Eikonal analysis of Coulomb distortion in quasi-elastic electron scattering

An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order 1/k ², where k is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. A form of effective-momentum approximation is obtained using trajectory-dependent eikonal phases and focusing factors. Fixing the Coulomb distortion effects at the center of the nucleus, the often-used ema approximation is recovered. Comparisons of these approximations are made with full calculations using the electron eikonal wave functions. The ema results are found to agree well with the full calculations.     

Potential of multiphoton exchange in the scattering of light charged particles of a heavy target

Classical solution of the inverse problem of determing the potential for differential scattering cross section was obtained by O.B. Firsov in 1953. We use it to investigate the deviation from the Coulomb potential due to the exchange of two or more photons in the scattering of an electron in an external field produced by a heavy nucleus with charge Z _e . We also construct the effective potential acting on a charged particle in the problem of planar channeling.     

Parity-violating asymmetry in elastic electron scattering on nuclei: Partial-wave analysis

Elastic scattering of longitudinally polarized electrons on heavy nuclei is known to be a promising method for studying neutral parity violating, weak interactions. With the aim of investigating the effect of Coulomb distortion on the calculated asymmetry we develop a complete partial-wave analysis for the Dirac equation in the presence of a parity-odd potential in addition to the Coulomb potential. We apply our analysis to a set of selected nuclei with spin zero. The physical features of the resulting asymmetries are discussed and a comparison to the Born approximation is made.     

Long-range Coulomb forces in DIS: missed radiative corrections?

The Born approximation, one photon exchange, used for DIS (deep inelastic scattering) is subject to virtual radiative corrections which are related to the long-range Coulomb forces. They may be sizeable for heavy nuclei since Zα is not a small parameter. So far, these corrections are known only for two processes, elastic scattering and bremsstrahlung on the Coulomb field of a point-like target. While the former amplitude acquires only a phase, in the latter case also the cross-section is modified. Although the problem of Coulomb corrections for DIS on nuclei is extremely difficult, it should be challenged rather than “swept under the carpet”. The importance of these radiative corrections is questioned in the present paper. We show that, in the simplest case of a constant hadronic current, the Coulomb corrections provide a phase to the Born amplitude, therefore the cross-section remains the same. Inclusion of more realistic hadronic dynamics changes this conclusion. The example of coherent production of vector mesons off nuclei reveals large effects. So far a little progress has been made deriving lepton wave functions in the Coulomb field of an extended target. Employing available results based on the first-order approximation in Zα, we conclude that the Coulomb corrections are still important for heavy nuclei. We also consider an alternative approach for extended nuclear targets, the eikonal approximation, which we demonstrate to reproduce the known exact results for Coulomb corrections. Calculating electroproduction of vector mesons, we again arrive at a large deviation from the Born approximation. We conclude that one should accept with caution the experimental results for nuclear effects in DIS based on analyses done in the Born approximation. Received: 16 May 2001 / Accepted: 4 July 2001     

New Asymptotic Formulae for the Point Coulomb Phase Shift

We investigate the Coulomb phase shift, and derive and analyze new and more precise analytical formulae. We consider next to leading order terms to the Stirling’s approximation, and show that they are important at small values of the angular momentum l and other regimes. We employ the uniform approximation. The use of our expressions in low-energy scattering of charged particles is discussed and some comparisons are made with other approximation methods. Potential use of our results in the search for deviations from pure Mott scattering of sub-barrier scattering of very heavy ions is pointed out.     

Approximate scattering solutions of the dirac equation for electron-nucleus processes in light nuclei

Scattering solutions of the second-order Dirac equation for the case of the Coulomb potential and which are correct to first order in the coupling constantZe ²/hc are investigated and found to describe pure Coulomb scattering equally well as the Sommerfeld-Maue wave functions. Errors introduced by the use of these solutions are studied in a numerical calculation of cross sections for nuclear electric-quadrupole excitation by high-energy electrons. The use of these wave functions is suggested for simplified calculations of lowest-order Coulomb corrections to Born approximation results for various electron-nucleus processes.     

Eikonal expansion in electron scattering: I. Elastic scattering

A systematic eikonal expansion for the scattering of high-energy electrons from nuclei is derived which starts from the iterated Dirac equation. The resulting scattering amplitude is written in an impact parameter representation depending on eikonal phases which are proportional to inverse powers of the energy. The first two correction terms to the leading Glauber-Baker amplitude are calculated. For a Coulomb potential they agree with a sinθ-expansion of the relativistic Coulomb scattering amplitude. In the case of scattering from an extended charge distribution at sufficiently high energies numerical partial wave calculations are accurately reproduced.     

Energy loss of relativistic, multiply charged ions in an electron plasma

A simple equation is derived for calculating the energy loss of a relativistic, multiply charged ion moving in an electron plasma in the region where the Born approximation fails. The contribution of the energy losses from collisions with solitary electrons is calculated using the exact Dirac equation for relativistic Coulomb scattering. Zh. Tekh. Fiz. 68, 9–12 (February 1998)     

Neutrino nucleus cross sections for low energy neutrinos at SNS facilities

We calculate the neutrino nucleus cross sections for charged lepton production relevant for the experiments proposed with the stopped muon neutrinos using neutron spallation source facility. The calculations are done in local density approximation taking into account Pauli blocking, Fermi motion effects and renormalization of weak transition strengths in the nuclear medium. The effect of Coulomb distortion of the lepton produced in charge current reactions is taken into account by using the Fermi function as well as in a model where an effective momentum has been used for the lepton moving in the local Coulomb field of the final nucleus. The numerical results for the neutrino nucleus total cross sections averaged over Michel spectrum are presented for various nuclei.     

Determination of the Resultant Deflection Angle of a Particle Multiply Scattered by Nucleons of a Nucleus

The present paper considers scattering of high-energy nucleons by nuclei based on the diffraction approach that takes into account the effects of multiple scattering. The optical potential is used to describe multiple scattering in the inhomogeneous nuclear matter. A formula for the scattering wave intensity is derived in the heavy nucleus approximation. The results obtained are used to calculate the deflection angle of a charged particle multiply scattered by nucleons of a nucleus.     

Nuclear isospin mixing and elastic parity-violating electron scattering

The influence of nuclear isospin mixing on parity-violating elastic electron scattering is studied for the even–even, N=Z nuclei ¹²C, ²⁴Mg, ²⁸Si, and ³²S. Their ground-state wave functions have been obtained using a self-consistent axially-symmetric mean-field approximation with density-dependent effective two-body Skyrme interactions. Some differences from previous shell-model calculations appear for the isovector Coulomb form factors which play a role in determining the parity-violating asymmetry. To gain an understanding of how these differences arise, the results have been expanded in a spherical harmonic oscillator basis. Results are obtained not only within the plane-wave Born approximation, but also using the distorted-wave Born approximation for comparison with potential future experimental studies of parity-violating electron scattering. To this end, for each nucleus the focus is placed on kinematic ranges where the signal (isospin-mixing effects on the parity-violating asymmetry) and the experimental figure-of-merit are maximized. Strangeness contributions to the asymmetry are also briefly discussed, since they and the isospin mixing contributions may play comparable roles for the nuclei being studied at the low momentum transfers of interest in the present work.     

费密子与Dirac双子系统的耦合问题

除了库仑耦合和Kazama-杨振宁耦合——кqβ∑·r/2Mr³外,本文同时讨论了费密子Dirac双子应当存在的另一耦合iкzz_de²γ·r/2Mr³。结果表明,对所有角动量态,费密子径向波函数具有物理上合理的原点渐近行为。定性地分析了束缚态的必要条件。发现,对于双子情形,当额外磁矩к→0时,存在费密子束缚态是可能的;但对于磁单极情形,当к→0时,必不存在费密子束缚态。 关键词：     

Production of electron-positron pairs on nuclei in the field of a bichromatic plane electromagnetic wave

The exact solution of the Dirac equation for an electron in the field of a bichromatic plane electromagnetic wave — with components that are monochromatic waves propagating in one direction — is used to calculate the probability of e⁺e^– pair production on a nucleus in the field of such a wave. This influence of the nucleus is treated perturbatively as an external Coulomb field. The cases of small and large values of the intensity parameters of the wave components are considered and the passage to the limit of a crossed field is discussed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 33–40, September, 1978.We are very grateful to V. R. Khalilov for a fruitful discussion of the results.     

Angular correlations of electron-positron pairs in internal electric monopole conversion of aligned heavy nuclei

We consider the influence of the nuclear alignment which, e.g., may be caused by Coulomb excitation on the spatial distribution of the electron-positron pairs resulting from electric monopole conversion processes. E0 conversion is a pure penetration effect, i.e., there is no virtual photon exchange. Approximating the nucleus by a homogeneously charged sphere we find that the angular distribution of electrons and positrons is independent on the alignment axis of the excited nucleus and is determined solely by the opening angle of the emitted lepton pairs.     

A relaxation theory of plasma-broadened He II lines

The relaxation theory of plasma line broadening developed by Smith and Hooper, and extended by Smith, is applied to a charged radiator. The 304 Å Lyman alpha line of He II is chosen as an example. The radiator is assumed perturbed only by electronic and ionic electric microfields. The ions are treated in the static approximation. Two-component ion microfield distribution functions that allow for the presence of both He⁺ and He⁺⁺ perturbers are employed. The fact that the radiator is charged complicates the treatment of electron perturbation; two different approaches are included. The first neglects the effect of the charge of the radiator on the perturbing electron and assumes that the perturbing electrons can be represented by momentum wave functions. This method corresponds to Smith's treatment of the electron perturbers in neutral hydrogen. The second includes the effect of the charge of the radiator on the perturbing electrons and represents the perturbing electrons by Coulomb wave functions; this calculation requires evaluation of free-free gaunt factors. The theory, with both the momentum and Coulomb perturber wave functions, predicts a blue asymmetry in the near wings of the line. These two approaches can be compared with the classical path approach of Griem and Shen.     

Stability of QED Vacuum and 3+1 Dimensional Scattering Problem in the Presence of a Coulomb Scalar Potential and Vector Field

We show that, in the presence of a scalar field the range of the value of external field parameters a and b, at which corresponding Hamiltonian operator is hermitian, essentially wider than in its absence. It allows us to study precisely the question on stability of QED vacuum in the presence of a strong electric field of a point charge Z|e| and external scalar Coulomb field with respect to electron-positron pair production. Also, we consider the scattering of Dirac particle by the specified fields in 3+1 dimensions. The phase shift and wave functions are obtained exactly. We calculate the scattering amplitude in a quasi-classical approximation as a partial wave series. By means of figures obtained for the cross section σ(θ) in general and special cases, such as a≠b and a=b, we find that σ(θ) is not exactly symmetric about θ=π.     

New Exact Solution of Dirac-Coulomb Equation with Exact Boundary Condition

It usually writes the boundary condition of the wave equation in the Coulomb field as a rough form without considering the size of the atomic nucleus. The rough expression brings on that the solutions of the Klein-Gordon equation and the Dirac equation with the Coulomb potential are divergent at the origin of the coordinates, also the virtual energies, when the nuclear charges number Z>137, meaning the original solutions do not satisfy the conditions for determining solution. Any divergences of the wave functions also imply that the probability density of the meson or the electron would rapidly increase when they are closing to the atomic nucleus. What it predicts is not a truth that the atom in ground state would rapidly collapse to the neutron-like. We consider that the atomic nucleus has definite radius and write the exact boundary condition for the hydrogen and hydrogen-like atom, then newly solve the radial Dirac-Coulomb equation and obtain a new exact solution without any mathematical and physical difficulties. Unexpectedly, the K value constructed by Dirac is naturally written in the barrier width or the equivalent radius of the atomic nucleus in solving the Dirac equation with the exact boundary condition, and it is independent of the quantum energy. Without any divergent wave function and the virtual energies, we obtain a new formula of the energy levels that is different from the Dirac formula of the energy levels in the Coulomb field.     

Effect of Coulomb forces on the position of the pole in the scattering amplitude and on its residue

The vertex constant for the virtual decay of a nucleus to two charged particles having an arbitrary orbital angular momentum l was explicitly obtained for the first time in the case of a standard expansion of the effective-range function K _l (k ²), as well as in the case where the function K ₀(k ²) has a pole. The bound state of the 3He nucleus and the resonance states of the ²He and ³He nuclei in the S wave, as well as the resonance states of the ⁵He and ⁵Li nuclei in the P wave, are studied as physical examples. For the Np and N d systems, the trajectories of the pole in the complex planes of the momentum and the corresponding renormalized vertex constant are constructed for the transition from a resonance state to a virtual state as the Coulomb interaction is switched off gradually.     

An analytical expression of the amplitude of stripping reaction in the coulomb approximation

A method is derived for calculating the matrix element of stripping reaction (d,p) in the socalled distorted-wave Born approximation; only Coulomb scattering of incident and outgoing particles is taken into consideration. Coulomb wave functions are expressed by means of integral representation permitting integration over angular variables and, when the radial wave function of the trapped neutron is specially chosen, also calculation of the radial integral for non-zero orbital momentum of the trapped neutron. Relations are given for calculating the differential cross-section of reaction and the polarization of products. The special case, when the orbital momentum of the captured neutron is equal to one or two, is discussed in detail.