Cut-off Coulomb Potential Research Articles

Nonlinear electrical conductivity for a strongly coupled plasma

A nonlinear analysis of electrical conductivity in a plasma is given, stemming from the Uehling–Uhlenbeck equation. Anisotropy due to an applied electric field is incorporated through a Legendre polynomial expansion of the distribution function. The plasma is comprised of ions, electrons, and a neutral component. The electron–ion interaction is described by a shielded Debye potential at high energy and a cutoff Coulomb potential at low energy. A nonlinear equation for the distribution function is solved and yields f̄SL(x) =1/(1+BeA(x)) for the symmetric part of the solution. Nondimensional energy is x, B is a normalization constant, and A(x) is an explicit integral dependent on the electric field and specifics of the interaction. Resulting nondimensional conductivity σ̃, is given by σ̃ = (1)/(3) (2/π)3/2[ac(Z+1)1/2/ ΛQΓD] ∫∞0 f̄SL(x)(d/dx) (x/Q̃)dx, where Z is effective ionization, aC is the ratio of charge to total heavy-particle density, Q̃ is the dimensionless, weighted cross section, and ΛQ and ΓD are quantum and plasma parameters, respectively. Application is made to an aluminum plasma and plots of conductivity versus electric field are obtained. These plots exhibit three distinct regions; with an increase in field strength these are the Ohmic, Coulomb-dominated, and neutral-dominated regions.

Improved condition for the absence of bound states and converging analytic bounds to critical screening parameter

Converging lower bound to the critical screening parameterD c associated with the ground state of a two-particle system interacting through a cut-off Coulomb potential is obtained analytically using an improved condition for the absence of bound states. The predicted numerical result for the lower bound is found to be within 10−3% of the exact result. On the other hand, a multi-parameter variational approach yields a tight upper bound, within 0.54% of the exact result. It is shown that the critical screening parameter for the exciteds-states can also be determined in an approximate way. We obtainD ≈ [0.764435n −2+0.617737n −3]−1 wheren is the principal quantum number. The predictedD c for various quantum states (n=1 to 8) are in good agreement with the values obtained numerically by Singh and Varshni.

Contributions from off-energy-shell states to inner-shell electron capture.

It is shown that contributions from off-energy-shell intermediate states are small for inner-shell electron capture in highly asymmetric ion-atom collisions. We analyze the influence of the on-energy-shell discontinuities of the electron wave function by introducing a cut-off Coulomb potential. We found that these discontinuities, which are mainly responsible for large corrections introduced by the strong-potential Born approximation, do not have physical meaning.

Comparative study of the bound states of static screened Coulomb and cut-off Coulomb potentials

Comparative study of the bound states of static screened Coulomb and cut-off Coulomb potentials

Coulomb effects in e-2e collisions in the presence of a low-frequency laser field

When an electron ionises an atom one of the final state electrons experiences a Coulomb potential when it is far from the ion. This collision is described in the presence of a low-frequency laser. It is theoretically convenient and physically realistic to work with cut-off Coulomb potentials (at R) rather than 'pure' Coulomb potentials. The observable cross sections depend upon R in a way that has no limit for R to infinity . This is discussed and is shown to make this an experimentally unprofitable area of research.

Oscillator strengths in dense hydrogen plasma-no 'transparency window'

Energy levels, oscillator strengths and photoionisation cross sections of an electron in the Debye-Huckel and the cut-off Coulomb potential are obtained by numerically solving the Schrodinger equation. The shifted continuum of bound-free transitions takes over the oscillator strength of vanishing bound-bound transitions, the averaged oscillator strength remains very close to that of the unscreened Coulomb potential. Calculated emission spectra with broadening demonstrate that there is no 'transparency window' around threshold whose existence has been claimed by other authors. The results given for the Lyman series can be easily generalised to the Balmer and other series.

Limits of screened-Coulomb amplitudes

From two examples, one with an exponentially screened and the other with a smoothly cut-off Coulomb potential, arguments and partial proofs are given for the following conjecture. The absolute values of screened-Coulomb T matrices may converge in the limit of vanishing screening to the results of standard (i.e. short-range) theory. The condition is that the values of the momenta should be chosen before the limiting process.

Screened Coulomb scattering in the eikonal approximation

Scattering amplitudes and cross sections for screened Coulomb potentials are examined using the eikonal approximation. We use the method of $h$ transforms to show that if the screening function is sufficiently smooth, then the screened cross section ${\ensuremath{\sigma}}_{\ensuremath{\rho}}$ approaches the Coulomb cross section ${\ensuremath{\sigma}}_{C}$ as the screening radius $\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\infty}$. On the other hand, for a sharply cut-off Coulomb potential ${\ensuremath{\sigma}}_{\ensuremath{\rho}}$ does not approach ${\ensuremath{\sigma}}_{C}$ as $\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\infty}$. These results agree with results obtained earlier using the Born approximation.

Cross sections for screened potentials

We consider scattering by screened Coulomb and screened short-range potentials. We prove, in Born approximation, that the cross section for a sharply cutoff Coulomb potential does not converge to the Rutherford cross section as the screening radius ρ→∞. On the other hand, for certain ’’smooth’’ screening functions we show that the screened Coulomb cross section does approach the Rutherford cross section as ρ→∞. In the case of short-range potentials, we prove (exactly, not just in Born approximation) that the screened cross section approaches the unscreened cross section as ρ→∞, whether the screening function is smooth or not.

The giant glory effect in atomic collisions: calculations for Na-I scattering

The giant glory effect discovered in 1973 by Demkov and Los is considered for Na-I scattering. The cut-off Coulomb potential for a certain collision energy produces the ideal giant glory, i.e. total and exact backscattering in the classical approximation. For a real atomic system with its somewhat distorted potential, the scattering is characterized by superposition of rainbow and backscattering glory. The resulting complex interference structure is calculated in the semiclassical approximation.

Electron wave functions in over-critical electrostatic potentials

The mathematical properties of the solutions of the Dirac equation in over-critical external potentials are investigated. The 1/r Coulomb potential is treated as the limitR → 0 of cut-off Coulomb potentials (R is the cut-off parameter). The results are interpreted in terms of quantum electrodynamics. A number of new physical phenomena occur in quantum electrodynamics of strong fields. One of the most interesting ones is the autoionization of positrons (energyless creation of electron-positron pairs) in over-critical external fields.

The giant glory effect in atomic collisions

The effect of total backscattering in elastic collisions from cut-off Coulomb potentials is discussed.

Auto-ionization of positrons in heavy ion collisions

Autoionization of positrons occurs as a fundamentally new process of quantum electrodynamics, if empty 1s- or 2p 1/2− etc. electronic shells obtain binding energies larger than 2m e c 2. This effect should be experimentally observable in the scattering of very heavy ions (Z≧80) on each other since in such collisions superheavy electronic molecules are formed (superheavy quasi-molecules). The scattering mechanism and the distribution of autoionization positrons are discussed. The adiabaticity of the heavy ion collision is studied and the electron-positron pair production background to the ionization problem is estimated. Analytic solutions are obtained for 1/r-potentials for the caseZα≧1. The phase shifts of negative energy solutions in the case of cutoff Coulomb potentials reveal the accuracy of the autoionization formalism.

Delta-function contributions in the calculation of oscillator strengths for an electron in a coulomb potential

The operator associated with the so-called “time derivative of the dipole acceleration” formulation of the oscillator strength has previously been found to be invalid for excitations to or from s-orbitals. It is shown that the use of a cut-off Coulomb potential leads to contributions of delta functions and delta-function derivatives in the operator. These contributions restore the hermitian character of the operator with respect to s-orbitals, and this in turn leads to the correct values of the dipole transition moments for excitations involving s-orbitals.

Transport Cross Sections for Screened and Cutoff Coulomb Potentials

The analytic expressions for the transport cross sections of a cutoff Coulomb potential agree with the numerical results of an exponentially screened potential if the cutoff radius is suitably related to the screening Debye-Hückel length and the Landau length.

Transport Properties of a Nonequilibrium Partially Ionized Gas in a Magnetic Field

A modified Chapman—Enskog technique developed for a partially ionized gas in an electric field is generalized to include the effects of a magnetic field. The method allows the electron and heavy particle temperatures to differ while requiring all species to have the same macroscopic velocity to zero order. Expressions are obtained for the transport properties of such a gas and a complete set of self-contained magnetohydrodynamic equations is given. As an example, the transport properties of a fully ionized gas containing a single ion species are evaluated using the cutoff Coulomb potential. In the limit of equal electron and ion temperatures, the results are in agreement with previous results.

Transport Properties of a Nonequilibrium Partially Ionized Gas

A modified Chapman-Enskog approach for an ionized gas is presented. The method allows the electron and heavy particle temperatures to differ while requiring all species to have the same macroscopic velocity to zero order. Expressions are obtained for the transport properties of such a gas and a complete set of self-contained hydrodynamic equations is given. As an example, the transport properties of a fully ionized gas containing a single ion species are evaluated using the cutoff Coulomb potential. In the limit of equal electron and ion temperatures, the results are in agreement with previous results.

THE REGGE POLES OF CUT-OFF COULOMB POTENTIAL

In this paper, the analytical properties of the S matrix of nonrelativistic cut-off Coulomb potential in the complex angular momentum and complex energy planes are discussed. The Regge poles of this S matrix for four special cases are given, and the first two Regge trajectories are traced by means of numerical calculations.

Bremsstrahlung in a Dense Plasma

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A continuous absorption coefficient of negative hydrogen and lithium ions

Earlier calculations of the continuous absorption coefficient of H− ofChandrasekhar andHeinrich were based on the use of ground state wave functions obtained through theRitz variational method. LaterGeltman simplified the calculation of the continuous absorption coefficient of negative hydrogen and lithium ions, using a cut off Coulomb potential. BothHeinrich andChandrasekhar as well asGeltman obtained for the mentioned continuous absorption coefficient only numerical values and not an analytical expression. The purpose of this paper is to give a simple analytical expression for the continuous absorption coefficient of negative hydrogen and lithium ions. Comparing our andGeltman’s results with the most accurate numerical values ofChandrasekhar it can be seen that our results are somewhat better thanGeltman’s. Предварительные вычисления непрерывного абсорпционного коэффициента H− проведенные Чандрескером и Гайндрихом, основывались на применении волновых функций основного состояния, полученных вариационным методом Ритца. Позднее вычисления по отношению непрерывного абсорбционного коэффициента отрицательных ионов водорода и лития были упрощены Гельтманом применением кулоновского потенциала отсечки. Однако, Гайндрихом, Чандрескером, как и Гельтманом получены для упомянутого непрерывного абсорбционного коэффициента лишь численные значения, и ими никакой аналитической формулы по отношению данного коэффициента не выводилось. Цель настоящей работы — дать простое аналитическое выражение для определения непрерывного абсорбционного коэффициента отрицательных ионов водорода и лития. Сравнивая наши результаты и результаты Гельтмана с наиболее точными численными данными Чандрескера, видно, что наши результаты несколько лучшие, чем результаты Гельтмана.