Eikonal Approximation Research Articles

Birefringence and quasinormal modes of the Einstein-Euler-Heisenberg black hole

In this contribution we study the birefringence and the quasinormal modes (QNM) in the eikonal approximation, of the Einstein-Euler-Heisenberg black hole (EEH-BH) . The EEH-BH is an exact solution of the Einstein equations coupled to the Euler-Heisenberg nonlinear electrodynamics. It is well known that in the presence of strong electromagnetic fields light rays modify their trajectories and do follow the null geodesics of an effective metric as a result of the nonlinear interaction between light and the intense magnetic or electric background. In the Euler-Heisenberg theory the phenomenon of birefringence arises and then exist two possible light trajectories for polarized light in the vicinity of the EEH-BH. On the other hand, using the correspondence between the parameters of the null unstable geodesics and the quasinormal modes in the eikonal approximation. We determine these QNM for both, the electric and the magnetic EEH-BH and compare them with its linear counterpart, the Reissner-Nordstr\"{o}m black hole, since there are two effective metrics, to each one corresponds one null geodesic that renders two possible QNM from the same compact object.

Influence of gravitational waves upon light in the Minkowski background: From null geodesics to interferometry

We have recently derived a manifestly covariant evolution law, under the geometrical optics (or eikonal) approximation of the vacuum Maxwell equations, for the electric field along null geodesics in a general spacetime, relative to an arbitrary set of instantaneous observers [Phys. Rev. D 101, 081501(R) (2020)]. As one of its applications, we derive here the final detected intensity signal arising from a prototypical laser interferometric gravitational-wave (GW) Michelson-Morley detector, comoving with transverse-traceless (TT) observers, valid for both long and short GW wavelengths (as compared to the lengths of the interferometers arms). The motion of the test particles and light is described through the covariant kinematic and optical parameters. One of our main results is the presentation of the integrated null geodesic parametric equations exchanged between two TT observers in terms of explicitly observable quantities (laser initial frequency and positions of the observers) and the profile of the plane GW packet. This allows us to revisit the derivation of the consequential radar distance and Doppler shift, taking the opportunity to discuss some related subtle conceptual issues and how they might affect the interferometric process. Another achievement is the calculation of the electric field in each arm up to the detection event, for any relative orientations of the arms and the GW direction. The main quantitative result is the new expression for the final interference pattern, for normal GW incidence, which turns out to have three contributions: (i) the well-known traditional one due to the difference in optical paths, and two new ones due to (ii) the Doppler effect and (iii) the divergence of the laser beams. The quantitative relevance of the last two contributions is compared to the traditional one and shown to be negligible within the geometrical optics regime of light. Although in general further contributions from the nonparallel transport of the polarization vector are expected [cf. Phys. Rev. D 101, 081501(R) (2020)], again in the case of GW normal incidence, such a vector is indeed parallel transported, and those contributions are absent.

Relativistic Abrasion–Ablation De-excitation Fragmentation (RAADFRG) model

Astronauts are exposed to ionizing radiation that may pose significant health risks from missions to low Earth orbit (LEO) and beyond. The National Aeronautics and Space Administration (NASA) uses the deterministic radiation transport code, High charge (Z) and Energy TRaNsport (HZETRN), to estimate particle fluxes inside shielded vehicles to evaluate risk of radiation exposure to crew members. Highly efficient radiation transport algorithms and cross section models are needed to perform calculations in realistic vehicles with complex geometrical configurations. The HZETRN code uses the NUClear FRaGmentation (NUCFRG) model to evaluate fragmentation cross section products from nucleus–nucleus collisions. Although highly efficient, the NUCFRG model has some limitations that are based on its unique implementation of the abrasion–ablation formalism. NUCFRG performs well in predicting fragmentation cross sections on the average when compared to experimental data; however, even–odd nuclear structure effects observed in laboratory measurements are absent. The aim of the present work is to formulate a self-consistent theory that produces accurate nuclear fragmentation cross sections while maintaining numerical efficiency. To that end, the Relativistic Abrasion–Ablation FRaGmentation (RAADFRG) model has been developed. The theoretical framework for nuclear interaction is multiple scattering theory (MST), where relativistic kinematics may be included in the momentum–space representation of the Lippmann–Schwinger equation. The nuclear abrasion model employs the Eikonal (Eik) approximation and is used to predict prefragment cross sections. A novel approach is utilized for the excitation energy of prefragment, where in addition to differences of binding energies between two nuclei, energy is transferred to the prefragment from subsequent multiple scattering of abraded nucleons with the spectator nucleon constituents of the prefragment. Next, the excited prefragment liberates particles through the nuclear ablation process, and a nuclear coalescence model that forms aggregate particles for each prefragment channel is included in the yield. The ElectroMagnetic Dissociation FRaGmentation (EMDFRG) model is also included for peripheral interactions that stimulates particle emission via nuclear-photon field interactions. When compared to NUCFRG3, uncertainty quantification analysis shows that RAADFRG is better able to predict experimental nuclear fragmentation cross sections. RAADFRG is also shown to produce the even–odd nuclear structure effects, which is achieved by modification of isospin pairing correction in the prefragment excitation energy model.

Holographic teleportation in higher dimensions

We study higher-dimensional traversable wormholes in the context of Rindler-AdS/CFT. The hyperbolic slicing of a pure AdS geometry can be thought of as a topological black hole that is dual to a conformal field theory in the hyperbolic space. The maximally extended geometry contains two exterior regions (the Rindler wedges of AdS) which are connected by a wormhole. We show that this wormhole can be made traversable by a double trace deformation that violates the average null energy condition (ANEC) in the bulk. We find an analytic formula for the ANEC violation that generalizes Gao-Jafferis-Wall result to higher-dimensional cases, and we show that the same result can be obtained using the eikonal approximation. We show that the bound on the amount of information that can be transferred through the wormhole quickly reduces as we increase the dimensionality of spacetime. We also compute a two-sided commutator that diagnoses traversability and show that, under certain conditions, the information that is transferred through the wormhole propagates with butterfly speed {upsilon}_B=frac{1}{d-1} .

Quasinormal modes in the field of a dyon-like dilatonic black hole

Quasinormal modes of massless test scalar field in the background of gravitational field for a non-extremal dilatonic dyonic black hole are explored. The dyon-like black hole solution is considered in the gravitational 4d model involving two scalar fields and two 2-forms. It is governed by two 2-dimensional dilatonic coupling vectors {lambda }_i obeying {lambda }_i ({lambda }_1 + {lambda }_2) > 0, i =1,2. The first law of black hole thermodynamics is given and the Smarr relation is verified. Quasinormal modes for a massless scalar (test) field in the eikonal approximation are obtained and analysed. These modes depend upon a dimensionless parameter a (0 < a le 2) which is a function of {lambda }_i. For limiting strong (a = +0) and weak (a = 2) coupling cases, they coincide with the well-known results for the Schwarzschild and Reissner–Nordström solutions. It is shown that the Hod conjecture, connecting the damping rate and the Hawking temperature, is satisfied for 0 < a le 1 and all allowed values of parameters.

Models of breakup: a final state interaction problem

In this paper, we discuss the evolution of breakup models from fully quantum mechanical, such as the Ichimura–Austern–Vincent model to semiclassical, to eikonal approximations following the insight on the mechanism first proposed by Hussein and McVoy (HM) for the presently called stripping term. In particular we concentrate on, and stress that, the correct implementation of a quantum mechanical model of breakup requires the use of energy dependent interactions and the energy averaging procedure is a key point to understand the difference among models. On the other hand using fixed energy potentials is one of the steps towards the high energy eikonal limit first proposed by HM. However the intermediate semiclassical transfer to the continuum model of Bonaccorso and Brink does use an energy dependent nucleon–target optical potential, while fixing the core–target interaction at the incident energy. The relationship between these methods is clarified.

Geometric optics in the presence of axionlike particles in curved spacetime

We present a concise derivation of geometric optics in the presence of axionic fields in a curved space-time. Whenever light can be described via geometric optics (the eikonal approximation), the only difference to the situation without axionic field is the phenomenon of achromatic birefringence. Consequently, redshift of light and distance estimates based on propagating light rays, as well as shear and magnification due to gravitational lensing are not affected by the interaction of light with an axionic field.

Prediction of the analyzing power for p⃗+He6 elastic scattering at 200 MeV from p⃗+He4 elastic scattering at 200 MeV

We apply the cluster-folding (CF) model for $\vec{p}+^{6}$He scattering at 200 MeV, where the potential between $\vec{p}$ and $^{4}$He is fitted to data on $\vec{p}+^{4}$He scattering at 200 MeV. For $\vec{p}+^{6}$He scattering at 200 MeV, the CF model reproduces measured differential cross section with no free parameter, We then predict the analyzing power $A_y(q)$ with the CF model, where $q$ is the transfer momentum. Johnson, Al-Khalili and Tostevin construct a theory for one-neutron halo scattering, taking (1) the adiabatic approximation and (2) neglecting the interaction between a valence neutron and a target, and yield a simple relationship between the elastic scattering of a halo nucleus and of its core under certain conditions. We improve their theory with (3) the eikonal approximation in order to determine $A_y(q)$ for $^{6}$He from the data on $A_y(q)$ for $^{4}$He. The improved theory is accurate, when approximation (1)--(3) are good. Among the three approximations, approximation (2) is most essential. The CF model shows that approximation (2) is good in $0.9 < q < 2.4$ fm$^{-1}$. In the improved theory, the $A_y(q)$ for $^{6}$He is the same as that for $^{4}$He. In $0.9 < q < 2.4$ fm$^{-1}$, we then predict $A_y(q)$ for $\vec{p}+^{6}$He scattering at 200 MeV from measured $A_y(q)$ for $\vec{p}+^{4}$He scattering at 200 MeV. We thus predict $A_y(q)$ with the model-dependent and the model-independent prescription. The ratio of differential cross sections measured for $^{6}$He to that for $^{4}$He is related to the wave function of $^{6}$He. We then determine the radius between $^{4}$He and the center-of-mass of valence two neutrons in $^{6}$He. The radius is 5.77 fm.

Diffraction of electromagnetic waves by an extended gravitational lens

We continue our study of the optical properties of the solar gravitational lens (SGL). Taking the next step beyond representing it as an idealized monopole, we now characterize the gravitational field of the Sun using an infinite series of multipole moments. We consider the propagation of electromagnetic (EM) waves in this gravitational field within the first post-Newtonian approximation of the general theory of relativity. The problem is formulated within the Mie diffraction theory. We solve Maxwell's equations for the EM wave propagating in the background of a static gravitational field of an extended gravitating body, while accounting for multipole contributions. Using a wave-theoretical approach and the eikonal approximation, we find an exact closed form solution for the Debye potentials and determine the EM field at an image plane in the strong interference region of the lens. The resulting EM field is characterized by a new diffraction integral. We study this solution and show how the presence of multipoles affects the optical properties of the lens, resulting in distinct diffraction patterns. We identify the gravitational deflection angle with the individual contributions due to each of the multipoles. Treating the Sun as an extended, axisymmetric, rotating body, we show that each zonal harmonics causes light to diffract into an area whose boundary is a caustic of a particular shape. The appearance of the caustics modifies the point-spread function (PSF) of the lens, thus affecting its optical properties. The new wave-theoretical solution allows the study gravitational lensing by a realistic lens that possesses an arbitrary number of gravitational multipoles. This {\em angular eikonal method} represents an improved treatment of realistic gravitational lensing. It may be used for a wave-optical description of many astrophysical lenses.

The Coulomb effects in laser-assisted single photoionization

Attosecond photoionization time delays reveal information about an outgoing electron getting away from the Coulomb potential. In this study, we improve the eikonal approximation model that overestimates the laser-Coulomb coupling effect in the laser-assisted photoionization of atoms. The improved eikonal approximation model can be accurate on about the 2 asec level relative to the time-dependent Schrödinger equation results. The improvement of photoionization time delays demonstrates that the electrons ionized by extreme ultraviolet attosecond pulse possesses momentum larger than the asymptotical momentum due to the attractive Coulomb potential of the parent ion. These results will give a deeper insight into understanding the laser-assisted single photoionization.

An eikonal approximation model for two-color two-photon attosecond interferometric spectrum

The emission time of photoelectrons from atoms, molecules and solids can be accurately measured on an attosecond scale by using two-color two-photon attosecond interferometric spectroscopy, which helps us to understand the ultrafast electronic dynamics in laser-assisted single photoionization. Understanding the photoelectron emission time depends on the physical model, and the relevant theoretical model provides a better physical explanation and numerical prediction for the photoemission time delay. Although the numerical solution of the time-dependent Schrödinger equation can accurately predict the photoelectron emission time, but it cannot provide a physical explanation. Although some other current theoretical models can provide a more reasonable corresponding physical process, the quantitative prediction of the photoemission time delay has a large deviation. Therefore, we improve the exisating eikonal approximation model. Comparing with the existing eikonal approximation model, we use a more accurate final state wave function and calculate the photoelectron trajectory more accurately when calculating the phase accumulated in the photoelectron propagation process, so we can predict the photoemission time delay more accurately. By comparing our numerical simulation results, we find that when the final kinetic energy of photoelectron is low, the calculated results from the existing theoretical model are greatly different from those from the time-dependent Schrödinger equation, reaching tens of attoseconds. The resultsfrom the existing theoretical model are closer to those from the time-dependent Schrödinger equation with the increase of final kinetic energy of photoelectron. However, no matter what the final kinetic energy of the photoelectron is, the difference between the calculation result from the improved eikonal approximation model and that from the time-dependent Schrödinger equation is always very small. Therefore, our improved eikonal approximation model is closer to the results from the time-dependent Schrödinger equation than the existing theoretical model, which greatly deeps our understanding of the ultra-fast process of photoelectron emission.

Tunnelling around bends—Wave scattering in curved shell structures

A ray dynamics describing wave transport on curved and smooth thin shells can be obtained from the underlying wave equations via the Eikonal approximation. We analyse mid-frequency effects near the ring frequency for curved plates consisting of a cylindrical region smoothly connected to two flat plates. Using classical shell theory, we treat a corresponding ray-tracing limit derived in the short wavelength regime for bending, shear and pressure incident waves. A treatment based on real rays gives either total reflection or total transmission; the solution of the full wave equations shows in contrast a smooth transition and exhibits resonant states localised in and around the region of maximal curvature. We show here for the first time, that both the smooth transition from total reflection to total transmission and the occurrence of resonant states can be described in a ray tracing approximation by extending the treatment to complex rays. In this sense, wave transmission across bends is a tunnelling phenomenon similar to the tunnelling effects known in optics and quantum mechanics. Based on simplified graph models, we can make qualitative predictions for resonance positions in parameter and frequency spaces. We are thus able to approximate the scattering matrix for waves incident on the bend accounting for tunnelling mediated by resonant states and uniformly treating the transition between the limits of totally reflected and totally transmitted waves.

Solving the apparent inconsistency between GSI and RIKEN estimates of 11Be dB(El)/dE

11Be is the archetypical one-neutron halo nucleus. Due to its short lifetime, one of the only way to infer information about its exotic structure is to study reactions involving that nucleus, like breakup. When performed on a heavy target, like lead, breakup is dominated by the E1 transition from the bound state to the continuum, which is characterized by the dB(E1)/dE. This strength has been inferred from two experiments, one performed at 520A MeV at GSI and the other at 69A MeV at RIKEN. Strangely the analyses of both experiments provide different E1 strengths. In this work, we reanalyze them using the eikonal approximation to study this discrepancy. In particular, we properly take into account relativistic effects, and include a consistent treatment of both nuclear and Coulomb interactions and their interference at all orders. The description of the 11Be structure is provided by halo effective field theory (Halo-EFT). Our cross sections for the 11Be breakup are in good agreement with both RIKEN and GSI data. The dB(E1)/dE extracted from our 11Be model is in agreement with the RIKEN result and ab initio predictions. We can conclude that the discrepancy between GSI and RIKEN dB(E1)/dE arises from the method applied to extract this quantity. From our detailed analysis of the reaction, it seems that the most efficient way to extract the dB(E1)/dE from the breakup cross section is to select the data at small angles, where the reaction is dominated by the Coulomb interaction.

The eikonal approximation of the scattering theory for fast charged particles in a thin layer of crystalline and amorphous media

On the basis of the eikonal approximation of quantum scattering theory, the problem of fast charged particle scattering in a thin crystal when particles fall along one of its planes of atoms and in a thin layer of an amorphous matter is considered. It is shown that the scattering cross section in this problem for parameters which are beyond the scope of application of the Born perturbation theory, differs significantly from the corresponding result of the Born approximation. In this case, the scattering in the transverse to the plane direction is determined mainly by a continuous plane potential which is widely used in the channeling theory. The scattering of a particle in the longitudinal direction has features of scattering in a two-dimensional amorphous medium with the inhomogeneous density of atoms. The concept of a continuous potential of the crystal plane of atoms in the suggested approach appears automatically.

Extremal black hole scattering at mathcal{O} (G3): graviton dominance, eikonal exponentiation, and differential equations

We use mathcal{N} = 8 supergravity as a toy model for understanding the dynamics of black hole binary systems via the scattering amplitudes approach. We compute the conservative part of the classical scattering angle of two extremal (half-BPS) black holes with minimal charge misalignment at mathcal{O} (G3) using the eikonal approximation and effective field theory, finding agreement between both methods. We construct the massive loop integrands by Kaluza-Klein reduction of the known D-dimensional massless integrands. To carry out integration we formulate a novel method for calculating the post-Minkowskian expansion with exact velocity dependence, by solving velocity differential equations for the Feynman integrals subject to modified boundary conditions that isolate conservative contributions from the potential region. Motivated by a recent result for universality in massless scattering, we compare the scattering angle to the result found by Bern et. al. in Einstein gravity and find that they coincide in the high-energy limit, suggesting graviton dominance at this order.

Aspects of arbitrarily oriented dipoles scattering in a plane: Short-range interaction influence

The impact of the short-range interaction on the resonances occurrence in the anisotropic dipolar scattering in a plane was numerically investigated for the arbitrarily oriented dipoles and for a wide range of collision energies. We revealed the strong dependence of the cross section of the 2D dipolar scattering on the radius of short-range interaction, which is modeled by a hard wall potential and by the more realistic Lennard-Jones potential, and on the mutual orientations of the dipoles. We defined the critical (magic) tilt angle of one of the dipoles, depending on the direction of the second dipole for arbitrarily oriented dipoles. It was found that resonances arise only when this angle is exceeded. In contrast to the 3D case, the energy dependencies of the boson (fermion) 2D scattering cross section grows (is reduced) with an energy decrease in the absence of the resonances. We showed that the mutual orientation of dipoles strongly impacts the form of the energy dependencies, which begin to oscillate with the tilt angle increase, unlike the 3D dipolar scattering. The angular distributions of the differential cross section in the 2D dipolar scattering of both bosons and fermions are highly anisotropic at non-resonant points. The results of the accurate numerical calculations of the cross section agree well with the results obtained within the Born and eikonal approximations.

Neutrino oscillations in gravitational and cosmological backgrounds

We use the eikonal approximation in order to calculate the additional phase shift between two neutrino mass eigenstates during their propagation in a background of gravitational wave or scalar perturbations in the flat and the FRW spacetime metric. We comment on the dependence of the results on the characteristics of the perturbations, give some order-of-magnitude estimates, and find that, although small, the resulting phase difference persists for large redshifts, up to the validity of our approximations.

On the impact of non-factorisable corrections in VBF single and double Higgs production

We study the non-factorisable QCD corrections, computed in the eikonal approximation, to Vector-Boson Fusion single and double Higgs production and show the combined factorisable and non-factorisable corrections for both processes at mathcal{O}left({alpha}_s^2right) . We investigate the validity of the eikonal approximation with and without selection cuts, and carry out an in-depth study of the relative size of the non-factorisable next-to-next-to-leading order corrections compared to the factorisable ones. In the case of single Higgs production, after selection cuts are applied, the non-factorisable corrections are found to be mostly contained within the factorisable scale uncertainty bands. When no cuts are applied, instead, the non-factorisable corrections are slightly outside the scale uncertainty band. Interestingly, for double Higgs production, we find that both before and after applying cuts, non-factorisable corrections are enhanced compared to the single Higgs case. We trace this enhancement to the existence of delicate cancellations between the various leading-order Feynman diagrams, which are partly spoiled by radiative corrections. All contributions studied here have been implemented in proVBFH v1.2.0 and proVBFHH v1.1.0.

Double charge exchange reactions as a probe for neutrinoless double beta decay nuclear matrix elements

The formalism to describe heavy-ion double charge exchange (DCE) processes in the eikonal and small-momentum transfer approximations introduced in Phys. Rev. C 98, 061601(R) (2018) is briefly discussed. It is also shown that, under the previous approximations, the heavy-ion DCE cross-section can be factorized in terms of a reaction and a nuclear part. A double charge exchange effective potential is explicitly derived in the closure approximation and also for the first time the explicit form of the DCE nuclear matrix elements, that are of the form of double Gamow-Teller and double Fermi. The recent hypothesis of a linear correlation between double Gamow-Teller neutrinoless double beta decay and DCE nuclear matrix elements is confirmed thanks to the first explicit derivation of DCE nuclear matrix elements, and by means of microscopic IBM2 calculations.

Eikonal phase matrix, deflection angle, and time delay in effective field theories of gravity

The eikonal approximation is an ideal tool to extract classical observables in gauge theory and gravity directly from scattering amplitudes. Here we consider effective theories of gravity where in addition to the Einstein-Hilbert term we include nonminimal couplings of the type ${R}^{3}$, ${R}^{4}$ and FFR. In particular, we study the scattering of gravitons and photons of frequency $\ensuremath{\omega}$ off heavy scalars of mass $m$ in the limit $m\ensuremath{\gg}\ensuremath{\omega}\ensuremath{\gg}|\stackrel{\ensuremath{\rightarrow}}{q}|$, where $\stackrel{\ensuremath{\rightarrow}}{q}$ is the momentum transfer. The presence of nonminimal couplings induces helicity-flip processes which survive the eikonal limit, thereby promoting the eikonal phase to an eikonal phase matrix. We obtain the latter from the relevant two-to-two helicity amplitudes that we compute up to one-loop order, and confirm that the leading-order terms in $\ensuremath{\omega}$ exponentiate \`a la Amati, Ciafaloni and Veneziano. From the eigenvalues of the eikonal phase matrix we then extract two physical observables, to 2PM order: the classical deflection angle and Shapiro time delay/advance. Whenever the classical expectation of helicity conservation of the massless scattered particle is violated, i.e., the eigenvalues of the eikonal matrix are nondegenerate, causality violation due to time advance is a generic possibility for small impact parameter. We show that for graviton scattering in the ${R}^{4}$ and FFR theories, time advance is circumvented if the couplings of these interactions satisfy certain positivity conditions, while it is unavoidable for graviton scattering in the ${R}^{3}$ theory and photon scattering in the FFR theory. The scattering processes we consider mimic the deflection of photons and gravitons off spinless heavy objects such as black holes.