Modified Glauber Approximation Research Articles

Total cross sections for electron and positron collisions with rubidium in a model-potential approach

The total cross sections for electron and positron collisions with rubidium are calculated in the energy range 15-1000 eV, employing the modified Glauber approximations within the model-potential approach. The total cross sections for positron collision are in better agreement with experimental data, in comparison to those previously calculated in the frozen-core approach. The effect of the core polarization is significant. As in the case of scattering from Na and K, this effect causes the electron and positron cross sections obtained in the model-potential approach to no longer merge with each other at low energies.

Elastic scattering of electrons and positrons from rubidium.

The elastic scatterings of electrons and positrons from rubidium are calculated at intermediate energies in the Born, Glauber, modified Glauber (MG), and eikonal-Born-series approximations. The results of differential cross sections (DCS) for elastic scattering obtained within these various methods of approximation are presented with discussion. The modified Glauber results predict the existence of structures for the DCS, similar to those of scattering from potassium and sodium. Furthermore, the structures in this case persist even at a scattering energy as high as 500 eV. The DCS in the modified Glauber approximation at small scattering angles are used to estimate the ``effective'' total cross sections for positron and electron scatterings from rubidium. The effective MG total cross sections are found to be in better agreement with experimental data.

Total cross sections for positron collisions with rubidium

The total cross sections for positron and electron collisions with rubidium are calculated in the energy range 15-1000 eV, employing the modified Glauber approximation. The MG total cross sections are found to be in reasonably good agreement with experimental data at energies below 100 eV, and consistent with the total cross sections calculated at energies below 30 eV in the close-coupling approximations.

Elastic scattering of intermediate-energy electrons by alkali-metal atoms

The differential cross sections for electron elastic scattering off alkali-metal atoms (K, Na and Li) at intermediate energies are calculated, employing the modified Glauber approximation. It is found that the modified Glauber approximation predicts correctly the existence of a dip (or kink) structure in the differential cross sections, and that the number of these dips would reduce from two for e--K to just one for e--Na and to nil for e--Li scattering, exactly as was observed in experimental data.

A Modified Glauber Approximation and the Stopping Power of the Nuclear Matter

A Modified Glauber Approximation and the Stopping Power of the Nuclear Matter

Core-corrected modified Glauber approximation for e ±-alkali-metal-atom collisions

The total cross sections for electron and positron scattering by alkali-metal atoms (Li, Na and K) are calculated in a core-corrected modified Glauber approximation using the model potential approach. The results at low intermediate energies are found to be closer to the experimental values of e ± −K total cross section recently measured by Stein et al. (Phys. Rev. Letters 55 (1985) 488). The positron cross sections obtained are also somewhat smaller than the electron ones, as experimental results seem to indicate. Calculations are also performed with the frozen-core approximation.

Elastic scattering of electrons by potassium

The modified Glauber approximation is employed to calculate the differential cross sections for electron-potassium elastic scattering at intermediate energies. The results are found to reproduce the two 'dips' (kinks) observed in experimental data by Buckman et al. (1979). At low scattering angles, the modified Glauber values agree better with the experimental data than those of other Glauber calculations.

Triple differential cross sections for the positron-impact ionization of hydrogen and helium

Triple differential cross sections for the positron-impact ionization of hydrogen and helium in a coplanar, asymmetric geometry are calculated by using the second Born and the modified Glauber approximations. The present results are compared with those for the corresponding electron-impact case. The positron gives a larger binary- to recoil-peak maxima ratio than the electron.

2s-2p excitation of Li by electron impact

The results of an analysis of the 2s-2p resonance transition of the Li atom as a result of electron impact in the Glauber and modified Glauber approximations are reported. The cross sections of the process in the energy range 20-400 eV are calculated, using a model potential approach. The analytic expressions of the relevant scattering terms which constitute the Glauber and modified Glauber amplitudes of the process are derived and then reduced to forms which are accessible to numerical computation. Numerical techniques are developed to help alleviate the difficulties encountered in the evaluation of these amplitudes. The theoretical differential and integrated cross sections obtained are compared with experimental data.

Higher-order effects in the large-angle coplanar symmetric He(e-,2e-)He+ process: A modified-Glauber-approximation study.

The triple-differential cross sections for the ionization of helium by fast electrons in the large-angle coplanar symmetric energy-sharing case are studied by using the modified Glauber approximation. Comparison with experimental data indicates that the higher-order terms of the scattering amplitude contribute quite significantly to the cross section. They, however, make the results worse than those of the second-Born approximation.

On the higher-order effects in the fast electron impact ionisation of atoms

The absolute coplanar asymmetric triple differential cross section data of Schlemmer et al. (1985) for the ionisation of atomic hydrogen at an incident electron energy of 150 eV and scattering angle of 16 degrees are employed to demonstrate that higher-order (n>2) terms of the scattering amplitude are quite important if the scattering angle is not too small. The calculations have been done in the second Born and the modified Glauber approximations with exchange.

On the effect of the helium ground state wave function on the electron impact triple differential ionization cross section in asymmetric geometry

The sensitivity of the triple differential cross sections for the electron impact ionization of helium to the target ground state wave function is investigated at high energies in the asymmetric Ehrhardt geometry. The calculation is done in the modified Glauber approximation using (i) one-parameter Hartree wave function and (ii) three-parameter analytical fit of Byron and Joachain to the Hartree–Fock wave function for the helium ground state. The latter choice leads to somewhat better agreement with the recent absolute data of Jung et al. at 600 eV incident energy. The results are however not very sensitive to this choice.

A Modified Glauber Approximation for High-Energy Heavy Ion Collision. II: Effect of the Internal Excitation of the Projectile Nucleus

A modified Glauber approximation presented in a previous paper (I) is reformulated by using the Green function and is applied to the high energy heavy ion collisions: Ne+U. The internal excitation of the projectile nucleus which is neglected in (I) is taken into accound adiabatically. It is shown that the slowing-down of the relative velocity between colliding nuclei weakens the collectivity of emmitted nucleons. It is also pointed out that the internal excitation of the projectile plays an important role for enhancement of the high-energy component of the emitted nucleons.

Erratum: Triple-differential cross sections for the fast-electron-impact ionization of atomic hydrogen

The triple-differential cross sections for the ionization of atomic hydrogen by fast electrons are analyzed in the case of coplanar asymmetric geometry with use of the modified Glauber approximation. Our results show an improved agreement with the recent measurements taken at 250 eV incident electron energy, compared to the second-Born-approximation or the eikonal Born-series results.

A multiple scattering theory for electron-atom collisions

A model for electron-atom scattering was recently proposed and applied to e-H(2s) excitation but no derivation was given for it. The authors derive the model and analyse the multiple scattering contributions it contains. They show that the Glauber approximation, the eikonal-Born series method and the modified Glauber approximation can be obtained from the model by introducing further approximations in it.

Comparison of integral-equation approximations fore±-H scattering at intermediate energies

It has been shown that the approximate solutions of the Fredholm integral equation for the scattering amplitude obtained by demanding that ${f}_{\mathrm{out}={f}_{\mathrm{in}={\ensuremath{\lambda}}_{p}}}$,n${\mathrm{f}}_{\mathrm{Bn}}$ on the mass shell in the integral equation (where ${f}_{\mathrm{Bn}}$ is the scattering amplitude in the nth Born approximation, n and p are nonzero positive integers, and ${\ensuremath{\lambda}}_{p}$,n is a scattering-angle- and energy-dependent complex multiplying factor) are identical to those obtained from the Schwinger variational principle with incoming and outgoing trial wave functions which are correct to (p-1)th and (n-1)th order in the interaction potential in a Born approximation. Further, the scattering amplitude obtained from the Schwinger variational principle, with outgoing and incoming scattering waves correct up to first order in the interaction potential in the Born approximation, has been employed to calculate total collisional cross sections for ${e}^{\ifmmode\pm\else\textpm\fi{}}$-H scattering in the 20--500-eV energy range. The results are in good agreement with the adopted cross section of de Heer et al. and those obtained in the modified Glauber approximation and the [2,2] Pad\'e approximant for E\ensuremath{\ge}30 eV.

Triple-differential cross sections for the fast-electron-impact ionization of atomic hydrogen.

The triple-differential cross sections for the ionization of atomic hydrogen by fast electrons are analyzed in the case of coplanar asymmetric geometry with use of the modified Glauber approximation. Our results show an improved agreement with the recent measurements taken at 250 eV incident electron energy, compared to the second-Born-approximation or the eikonal Born-series results.

Electron impact excitation of the 3s state of lithium at intermediate and high energies

Calculations of differential cross sections for the excitation of the 2s-3s transition in lithium by electrons in the energy range of 20-200 eV are reported. The results are obtained in Born, Glauber, simplified second Born, eikonal Born series and modified Glauber approximations. The present results are compared with the measurement of Williams et al. (1976) and other recent theoretical results. In addition, the authors have also calculated the generalised oscillator strength employing a variety of target wavefunctions.

Excitation of He+by electron impact in the modified Glauber approximation. II. 1s-2p transitions

For pt.I see ibid., vol.17, no.6, p.1123-35 (1984). The modified Glauber approximation is employed to investigate the 1s-2p excitation of hydrogen-like ions by structureless charged particles at intermediate energies. Expressions for the relevant terms which constitute the modified Glauber amplitudes of such 1s-2p excitation are derived and reduced to forms which are easily accessible for numerical computations. The author applies these results to calculations of differential and integrated cross sections of 1s-2p excitation of He+ by electron impact. The modified Glauber values of the integrated cross section obtained are compared with experimental data and with those calculated in other methods of approximation.

1s-2s excitation of He+by electron impact in modified Glauber approximation

The modified Glauber approximation is used to investigate the 1s-2s excitation of He+ by electron impact at intermediate scattering energies. Formulae of the relevant amplitudes in electron-hydrogen-like ion scattering to be used in the calculations are derived and put in forms which are easily accessible for numerical computations. Especially in the case of the 1s-2s transition considered, the formulae are shown to be reducible to closed forms. The differential and integrated cross sections of e--He+ collision (1s-2s transition) are calculated at several energies and the results are compared with experimental data and with those obtained in other methods of approximation. In general, the modified Glauber method fares reasonably well at medium scattering energies in comparison with other methods of approximation.