Strong-potential Born Research Articles

Strong potential second Born theory for low-energy electron emission in asymmetric collisions

The ejection of low-energy target electrons by heavy projectiles is calculated in a second Born approximation, allowing for propagation of the electrons in the strong projectile field. For neutral projectile impact this theory provides a satisfactory description of the collision process down to quite low impact velocities. This is shown by comparing the theory with experimental electron spectra from 0.1 MeV/amu Ne0 on He. However, when the projectile is charged the influence of its potential on the electronic final state may only be neglected for ejection of very low-energy electrons into the backward direction.

K-shell electron capture from negative ions

Electron capture from the K-shell of a negative ion by protons is considered by accounting for the interplay between the final channel-distorted projectile and off-shell electronic scattering motions using the distorted strong-potential Born approximation. The distorted motion accounts for the ionized state of the target core and the short-range shielding of the K-shell by the passive outer-shell electrons. Total cross sections versus incident energy are compared for the negative-ion, neutral, and singly-ionized forms of the second- and third-row elements C, O, F and Si, S, Cl. Target core neutrality and diffuseness of the negative-ion screening consistently lower the cross section by amounts ranging from 22 to 37% while the positive-ion results are larger by only 1 to 15%. Previous comparison with experiment and coupled-Sturmian-pseudostate results for neutrals has shown very good agreement.

Nearly normalized, distorted strong-potential Born state vector.

Nearly normalized, distorted strong-potential Born state vector.

Positronium formation by electron capture from hydrogen-like ions

Two different impulse approximations are provided for the problem of fast positron collisions with hydrogen-like ions. One of the impulse approximations is formulated by making a consistent expansion of the scattering wave function in powers of the weak interaction to the strong. The other impulse approximation is formulated by making a consistent expansion of theT-matrix in powers of the weak interaction to the strong. In this impulse approximation, the opposite limits of the target nuclear charge tending to zero and to infinity are examined. Differential and angle-integrated cross sections are computed for ground-state positronium formation from hydrogen within the impulse approximations. The full peaking approximation is employed in the evaluation of theT-matrix. By 300 eV, the impulse approximations for the angle-integrated cross section are in close agreement with the strong potential Born and the exact second Born calculations.

Influence of the projectile field on free target electrons.

The spectral distribution of loosely bound target electrons emitted in collisions with fast bare projectiles is described in terms of electron capture to the projectile continuum. Comparison with experimental data on electron ejection from He by 1--5-MeV/amu H[sup +], C[sup 6+], O[sup 8+], and F[sup 9+] impact into forward directions shows that the impulse approximation for rearrangement is able to describe the shape of the energy distribution not only at the cusp, but also in the binary-encounter region and beyond. The results of the post form of the impulse approximation are discussed in relation to the first-order Born approximation, the continuum distorted-wave theory, the fully peaked prior impulse approximation, and in particular the recently presented distorted-wave strong-potential Born approximation.

Inner-shell capture using atomic potentials: A distorted strong-potential Born treatment.

The influence of a distorted nuclear motion on electron capture from the inner shells of atoms, when atomic model potentials, rather than scaled Coulomb potentials, are used in the motion of the active target electron, is investigated in the distorted strong-potential Born approximation to the exact capture amplitude. A comparison is made with the earlier undistorted strong-potential Born approximation and other theories, and with experiment. The modification of the impulse-approximation cross section is shown to be generally much less in the distorted theory and is shown to give quite good agreement with the experimental data. At energies below the peak in the capture cross sections, the present results show significantly better agreement with experiment and also good agreement with the recent coupled-Sturmian-pseudostate results of Winter [Phys. Rev. A 47, 264 (1993)], who used the same atomic model potential.

Theory of binary encounter electrons in ion-atom collisions

An intuitive model of the binary encounter peak in the energy and angular distribution of ionization electrons employs the elastic scattering amplitude for electron-projectile scattering. When the projectile carries some electrons, electron exchange contributes to the elastic scattering. The authors show that the elastic scattering model, including exchange, derives from a distorted-wave strong-potential Born approximation for ionization to the projectile continuum. This theory incorporates both the binary encounter peak and the continuum capture cusp.

Total cross sections for K-K electron transfer in fast ion-atom collisions: the impulse and strong potential Born approximations

For the first time the strong potential Born (SPB) and the impulse (IA) approximation for K-K electron capture are evaluated exactly using non-hydrogenic (Herman-Skillman) wavefunctions. It is shown that the long-range tail of the target nucleus potential leads to a loss of normalization of off-shell electronic wavefunctions and results in cross sections in disagreement with experiment. A wavepacket renormalization procedure restores agreement with experiment and for proton impact leads to cross sections close to those provided by the IA. However, for projectiles of higher charge, off-shell effects persist and the renormalized SPB cross sections are more accurate than those of the IA.

Ion-impact ionization of He targets.

We calculate double-differential cross sections for the impact ionization of He targets by 1.5-MeV ${\mathrm{H}}^{+}$ and 28.5-MeV ${\mathrm{F}}^{9+}$ ions using the distorted-wave strong-potential Born approximation. The theory is compared with the experimental electron spectrum. Both theory and experiment show the low-energy electron distribution, the electron capture to the continuum cusp, and the binary-encounter peak.

Coupled-Sturmian and perturbative treatments of electron transfer and ionization in high-energy p-He+ collisions.

Cross sections have been determined for electron transfer and ionization in collisions between protons and ${\mathrm{He}}^{+}$ ions at proton energies from several hundred kilo-electron-volts to 2 MeV. A coupled-Sturmian approach is taken, extending the work of Winter [Phys. Rev. A 35, 3799 (1987)] and Stodden et al. [Phys. Rev. A 41, 1281 (1990)] to high energies where perturbative approaches are expected to be valid. An explicit connection is made with the first-order Born approximation for ionization and the impulse version of the distorted, strong-potential Born approximation for electron transfer. The capture cross section is shown to be affected by the presence of target basis functions of positive energy near ${\mathit{v}}^{2}$/2, corresponding to the Thomas mechanism.

The distorted-wave impulse approximation for electron capture processes at intermediate collision energies

The author presents exact calculations of the distorted-wave impulse approximation for electron capture by fast protons from hydrogen and by lithium ions from neon. Results for total and differential cross sections are presented, and comparison is made with other models of electron capture as well as experimental measurements. A detailed derivation of the impulse approximation is presented within the framework of the distorted-wave approximation, and its relation to the strong-potential Born approximation is clarified. It is indicated that the approximations involved in the impulse approximation are less severe than those of the Born approximation for simple rearrangement collisions. The validity of certain peaking approximations is analysed. The implications for highly asymmetric and nearly symmetric charge transfer collisions are briefly discussed.

Reply to A Salin: Some remarks on strong-potential-Born expansions for ion-atom collisions

For original paper see A. Salin, Comment At. Mol. Phys., vol.26, p.1-11 (1991) Perturbation theories for Coulomb potentials are discussed. The equations of perturbation theory for such potentials cannot be solved by conventional Green function techniques, thus solutions employing more general methods are used. The author applies these more general methods to the distorted-wave strong-potential-Born (SPB) approximation for electron capture. The amplitudes are shown to be unique and well represented in a commonly used peaking approximation. An elementary discussion is given in response to recent criticisms of the theory.

Generalized distorted-wave Born approximation for electron capture in ion-ion collisions.

By starting with the distorted-wave form of the exact transition amplitude and introducing a second distorting potential, a generalized distorted-wave Born theory of electron capture is developed that is applicable to ion-ion collisions. The theory reduces to the distorted-wave Born theory developed by Taulbjerg and Briggs [J. Phys. B 14, 3523 (1983)] in the ion-atom case. Other theories, including the distorted strong-potential Born theory, the boundary-corrected first- and second-order Born theories, and the Coulomb Born theory, are seen to be approximations to the new amplitude.

Three-particle one-dimensional collision model - II. Capture

Using the same one-dimensional model as in the preceding paper, the capture process is studied as a function of the projectile velocity and strength of the target nucleus. Ten theoretical methods are calculated and compared with the exact results. In spite of its simplicity, the continuum distorted wave method presents the best performance to treat symmetric systems, while the semigeneralised impulse approximation seems to cope better with strong target perturbation. Unexpectedly, the strong potential Born, which is exactly calculated, does not match the exact results within the range studied here.

Variational principle for time-dependent interactions.

A Schwinger-type variational principle for time-dependent interactions is developed for the S matrix using a separable operator approach. The S matrix has an implicit fractional form by which we mean that an integral equation has to be solved to compute the wave function. This principle shares the important features of the fractional form of Schwinger's variational principle and reduces to it for time-independent interactions. We discuss the relationship with the Lippmann-Schwinger variational principle. The variational principle is generalized to treat direct and rearrangement processes in ion-atom collisions in both the time-dependent and time-independent representations. It is shown to yield the correct asymptotic form for capture. Using free states as trial functions, the channel-distorted strong-potential Born S matrix is obtained. The distortion potential is determined variationally and is found to have the correct form at large distances.

L3-subshell alignment of argon following charge-changing collisions with protons

The alignment of the L3 subshell of Ar induced by electron capture has been studied experimentally for proton impact in the energy range 0.3-1.0 MeV. The experiment is based on the measurement of the angular distribution of the L-MM Auger electrons detected in coincidence with the outgoing neutral H atoms. The results have been compared with the predictions of the Oppenheimer-Brinkmann-Kramers approximation, the strong potential Born approximation, the continuum distorted wave theory and the impulse approximation. The tendency of the measured data towards large negative alignment at high collision energies is in accordance with the asymptotical behaviour characteristic of the capture theories. At lower energies large deviations have been found between the experiment and the theories which can only be partly explained by experimental effects. This finding indicates the failure to understand the capture-induced alignment by the existing theories.

Perturbation theory for strongly interacting atomic systems.

The strong-potential Born approximation has been formulated to include effects of elastic scattering in initial and final states. We use the standard distorted-wave theory and the eikonal approximation to derive closed-form expressions for scattering wave functions. Our results show that lowest-order theories must account for off-energy-shell electron propagation in the strong potential as well as for elastic scattering in initial and final states. Capture from inner shells and radiative electron capture are computed to illustrate the theory.

Theoretical study of radiative electron capture in ion-atom collisions

The present status of theoretical studies of radiative electron capture (REC) is discussed. Difficulty in the formulation comes from the fact that we do not have enough knowledge concerning the exact wave functions of three-body scattering states. The validity of the inverse-photoionization concept for REC is examined. A problem occurring in the calculations in the strong potential Born approximation is also discussed. We have made calculations of the total REC cross section in the relativistic impulse approximation including the intermediate process of positron-electron pair creation. Various characteristic features of REC X-rays are discussed in the relativistic impulse approximation.

Strong potential wave functions with elastic channel distortion.

The strong-potential Born approximation is analyzed in a channel-distorted-wave approach. Channel-distorted SPB wave functions are reduced to a conventional form in which the standard off-energy-shell factor g has been replaced by a modified factor \ensuremath{\gamma}, which represents a suitable average of g over the momentum distribution of the distorted-channel function. The modified factor is evaluated in a physically realistic model for the distortion potential, and it is found that \ensuremath{\gamma} is well represented by a slowly varying phase factor. The channel-distorted SPB approximation is accordingly identical to the impulse approximation if the phase variation of \ensuremath{\gamma} can be ignored. This is generally the case in applications to radiative electron capture and to a good approximation for ordinary capture at not too small velocities.

The capture of inner-shell electrons in the strong-potential born (SPB) approximation

For the first time the capture of inner-shell electrons by protons is calculated by the SPB method without further approximation and using Hartree-Slater wavefunctions. The resulting cross-section has roughly the correct shape, but is much too large. The problem is traced to a loss of normalization caused by the SPB approximation. A suitably renormalized SPB gives close agreement with experiment.