Eikonal-Glauber Thomas–Fermi model for atomic collisions with many-electron atoms for plasma applications

2018 ◽  
Vol 84 (3) ◽  
Author(s):  
Myoung-Jae Lee ◽  
Young-Dae Jung
Keyword(s):  
Form Factor ◽  
Phase Shift ◽  
Momentum Transfer ◽  
Cross Section ◽  
Atomic Charge ◽  
Fermi Model ◽  
Thomas Fermi ◽  
Scattering Phase ◽  
Effective Atomic Charge ◽  
Atomic Form Factor

We have derived the universal eikonal-Glauber Thomas–Fermi model for atomic collision cross-sections with many-electron atoms, such as iron and tungsten atoms, including the influence of atomic screening in fusion devices and plasma technologies. The eikonal-Glauber method is employed to obtain the analytic expressions for the effective atomic charge, the scattering phase shift and the atomic cross-section in terms of the atomic form factor and the Mott–Massey screening parameter. The result shows that the effective atomic charge would be the same as the case of the net nuclear charge for the large momentum transfer domain and becomes zero without momentum transfer due to the influence of bound atomic electrons. It is shown that the eikonal scattering phase shift and the total eikonal-Glauber scattering cross-section increase with increasing charge number$Z$of the nucleus of the target atom. It is also found that the charge dependence of the total eikonal-Glauber scattering cross-section decreases with an increase of the scaled collision energy since the atomic form factor is small for large collision energies.

THE ANOMALOUS PROCESS γπ → ππ AND ITS IMPACT ON THE π0 TRANSITION FORM FACTOR

2014 ◽  
Vol 35 ◽  
pp. 1460397
Author(s):  
BASTIAN KUBIS
Keyword(s):  
Form Factor ◽  
Phase Shift ◽  
Theoretical Analysis ◽  
Cross Section ◽  
Transition Form Factor ◽  
P Wave ◽  
Chiral Anomaly ◽  
Transition Form ◽  
Dispersive Representation ◽  
Important Input

The process γπ → ππ, in the limit of vanishing photon and pion energies, is determined by the chiral anomaly. This reaction can be investigated experimentally using Primakoff reactions, as currently done at COMPASS. We derive a dispersive representation that allows one to extract the chiral anomaly from cross-section measurements up to 1 GeV, where effects of the ρ resonance are included model-independently via the ππ P-wave phase shift. We discuss how this amplitude serves as an important input to a dispersion-theoretical analysis of the π0 transition form factor, which in turn is a vital ingredient to the hadronic light-by-light contribution to the anomalous magnetic moment of the muon.

THE THOMAS–FERMI–GOMBÁS ATOM MODELS IN WHICH THE ELECTRONS ARE GROUPED INTO n- AND nl-SHELLS AND A CALCULATION OF THE ATOMIC FORM FACTOR

2004 ◽  
Vol 18 (03) ◽  
pp. 409-419
Author(s):  
V. F. TARASOV
Keyword(s):  
Form Factor ◽  
Kinetic Energy ◽  
Total Energy ◽  
Hypergeometric Functions ◽  
Fermi Theory ◽  
Thomas Fermi ◽  
Atomic Form Factor ◽  
First Time ◽  
Analytical Expressions ◽  
Gradient Correction

This article, considers in detail P. Gombás's idea of grouping electrons into n- and nl-shells in the Thomas–Fermi theory of free atoms briefly, the TFG n- and TFG nl-models respectively). Using these models, exact analytical expressions for the total energy E and the atomic form factor F(κ) are obtained. All integrals of the TFG nl-model are computed by means of the hypergeometric functions 2F1(x), 3F2(x), F2(x,y) and FA(x1,…,x6) for the first time. In particular, Weizsäcker's gradient correction to the kinetic energy of the nl-th shell [Formula: see text] generates a new numerical triangle [Formula: see text] with coefficients bw=n+2l(n-l-1).

Influence of Electron Exchange and Quantum Shielding on the Elastic Collisions in Quantum Plasmas

2013 ◽  
Vol 68 (10-11) ◽  
pp. 686-692
Author(s):  
Gyeong Won Lee ◽  
Young-Dae Jung
Keyword(s):  
Phase Shift ◽  
Cross Section ◽  
Fermi Energy ◽  
Collision Energy ◽  
Collision Cross Section ◽  
Electron Exchange ◽  
Plasmon Energy ◽  
Exchange Effect ◽  
Quantum Plasmas ◽  
Scattering Phase

The influence of electron exchange and quantum shielding on the elastic electron-ion collision is investigated in degenerate quantum plasmas. The second-order eikonal method and effective screened potential are employed to obtain the scattering phase shift and collision cross section as functions of the impact parameter, collision energy, electron-exchange parameter, Fermi energy, and plasmon energy. It is found that the electron-exchange effect enhances the eikonal scattering phase shift as well as the eikonal collision cross section in quantum plasmas. The maximum position of the differential eikonal collision cross section is found to be receded from the collision center with an increase of the electron-exchange effect. It is interesting to note that the influence of the electron exchange on the eikonal collision cross section decreases with increasing collision energy. It is also found that the eikonal collision cross section decreases with an increase of the plasmon energy and, however, increases with increasing Fermi energy.

Nonthermal effects on the elastic electron–atom collision in generalized Lorentzian semiclassical plasmas: Lorentzian renormalization shielding

2015 ◽  
Vol 81 (2) ◽  
Author(s):  
Woo-Pyo Hong ◽  
Young-Dae Jung
Keyword(s):  
Phase Shift ◽  
Cross Section ◽  
Collision Cross Section ◽  
Effective Interaction ◽  
Elastic Electron ◽  
Electron Atom ◽  
Energy Impact ◽  
Scattering Phase ◽  
Total Collision ◽  
Atom Collision

The Lorentzian renormalization plasma shielding effects on the elastic electron–atom collision are investigated in generalized Lorentzian semiclassical plasmas. The eikonal analysis and the effective interaction potential are employed to obtain the eikonal scattering phase shift, differential eikonal collision cross section, and total eikonal collision cross section as functions of the collision energy, impact parameter, nonthermal renormalization parameter, and spectral index of the Lorentzian plasma. It is found that the influence of Lorentzian renormalization shielding suppresses the eikonal scattering phase shift and, however, enhances the eikonal collision cross section in Lorentzian semiclassical plasmas. Additionally, the energy dependence on the total collision cross section in nonthermal plasmas is found to be more significant than that in thermal plasmas.

ON THE t(d, n)α REACTIVITY IN FUSION REACTORS

1989 ◽  
Vol 04 (22) ◽  
pp. 2101-2112 ◽  
Author(s):  
K. LANGANKE ◽  
C. ROLFS
Keyword(s):  
Energy Range ◽  
Cross Section ◽  
Thermal Equilibrium ◽  
Electron Screening ◽  
Fusion Reactors ◽  
Cross Section Data ◽  
Fermi Model ◽  
Thomas Fermi ◽  
Hartree Fock ◽  
Section Data

We argue that the most accurate t(d, n)α cross section data obtained by the Los Alamos group are enhanced at energies smaller than Ecm≈16 keV due to screening effects caused by the electrons present in the target. We show that these data in the energy range Ecm=16–70 keV can be well reproduced by a single Breit-Wigner resonance formula which, however, disagrees with the data at lower energies. Consistently the observed deviations can be associated with electron screening effects where the latter are estimated within the Thomas-Fermi model or a static Hartree-Fock approach. Adopting the present Breit-Wigner fit to the data at Ecm≥16 keV , we have calculated the reactivity of a d+t plasma at thermal equilibrium in the temperature range kT<10 keV as it might be important for future fusion reactors.

Quantum Shielding Effects on the Eikonal Collision Cross Section in Strongly Coupled Two-temperature Plasmas

2017 ◽  
Vol 72 (5) ◽  
pp. 433-439
Author(s):  
Myoung-Jae Lee ◽  
Young-Dae Jung
Keyword(s):  
Phase Shift ◽  
Cross Section ◽  
Strongly Coupled ◽  
Scattering Phase ◽  
Impact Parameters ◽  
De Broglie Wavelength ◽  
Ion Collision ◽  
The Impact ◽  
Two Temperature ◽  
Shielding Effects

AbstractThe influence of nonisothermal and quantum shielding on the electron-ion collision process is investigated in strongly coupled two-temperature plasmas. The eikonal method is employed to obtain the eikonal scattering phase shift and eikonal cross section as functions of the impact parameter, collision energy, electron temperature, ion temperature, Debye length, and de Broglie wavelength. The results show that the quantum effect suppresses the eikonal scattering phase shift for the electron-ion collision in two-temperature dense plasmas. It is also found that the differential eikonal cross section decreases for small impact parameters. However, it increases for large impact parameters with increasing de Broglie wavelength. It is also found that the maximum position of the differential eikonal cross section is receded from the collision center with an increase in the nonisothermal character of the plasma. In addition, it is found that the total eikonal cross sections in isothermal plasmas are always greater than those in two-temperature plasmas. The variations of the eikonal cross section due to the two-temperature and quantum shielding effects are also discussed.

scholarly journals The most correct ρ0(770) meson mass and width values

2019 ◽  
Vol 199 ◽  
pp. 02023
Author(s):  
Erik Bartoš ◽  
Stanislav Dubnička ◽  
Anna Z. Dubničková ◽  
Robert Kamiński ◽  
Andrej Liptaj
Keyword(s):  
Form Factor ◽  
Phase Shift ◽  
First Principles ◽  
Electromagnetic Form Factor ◽  
P Wave ◽  
Meson Mass ◽  
Accurate Data ◽  
Pion Electromagnetic Form Factor ◽  
Scattering Phase ◽  
Pion Electromagnetic Form

By application of the pion electromagnetic form factor and also the P-wave isovector ππ scattering phase shift parametrizations, following from the first principles, like unitarity and analyticity, for a description of the corresponding accurate data, it is clearly demonstrated that the ρ0(770) meson mass and width values obtained by the Gounaris-Sakurai model in a description of the same data can not be accepted as correct ones.

Non-thermal renormalization shielding on the electron–atom collision in partially ionized generalized Lorentzian non-thermal plasmas

2013 ◽  
Vol 79 (5) ◽  
pp. 783-788 ◽  
Author(s):  
YOUNG-DAE JUNG ◽  
WOO-PYO HONG
Keyword(s):  
Phase Shift ◽  
Cross Section ◽  
Impact Parameter ◽  
Collision Cross Section ◽  
Thermal Plasmas ◽  
Shielding Effect ◽  
Electron Atom ◽  
Scattering Phase ◽  
Partially Ionized ◽  
Atom Collision

AbstractThe non-thermal renormalization shielding effects on the elastic electron–atom collision process are investigated in partially ionized generalized Lorentzian non-thermal plasmas. The eikonal analysis for the Hamilton–Jacobi solution and impact parameter method are employed to obtain the eikonal scattering phase shift and eikonal cross section as functions of the collision energy, Debye length, impact parameter, and spectral index of the Lorentzian plasma. It is found that the non-thermal renormalization shielding effect enhances the eikonal scattering phase shift as well as the eikonal collision cross section, especially for small impact parameter domains. It is also found that the non-thermal renormalization shielding effect on the eikonal scattering phase shift decreases with an increase of the impact parameter. In addition, it is found that the maximum position of the eikonal collision cross section has receded from the collision center with an increase of the non-thermal character of the plasma.

scholarly journals Electron scattering in helium. Absolute measurements at 90° and 45°

1933 ◽  
Vol 139 (837) ◽  
pp. 113-129 ◽  
Keyword(s):  
Form Factor ◽  
Cross Section ◽  
Electron Scattering ◽  
Unit Volume ◽  
Solid Angle ◽  
Potential Difference ◽  
X Rays ◽  
Scattered Intensity ◽  
Atomic Form Factor ◽  
Absolute Measurements

The scattering formula of Rutherford gives an expression for the number n 1 d Ω of electrons in a gas which are scattered from a beam of electrons over the solid angle d Ω by impacts with atoms, which are to be found along a certain length l of this beam. If + Z e is the charge of the nucleus of the atoms, — e and m the charge and the mass of the electron, V the potential difference through which the electrons are accelerated, N the number of atoms in unit volume and n 0 the total number of electrons which pass a certain cross-section of the beam, we have the well-known formula: n 1 d Ω = n 0 N l (Z e /4V) 2 d Ω/sin 4 ½Θ, (1) where Θ is the angle of scattering. When n 0 = 1, N = 1, and l = 1 the scattering is usually expressed by I θ d Ω, where I θ is the so-called “scattered intensity.’’ According to Rutherford’s formula we get for the classical scattering due to the nucleus: I θ = ( e /4V) 2 Z 2 /sin 4 ½Θ. (2) Taking into consideration the electrons around the nucleus Mott and Bethe find: I θ = ( e /4V) 2 (Z -F) 2 /sin 4 ½Θ, (3) where F is the atomic form factor, known from the scattering of X-rays, and also a function of (V sin 2 ½Θ). The values calculated for helium by James have been used for F in this paper.

Sign in / Sign up

Export Citation Format

Share Document