallic film

Light scattering in an axially symmetric composite system of a nanoparticle, an oscillating dipole and a metal film (covering a dielectric support) is considered. Nanoparticle and dipole are placed on the axis of symmetry. The axially oriented dipole is situated between film and nanoparticle. The field-enhancement factor at the position of the dipole and dipole radiation is calculated on the basis of Maxwell's equations, reduced by Green's functions to a system of boundary integral equations. The total enhancement of the light scattering, which is a product of the enhancement of the field intensity and the dipole radiation, depends on many parameters: the wavelength of light, the metal permittivity, film thickness, geometry of the nanoparticle, angle of incidence of the laser beam, but most strongly on the distance between the nanoparticle and film surface. According to our calculations, the total enhancement factor for Raman radiation can reach huge values in the order of ${10}^{10}--{10}^{11}$. The angular spectrum of the radiating dipole is derived and the accuracy of calculations is checked by the optical theorem of reciprocity.

Radiative corrections to the polarizability tensor of an electrically small anisotropic dielectric particle

Radiative corrections to the polarizability tensor of isotropic particles are fundamental to understand the energy balance between absorption and scattering processes. Equivalent radiative corrections for anisotropic particles are not well known. Assuming that the polarization within the particle is uniform, we derived a closed-form expression for the polarizability tensor which includes radiative corrections. In the absence of absorption, this expression of the polarizability tensor is consistent with the optical theorem. An analogous result for infinitely long cylinders was also derived. Magneto optical Kerr effects in non-absorbing nanoparticles with magneto-optical activity arise as a consequence of radiative corrections to the electrostatic polarizability tensor.

Unitarity-Cuts and Berry’s Phase

Elaborating on the observation that two-particle unitarity-cuts of scattering amplitudes can be computed by applying Stokes' Theorem, we relate the Optical Theorem to the Berry Phase, showing how the imaginary part of arbitrary one-loop Feynman amplitudes can be interpreted as the flux of a complex 2-form.

Neutrino Processes in Neutron Stars

The aim of these lectures is to introduce basic processes responsible for cooling of neutron stars and to show how to calculate the neutrino production rate in dense strongly interacting nuclear medium. The formalism is presented that treats on equal footing one-nucleon and multiple-nucleon processes and reactions with virtual bosonic modes and condensates. We demonstrate that neutrino emission from dense hadronic component in neutron stars is subject of strong modifications due to collective effects in the nuclear matter. With the most important in-medium processes incorporated in the cooling code an overall agreement with available soft X ray data can be easily achieved. With these findings the so-called “standard” and “non-standard” cooling scenarios are replaced by one general “nuclear medium cooling scenario” which relates slow and rapid neutron star coolings to the star masses (interior densities).The lectures are split in four parts. Part I : After short introduction to the neutron star cooling problem we show how to calculate neutrino reaction rates of the most efficient one-nucleon and two-nucleon processes. No medium effects are taken into account in this instance. The effects of a possible nucleon pairing are discussed. We demonstrate that the data on neutron star cooling cannot be described without inclusion of medium effects. It motivates an assumption that masses of the neutron stars are different and that neutrino reaction rates should be strongly density dependent. Part II : We introduce the Green’s function diagram technique for systems in and out of equilibrium and the optical theorem formalism. The latter allows to perform calculations of production rates with full Green’s functions including all off-mass-shell effects. We demonstrate how this formalism works within the quasiparticle approximation.Part III : The basic concepts of the nuclear Fermi liquid approach are introduced. We show how strong interaction effects can be included within the Green’s function formalism. Softening of the pion mode with an baryon density increase is explicitly incorporated. We show examples of inconsistencies in calculations without inclusion of medium effects. Then we demonstrate calculations of different reaction rates in non-superfluid nuclear matter with taking into account medium effects. Many new reaction channels are open up in the medium and should be analyzed. Part IV : We discuss the neutrino production reactions in superfluid nuclear systems. The reaction rates of processes associated with the pair breaking and formation are calculated. Special attention is focused on the gauge invariance and the exact fulfillment of the Ward identities for the vector current. Finally we present comparison of calculations of neutron star cooling performed within nuclear medium cooling scenario with the available data.

Effect of the counterrotating terms on polarizability in atom-field interactions

The effect of the counterrotating terms on the linear polarizability is investigated, which is responsible for the validity of the optical theorem in all frequency regions. A unitary transformation method [H. Zheng, S. -Y. Zhu, and M.S. Zubairy, Rev. Lett. 101, 200404 (2008)] is adopted to overcome the difficulty brought in by the counterrotating terms, which yields a rotating-wave-approximation-like Hamiltonian with modified coupling constant due to the counterrotating terms. A simple expression for the polarizability is obtained, which is a sum of resonant (-) and antiresonant (+) parts, and from which the role of the counterrotating terms and quantum interference between the counterrotating terms and rotating terms at far off-resonance are discussed.

Optical theorem for the Kramers’ problem

Optical theorem formulation of the Kramers’ problem is proposed. A new technique to estimate the rate of escape in the Kramers model is developed, making use of analyticity relations analogous to those of the scattering amplitude appearing in particle physics. The formalism is shown to provide a very short derivation of the Mel'nikov–Meshkov solution for energy distribution functions in the barrier region, because of analyticity requirements alone. When the escape event is viewed as a causal one, appropriate analytic functions yielding the rate constant obey some relations in the Fourier space very analogous to those of the Kramers and Krönig for the dielectric function. While it seems to be rather a simplistic description, it reveals a linkage between the refractive index and the superionic conduction. We briefly discuss other relevant aspects as the ac conductivity of ionic solids and relationships between the activation energy of superionic conductors and dielectric constant quite similar with those reported by Wakamura (JPCS, 59 (1998) 591).

Quantum dwell-correlation times in the scattering of two nonrelativistic particles

In a previous paper [G. E. Hahne, J. Phys. A 36, 7149 (2003)] the author studied a nontraditional boundary value problem associated with Schr\"odinger's partial differential equation for the wave function of a structureless particle moving in four-dimensional spacetime: in this boundary value problem, instead of the conventional specification of initial wave-function values on a $\text{time}=\text{constant}$ surface, suitable time-dependent boundary and normal-derivative values are given on a three-dimensional space-time surface surrounding a slablike region of interaction in four-dimensional spacetime. The particle's time coordinate plays a natural role as an operator and observable in the modified formalism. In the present paper, the formalism is extended to describe a system of two nonrelativistic particles---each with its own time coordinate---scattering from background potentials and from one another in four-dimensional spacetime. The two-body interaction is taken as a generic noninstantaneous action-at-a-distance, which depends independently on the space-time positions of the two particles. The dynamics is expressed in terms of an integral equation for the wave function, that is, a nonrelativistic version of the Bethe-Salpeter equation. An optical theorem is derived for the transition operator associated with scattering processes; when the theorem holds, the pointwise probability current density derivable from the wave function is conserved globally, that is, in a region covering the space-time domain of significant interparticle interaction. A general formula for the expected dwell-correlation time for the two particles in the space-time region in terms of the scattering matrices is worked out.

On the optical theorem and non-plane-wave scattering in quantum mechanics

In quantum mechanics, the optical theorem states that the extinction cross section is equal (within a prefactor 4π∕k, in which k is a quantum wave number) to the imaginary part of the forward scattering angular function. This theorem is valid for plane wave scattering. We discuss modifications required for non-plane-wave scattering and establish a generalized expression for the extinction cross section in quantum mechanics. Examples are provided for two kinds of quantum shaped beams, namely, Gaussian and Bessel beams.

Theoretical aspects of image formation in the aberration-corrected electron microscope

The theoretical aspects of image formation in the transmission electron microscope (TEM) are outlined and revisited in detail by taking into account the elastic and inelastic scattering. In particular, the connection between the exit wave and the scattering amplitude is formulated for non-isoplanatic conditions. Different imaging modes are investigated by utilizing the scattering amplitude and employing the generalized optical theorem. A novel obstruction-free anamorphotic phase shifter is proposed which enables one to shift the phase of the scattered wave by an arbitrary amount over a large range of spatial frequencies. In the optimum case, the phase of the scattered wave and the introduced phase shift add up to − π/2 giving negative contrast. We obtain these optimum imaging conditions by employing an aberration-corrected electron microscope operating at voltages below the knock-on threshold for atom displacement and by shifting optimally the phase of the scattered electron wave. The optimum phase shift is achieved by adjusting appropriately the constant phase shift of the phase plate and the phase shift resulting from the defocus and the spherical aberration of the corrected objective lens. The realization of this imaging mode is the aim of the SALVE project ( Sub- Å Low- Voltage Electron microscope).

Molecule Non-Radiative Coupling to a Metallic Nanosphere: An Optical Theorem Treatment

The non-radiative coupling of a molecule to a metallic spherical particle is approximated by a sum involving particle quasistatic polarizabilities. We demonstrate that energy transfer from molecule to particle satisfies the optical theorem if size effects corrections are properly introduced into the quasistatic polarizabilities. We hope that this simplified model gives valuable information on the coupling mechanism between molecule and metallic nanos-tructures available for, e.g., surface enhanced spectroscopy signal analysis.

The feasibility of the TRIC experiment at COSY

For the Time Reversal Invariance experiment at COSY (TRIC) that had been proposed at the Forschungszentrum Julich a novel technique for measuring total cross sections in internal experiments was developed and the achievable precision of this measuring technique was tested. The experimental idea constitutes a true P-even T-odd null test of TRI. In order to compare to the theoretical upper bound from edm measurements (Haxton and Horing, Nucl Phys A560:469, 1993), the TRI violating observable Ay,xz in proton-deuteron forward scattering has to be measured with an accuracy of 10 − 6. An internal TRI experiment can determine the total cross section via the optical theorem by measuring the forward scattering amplitude. In contrast to external experiments, the only calibrated device that is needed is a precise beam current transformer (BCT). The feasibility of an internal TRI experiment was tested at COSY in a measurement of Ay,y in p-p scattering, since these values are known. The analysis of the data showed the presence of unexpected large 1/f noise contributions, which eventually reduced the achievable accuracy by a factor 3. The origin of the 1/f noise was traced and found to be the Barkhausen noise from the ferrite-core of the BCT. A global weighted fitting technique based on a modified Wiener-Khinchin method was applied to suppress the influence of the 1/f noise.