Strong-potential Born Research Articles

Strong-potential Born-approximation electron-capture cross sections for realistic atomic potentials.

The strong-potential Born approximation to the single-electron capture amplitude in asymmetric ion-atom collisions is discussed in the context of a realistic atomic potential. When finalstate binding effects of the captured electron are neglected, a simple connection between the amplitude in the actual atomic-potential case and the one obtained employing a scaled-hydrogenic model is derived which involves the competing effects of an off-shell multiplicative term depending on the residual, target-ion charge and a phase factor containing the difference of the $s$-wave phase shifts for the two potentials.

Evaluation of nlm-n'l'm' capture amplitude in the target continuum distorted-wave theory.

We present a technique to evaluate the capture amplitude from an arbitrary initial state of the target to an arbitrary final state of the projectile within the framework of target continuum distorted-wave theory recently derived and developed by Crothers and Dunseath. Both integrals in their first-order transition amplitude, T/sup (1)/, are evaluated into closed form, resulting in a finite number of terms. From our general expression of the nlm-n'l'm' amplitude, the evaluation of T/sup (1)/ for the 1s-1s capture is straightforward. With this technique, it is now convenient to calculate capture cross sections from higher angular momentum states of the target to any projectile states, which are not so easy to calculate in other second-order theories such as the strong-potential Born approximation.

Nuclear resonance effect in atomic electron capture by protons.

We have investigated electron capture accompanied by nuclear scattering by studying the probability for electron capture from $^{22}\mathrm{Ne}$ in the vicinity of the 1.510-MeV elastic nuclear resonance $^{22}\mathrm{Ne}$(p,p${)}^{22}$Ne. We have found a large nuclear resonance effect in the probability for electron capture. The data are in some disagreement with theoretical calculations by Jakubassa-Amundsen and Amundsen, based on the strong-potential Born approximation for electron capture.

Distorted-wave Born theory for electron capture during resonant nuclear scattering

A quantum mechanical formulation of the distorted-wave Born theory is presented, taking full account of the internuclear potential. Upon expansion in terms of one of the two electronic potentials, the strong-potential Born theory is rederived. Thereby an additional term emerges which had not been considered previously and which has considerable influence on the capture probability at large scattering angles.

On the calculation of the electron capture within the strong potential born approximation

A new method to perform the calculation the limits of the electron capture cross-section in the Strong Potential Born Approximation is presented. Within this approach, the high velocity limit is obtained by a simple algebraic procedure as an alternative derivation to the complex variable analysis used previously.

Target continuum distorted-wave theory for capture of inner-shell electrons by fully stripped ions

The target continuum distorted wave (TCDW) theory is derived and developed. It describes charge exchange in asymmetric collisions, in particular the collision of a projectile ion of low charge with a target ion of high charge. The final state is represented by a TCDW function. The initial state is taken as a travelling atomic orbital, while the intermediate states are represented by a Coulomb-Green function. The theory is applied to capture by protons from the inner shells of heavy atoms. For s-s transitions, it is found that within a standard on-shell full-peaking approximation the second-order amplitude does not contribute. The total cross section for K-K electron capture in proton-carbon, neon and argon atom collisions is calculated in the energy range corresponding to values of ZT/v from 0.5 to 3.0, where ZT is the nuclear charge of the target and v the velocity of impact in atomic units. Agreement with experiment is excellent in all three cases and the cross section values compare extremely favourably with those of the well known strong-potential Born theory.

Cross sections of relativistic radiative electron capture by use of the strong-potential Born calculation.

The relativistically extended strong-potential Born (SPB) formalism is applied to the radiative electron capture process caused by the bombardment of a heavy and highly stripped charged particle with relativistically high velocity. The results are compared with those by use of nonrelativistic SPB calculations and with those by use of the relativistic Born calculation (Sauter's formula), which includes no distortion effects between a heavy projectile ion and an active electron. Even if the strong distortion effects are taken into consideration, the shapes of photon angular distributions in the laboratory frame still nearly depend on sin/sup 2/theta/sub L/(theta/sub L/ is the angle of the emitted photon) in the vicinity of the angle of 90/sup 0/, which is the same as the results by use of Sauter's formula. The higher the charge of a projectile ion becomes, however, the greater the discrepancy between the angular shape of our results and that of Sauter's becomes at both smaller and larger angles than at 90/sup 0/. As is expected, the magnitudes of the differential and the total cross sections are drastically influenced by the distortion effects ascribable to a large charge of a heavy projectile ion such as U/sup 92+/. Our results are in goodmore » agreement with recent experiments. In addition, the Coulomb off-shell factor introduced by the SPB theory is found playing important roles in the case of the relativistic radiative electron capture process because the results calculated by using the relativistic impulse approximation are too underestimated.« less

Measurement of the total cross sections for electron capture of 2.0-7.5 MeV H+in H, H2and He

The total cross sections for electron capture of protons in atomic and molecular hydrogen and in helium gas targets are measured in the high proton velocity regime of 2.0, 3.5, 5.0 and 7.5 MeV. The results are compared with first- and higher-order perturbation theories (Oppenheimer-Brinkmann-Kramers, true first Born approximation, eikonal approximation, continuum distorted wave, strong potential Born, strong potential Born full peaking) for electron capture and are found to be in good agreement with the CDW, EA and TFBA approximations.

Third-Born-approximation effects in electron capture.

We have calculated corrections to the strong-potential Born approximation using the distorted-wave Born formalism of Taulbjerg and Briggs. In the sense of a plane-wave Born expansion, all terms of the third Born approximation, and all ``single switching'' fourth Born terms are included, but a peaking approximation is needed to reduce the calculation to tractable form. We believe this to be the first calculation to be so complete in the Born sense. Effects of the higher terms are most visible in the valley between the Thomas peak and the forward peak. The Thomas peak is visible in the correction term even though it includes no second Born contributions. We suggest that this may be interpreted as a third Born effect with two ``hard'' collisions followed by a ``soft'' collision.

Third-Born-approximation calculation of electron capture.

Calculations of electron-capture cross sections are presented in the symmetrized strong-potential Born approximation for p+H. These calculations are complete through the third Born term. Our amplitudes may be expressed as a finite sum of hypergeometric functions and derivatives of hypergeometric functions. No evidence is found for new observable singular structure due to third Born contributions.

On the ultimate sharpness of the ECC cusp

In electron capture to the continuum (ECC) the distribution of scattered electrons is sharply peaked when the velocity of the electron v e matches the velocity of the projectile v p. We discuss the significance of this cusp and present a closed form expre this cusp in the fully peaked strong potential Born approximation (SPB-FP). This cusp diverges at v e = v p for scattering with unscreened Coulomb potentials. In reality this divergence is removed by various effects, including screening of Coulomb potentials in atomic collisions.

Evaluation and application of integral Ylm(P-hat)(A+2L.P)-ivdΩp

The integral I= integral Ylm(P-hat)(A+2L.P)-ivd Omega p is evaluated analytically in terms of Gauss hypergeometric functions and the result has been checked by comparison with the known results corresponding to v=0, +or-i. Two applications of this result are given: (i) analytic evaluation of the zeroth-order strong potential Born amplitude for electron capture into arbitrary hydrogenic states, and (ii) expansion of (P-K)2iv-2 in spherical harmonics and evaluation of a partial-wave expansion of Coulomb continuum wavefunctions in momentum space. By analytic continuation it has been shown that the radial part of the partial-wave expansion in case (ii) gives the corresponding bound-state wavefunction in momentum space obtained by Podolsky and Pauling (1929).

On the applicability of the impulse approximation for radiative electron capture into bound and continuum states

A comparison between the impulse approximation (IA) and the strong-potential Born approximation (SPB) is carried out for radiative capture of a target electron into excited bound states (REC) and into continuum states (radiative ionisation, RI) of the projectile. It is found that in the vicinity of the peak in the photon spectrum, the deviations of the SPB from the IA are small but do not disappear either for excited states or for continuum states with low momentum kappa /sub /f. The contribution of RI to the forward peak is calculated for the systems C6+ to He and Ne10+ to He, showing a strong skewness towards the high-energy side. For electrons with high kappa /sub /f, large deviations between SPB and IA indicate the breakdown of an atomic description.

Experimental test of higher-order electron-capture processes in collisions of fast protons with atomic hydrogen.

We present measurements of the angular distribution of fast hydrogen atoms formed by electron capture of 2.8- and 5.0-MeV protons in atomic hydrogen. In the angular region of the Thomas peak (0.47 mrad) the experimental results obtained with this pure three-body collision system are in reasonable agreement with a strong potential Born calculation and the impulse approximation, but not with other higher-order theories.

Strong-potential Born-approximation calculations of 1s-2p electron capture.

Cross sections for electron capture into the 2p level evaluated with use of the strong potential Born approximation are presented. While these 2p cross sections are smaller than cross sections for capture into the 1s and 2s levels at high velocities, nevertheless the Thomas peak is clearly evident at energies above 1 MeV in both the m=0 and \ensuremath{\Vert}m\ensuremath{\Vert}=1 magnetic substates in atomic hydrogen. At energies above 10 MeV where the Thomas peak is important, cross sections for capture into m=0 and \ensuremath{\Vert}m\ensuremath{\Vert}=1 are comparable. Consequently, the polarization fraction becomes negative at high energies in sharp contrast to Brinkman-Kramers results where the polarization fraction stays near its maximum value.

Convergence of the strong-potential-Born approximation in Z

Convergence of the strong-potential Born (SPB) approximation as a function of the charges of the projectile and target is studied numerically. Time-reversal invariance (or detailed balance) is satisfied at sufficiently high velocities even when the charges are asymmetric. This demonstarates that the SPB approximation converges to the correct result even when the charge of the ''weak'' potential, which is kept to first order, is larger than the charge of the ''strong'' potential, which is retained to all orders. Consequently, the SPB approximation is valid for systems of arbitrary charge symmetry (including symmetric systems) at sufficiently high velocities.

Analytic strong-potential Born approximation cross sections for electron capture from the K shell by fast ions

The strong potential Born approximation has been applied to evaluate the transition amplitude for the collision process in which a fast ion of charge ZP captures an electron from the K shell of an atomic target with nuclear charge ZT, where ZT ≥ZP. The transition amplitude has been evaluated analytically in terms of Gauss hypergeometric functions. No peaking approximation has been made. We have considered the K-shell capture of electrons by high-energy protons from Li, C, Ne, Na, and Ar. Our results for C, Ne, and Ar are in good agreement with the available experimental data.

Strong-potential Born calculations for 1s-1s electron capture from atoms by protons.

The strong-potential Born (SPB) approximation is examined by comparing various SPB calculations of high-velocity 1s-1s electron capture cross sections with one another and with experimental data. Above about 1 MeV, calculations using the SPB method of McGuire and Sil (SPMS) (Phys. Rev. A 28, 3679 (1983)) are in good agreement with total-cross-section observations for protons on H, He, C, Ne, and Ar as expected. For p+H and p+He, the SPB full-peaking (SPB-FP) approximation of Macek and Alston (Phys. Rev. A 26, 250 (1982)) and the SPB transverse-peaking (SPB-TP) approximation of Alston (Phys. Rev. A 27, 2342 (1982)) differ from our SPMS total cross sections by typically a factor of 2, as expected from general validity criteria. However, the differential cross sections at very forward angles (well within the Thomas angle) are the same in SPMS, SPB-FP, and SPB-TP methods in all cases. Below 1 MeV, cross sections obtained with use of various SPB methods differ considerably from one another, placing a limit of validity for these SPB calculations. We also suggest that in the gap between those energies where continuum intermediate states simply dominate, and above those energies where bound intermediate states simply dominate, detailed conceptual understanding of electron capturemore » is incomplete.« less

Radiative electron capture accompanying resonant nuclear scattering

A quantum mechanical theory for the radiative capture (REC) of a target electron by a heavy, swift projectile is formulated, allowing for resonant nuclear scattering through the use of distorted waves. Calculations are performed for the systems O16, Ne20→He within the exact strong potential Born theory and the impulse approximation. Similar structures as in the case of Coulomb capture are found in the transition probability.

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.