Equivalent Photon Method Research Articles

Multiturn simulation of radiative Bhabha scattering in the equivalent photon approximation

In this paper, we present a Monte Carlo event generator for radiative Bhabha scattering, based on the method of equivalent photons, and optimized for multiturn tracking simulations in the framework. We demonstrate the accuracy of the event generator with successful benchmarks of the luminosity and event cross section against currently existing alternative tools. Consequently, we use it to investigate existing estimates of the radiative Bhabha scattering beam lifetime at the FCC-ee, as well as the impact of radiative Bhabha scattering on the beam dynamics, using full nonlinear tracking models. Published by the American Physical Society 2024

Alternative Origin of Galactic Positrons Generated by Ultraperipheral Collisions of Cosmic Rays

We suggest a new alternative model of positron origin in the Galaxy. It is shown in our model that interactions of the electromagnetic fields of colliding ions (ultraperipheral ion collisions) can contribute to the total production of Galactic positrons. The corresponding cross-section is estimated by using the Born approximation and the equivalent photon method. This process of ion collisions dominates in the range of subrelativistic energies and produces positrons with energies of several MeV. Despite its low efficiency, as it requires more than 0.1 erg to produce a single positron, this process may be an effective source of positrons in the Galactic medium.

Geant4 Electron–Proton Integral Inelastic Cross Section Models

Electron-proton integral inelastic cross section is calculated based on the proton structure function formalism. The cross section is compared with the GEANT4 CHIPS model calculations utilizing the equivalent photon method.

Determining B(E1) distributions of weakly bound nuclei from breakup cross sections using Continuum Discretized Coupled Channels calculations. Application to 11Be

A novel method to extract the B(E1) strength of a weakly bound nucleus from experimental Coulomb dissociation data is proposed. The method makes use of continuum discretized coupled channels (CDCC) calculations, in which both nuclear and Coulomb forces are taken into account to all orders. This is a crucial advantage with respect to the standard procedure based on the Equivalent Photon Method (EPM) which does not properly take into account nuclear distortion, higher order coupling effects, or Coulomb-nuclear interference terms. The systematic and statistical uncertainties of this procedure are evaluated. The procedure is applied to the 11Be nucleus using two sets of available experimental data at different energies, for which seemingly incompatible B(E1) have been reported using the EPM. We show that the present procedure gives consistent B(E1) strengths, thus solving the aforementioned long-standing discrepancy between the two measurements.

Ultraperipheral nuclear interactions

Long-distance ultraperipheral collisions of two relativistic ions are considered. Clouds of photons surrounding the ions are responsible for their distant electromagnetic interaction. The perturbative approach and the method of equivalent photons are described. It is shown that the total cross section of these collisions rapidly increases with an energy increase and is especially large for heavy ions. Some experimental data and their comparison with theoretical approaches are described. Further proposals are discussed.

Ultraperipheral vs. Ordinary Nuclear Interactions

It is argued that the cross sections of ultraperipheral interactions of heavy nuclei can become comparable in value to those of their ordinary hadronic interactions at high energies. Simple estimates of corresponding “preasymptotic energy thresholds” are provided. The method of equivalent photons is compared with the perturbative approach. The situation at NICA/FAIR energies is discussed.

Low-lying electric-dipole strengths of Ca, Ni, and Sn isotopes imprinted on total reaction cross sections

Low-lying electric-dipole ($E1$) strength of a neutron-rich nucleus contains information on neutron-skin thickness, deformation, and shell evolution. We discuss the possibility of making use of total reaction cross sections on $^{40}$Ca, $^{120}$Sn, and $^{208}$Pb targets to probe the $E1$ strength of neutron-rich Ca, Ni, and Sn isotopes. They exhibit large enhancement of the $E1$ strength at neutron number $N > 28$, $50$, and $82$, respectively, due to a change of the single-particle orbits near the Fermi surface participating in the transitions. The density distributions and the electric-multipole strength functions of those isotopes are calculated by the Hartree-Fock+BCS and the canonical-basis-time-dependent-Hartree-Fock-Bogoliubov methods, respectively, using three kinds of Skyrme-type effective interaction. The nuclear and Coulomb breakup processes are respectively described with the Glauber model and the equivalent photon method in which the effect of finite-charge distribution is taken into account. The three Skyrme interactions give different results for the total reaction cross sections because of different Coulomb breakup contributions. The contribution of the low-lying $E1$ strength is amplified when the low-incident energy is chosen. With an appropriate choice of the incident energy and target nucleus, the total reaction cross section can be complementary to the Coulomb excitation for analysing the low-lying $E1$ strength of unstable nuclei.

Polarization bremsstrahlung of fast electrons on metal nanospheres in a dielectric matrix in view of plasmon interference effects

The paper is devoted to the theoretical analysis of polarization bremsstrahlung (PB) [1] due to scattering of fast electrons by a metal nanosphere embedded in a dielectric matrix in a frequency region in the vicinity of dipole and quadrupole plasmon resonances. Here we take into account plasmon interference effects that arise in the frequency-angular distribution of PB. These effects are a consequence of interrelation between contributions to PBs due to a plasmon on the sphere surface of different multipolarity. Our approach is based on the Fermi method of equivalent photons [2] and the Mie theory of radiation scattering by small metal particles [3]. It is shown that taking into account plasmon interference in the PB differential cross-section results in specific features in the spectral distribution of an emitted photon that depend strongly on the radiation angle and nanosphere radius.

Generalized scaling laws for ionization of atomic states by ultra-short electromagnetic pulses

It is demonstrated that in the framework of the perturbation theory on laser field strength and the Fermi equivalent photon method expressions for photon transition, probabilities can be obtained that permit the derivation of scaling laws in terms of atomic state quantum numbers and pulse duration. A unified approach is developed that identifies universal scaling parameters for energy and pulse duration that allow analytical investigation of the interrelation of scaling laws for the two important regimes of above and below-threshold ionization. Numerical studies are presented that illuminate the conditions for linear and nonlinear regimes of photoionization, as dependent on the cycle number and carrier frequencies. We also discuss analytical asymptotic forms of the different regimes of photoionization. Finally, we develop a generalized unified approach that permits studies in terms of principal and orbital quantum numbers as well as in pulse duration for any regime of carrier frequencies.

Particle motion in a deformed potential using a transformed oscillator basis

The quantum description of a particle moving in a deformed potential is investigated. A pseudostate (PS) basis is used to represent the states of the composite system. This PS basis is obtained by diagonalizing the system Hamiltonian in a family of square integrable functions. In this work the Transformed Harmonic Oscillator (THO) functions, obtained from the solutions of the Harmonic Oscillator using a Local Scale Transformation (LST), are used. The proposed method is applied to the 11Be nucleus, treated in a two-body model (10Be+n). Both structure and reaction observables have been studied. Wavefunctions and energies obtained for the bound states and some low-lying resonances are compared with those obtained by direct integration of the Schroedinger equation. The dipole and quadrupole electric transition probabilities for the low-energy continuum have been calculated in the THO basis, and compared with the exact distributions obtained with the scattering states. Finally, the method is applied to describe the 11Be states in the Coulomb breakup of 11Be+208Pb at 69 MeV/nucleon. The energy and angular distributions of the exclusive breakup have been calculated using the Equivalent Photon Method, including both E1 and E2 contributions. The calculated distributions are found to be in good agreement with the available experimental data from RIKEN [Phys. Rev. C70, 054606]. At the very forward angles, the cross section is completely dominated by the dipole couplings.

Electroproduction of an electron-positron pair in a medium

The process of the electron-positron pair creation by a high-energy electron in a medium is analyzed. The spectral distribution over energies of created particles is calculated for the direct and cascade mechanisms of the process. The Coulomb corrections are included. The new formulation of the equivalent photon method is developed, which takes into account the influence of the multiple scattering. It is shown that the effects of multiple scattering can be quite effectively studied in the process under consideration.

On the eikonal approximation in the theory of transition radiation

The transition radiation of relativistic electrons in nonuniform media is considered. Based on the equivalent photon method and the eikonal approximation in wave mechanics, a method for describing this process is proposed. For the case in which the permittivity depends on several coordinates, equations for the spectral-angular density of transition radiation are obtained. The main results obtained in the Born and eikonal approximations of the theory of transition radiation are compared. The equations obtained are used to analyze the transition radiation process for a fiberlike target.

Neutrino magnetic moments and photo-disintegration of deuterium

Neutrinos with non-zero magnetic moments can dissociate deuterium nuclei by a photon exchange, in addition to the weak neutral current process. We calculate the neutrino magnetic moment induced photo-dissociation cross section of deuterium using the equivalent photon method. This process would contribute extra events to the neutral current reaction which is observed with high precision in the salt-phase of SNO experiment. Using the SNO data and the recent laboratory measurements of the 7 Be( p , γ ) 8 B reaction which give a more precise value of the solar 8 B flux we find that the neutrino effective magnetic moment is μ eff 2 =(−2.76±1.46)×10 −16 μ B 2 which can be interpreted as an upper bound | μ eff |<3.71×10 −9 μ B (at 95% C.L.) on the neutrino magnetic moments.

Neutrino magnetic moments and photo-disintegration of deuterium

Neutrinos with non-zero magnetic moments can dissociate deuterium nuclei by a photon exchange, in addition to the weak neutral current process. We calculate the neutrino magnetic moment induced photo-dissociation cross section of deuterium using the equivalent photon method. This process would contribute extra events to the neutral current reaction which is observed with high precision in the salt-phase of SNO experiment. Using the SNO data and the recent laboratory measurements of the 7Be(p,γ)8B reaction which give a more precise value of the solar 8B flux we find that the neutrino effective magnetic moment is μeff2=(−2.76±1.46)×10−16μB2 which can be interpreted as an upper bound |μeff|<3.71×10−9μB (at 95% C.L.) on the neutrino magnetic moments.

Equivalent-photon method study of differential cross sections for double ionization of helium by relativistic heavy-ion impact

We have calculated the probability for double ionization of helium by fast heavy-ion impact in the equivalent-photon picture. We find that the {ital shape} of differential cross sections is significantly affected by the inclusion of the electron-electron interaction in both the initial and the final channel, but is rather insensitive to the projectile charge and impact velocity. {copyright} {ital 1997} {ital The American Physical Society}

Effects of strong interaction on the electromagnetic dissociation

We investigate effects of strong interactions on the electromagnetic dissociation of nuclei in heavy-ion collisions. We start from the eikonal approach to the equivalent photon method to describe the electromagnetic contributions to the cross section of peripheral collisions. We summarize some results of this approach and characterize recent experiments in ‘universal plots’. In the second part of this work, we give a straightforward method to include transitions induced by the strong interactions between the ions. We introduce different methods to obtain the nuclear transition potential, and study the behavior of the resulting nuclear contributions.

Pion and neutron production by cosmic-ray muons underground.

The production of positive pions and neutrons by cosmic muons at underground sites of various depths is investigated. We first test the equivalent photon method in the particular case of \ensuremath{\Delta} excitation by the muon. We find that this method, when it neglects the momentum dependence of the transverse response, reproduces remarkably well the theoretical muon cross section. This success has lead us to apply the method to higher energies, where it has not been tested. We evaluate in this way the production of positive pions in liquid scintillator from known photo-absorption cross sections. At a shallow depth of 20 meters our estimate reproduces the measurement. As for the neutron emission, we include the obvious sources, such as the giant-resonance excitation, the quasideuteron process, the quasifree pion production as well as neutrons emitted following pion capture. Our evaluation underestimates the number of neutrons produced and finds a too weak dependence on the depth. This suggests that secondary neutron production is important at all depths.

Electromagnetic pair production with capture.

Calculations of the electron-positron pair production by a single photon in the Coulomb field of a nucleus with simultaneous capture of the electron into the K shell are presented. Numerical results are given for some nuclear charges up to 92 and energies from threshold to 15 MeV. Using the equivalent-photon method of Weizs\acker and Williams, reliable estimates of the cross sections for the production of ${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ (K orbit) pairs by very-high-energy fully stripped heavy ions can be made for arbitrary nuclear charges.

Coherent and incoherent radiation by channeled electrons

Abstract Based on the method of equivalent photons, incoherent bremsstrahlung probability is obtained as a function of impact parameter. It is shown that incoherent bremsstrahlung is caused by the fluctuation of atomic potential due to thermal vibrations. Numerical value of our result is considerably smaller than those of other theories.

Electromagnetic dissociation of Pb nuclei in peripheral ultrarelativistic heavy-ion collisions.

We calculate the total electromagnetic dissociation cross section in peripheral heavy-ion collisions $^{208}\mathrm{Pb}$${+}^{208}$Pb for the planned Brookhaven Relativistic Heavy Ion Collider, the CERN Large Hadron Collider, and the Superconducting Super Collider. The two nuclei interact via their Lorentz contracted electromagnetic fields leading to nuclear disintegration. We employ an impact parameter dependent version of the equivalent photon method with experimental photon-nucleus dissociation cross sections. The hadronic structure of the photon at large equivalent photon energies has been taken into account. In particular, we stress unitarity conservation of the dissociation probability for small impact parameters.