Electron capture to the continuum
The second-order Oppenheimer-Brinkman-Kramers approximation is used to obtain a simple analytical formula, evaluated to the lowest order in the fine structure constant α in the numerator, for the differential cross section for electron capture to the continuum (ECC) by incident bare ions having velocity v from target hydrogenic atomic systems. Both non-relativistic and relativistic forms are derived. Comparison of the theory with the experimental data of Dahl (1985) and Andersen et al (1986) for H+, He 2+ + He collisions is reasonably satisfactory for energies > 50 keV/amu. However, theory shows that although the velocity dependence obtained by Andersen et al is v−11.3±0.2 in the range of impact energies 1–2.6 MeV/amu, this does not mean that the asymptotic v−11 velocity dependence given by the non-relativistic second-order OBK cross section is nearly attained. In fact it is shown that this cannot happen until an energy > 500 MeV/amu is reached where the effect of relativity produces a significant change in the energy fall off. Also a modification of the second-order OBK approximation obtained by Shakeshaft and Spruch (1978) has been expanded to first order in the atomic number ZP of the projectile ion to get simple formulas for the yield of continuum electrons and the cusp asymmetry factor β. The accordance with the data of Andersen et al (1986) is fair at energies > 0.5 MeV/amu/ZP but the situation is uncertain at lower energies since there is disagreement between different experimental groups and CDW theory results in smaller values of β than the OBK2 theory.
KeywordsAtomic Number Impact Energy Differential Cross Section Helium Atom Relativistic Form
Unable to display preview. Download preview PDF.
- Andersen L H, Jensen K E and Knudsen H 1986 J Phys B: At. Mol. Phys. 19 L161Google Scholar
- Burgdorfer J 1986 Phys Rev A 33 1578Google Scholar
- Crothers D S F and McCann J F 1987 J Phys B: At. Mol. Phys. 20 L19Google Scholar
- Dahl P 1985 J Phys B: At. Mol. Phys. 18 1181Google Scholar
- Gulyas L, Szabo Gy., Berenyi D, Kover A, Groeneveld K O, Hoffmann D and Burkhard M 1986 Phys Rev A 34 2751Google Scholar
- Meckbach W, Nemirowsky I B and Garibotti C R 1981 Phys Rev A 24 1793Google Scholar
- Shakeshaft R and Spruch L 1978 Phys. Rev. Lett. 41 1037Google Scholar