First and second Born (e, 2e) calculations are presented for excitation-ionization of ground-state helium to He + (n = 2). Results for ionization to the ground-state ion He + (1s) are also given. The physical content of the approximations is discussed, in particular, the two-step mechanism which appears in the second-order term for excitation-ionization. The second Born term is calculated in the closure approximation using a new numerical method based on prolate spheroidal coordinates. Comparison is made with absolute experimental data from Paris and Rome in very asymmetric coplanar geometry-scattered electron energies of 5500, 1500 and 570 eV and ejected electron energies of 5, 10, 20, 40 and 75 eV. For excitation-ionization the second Born approximation generally gives improved agreement with the experimental data in the recoil region and second-order effects are found to be still significant at 5500 eV. The importance of the second-order term decreases with increasing ejected energy for the cases studied here. † Whereas the 2s → 1s transition is not 'optically allowed', the 2s state can decay radiatively to 1s by emission of two photons. These photons will have a distribution of energies and will therefore not appear as a single spectral line like the optically allowed 2p → 1s decay.‡ And also with collisions of other projectiles such as Li q+ , B q+ , C q+ , H + 2 and H +
A recently developed [Phys. Rev. A 79, 042707 (2009)] impact parameter coupled pseudostate approximation (CP) is applied to calculate triple differential cross sections for single ionization of He by C 6+ , Au 24+ , and Au 53+ projectiles at impact energies of 100 and 2 MeV/amu for C 6+ and 3.6 MeV/amu for Au 24+ and Au 53+ . For C 6+ , satisfactory, but not perfect, agreement is found with experimental measurements in coplanar geometry, but there is substantial disagreement with data taken in a perpendicular plane geometry. The CP calculations firmly contradict a projectile-nucleus interaction model which has been used to support the perpendicular plane measurements. For Au 24+ and Au 53+ , there is a complete lack of accord with the available experiments. However, for Au 24+ the theoretical position appears to be quite firm with clear indications of convergence in the CP approximation and very good agreement between CP and the completely different three-distorted-waves eikonal-initial-state (3DW-EIS) approximation. The situation for Au 53+ is different. At the momentum transfers at which the measurements were made, there are doubts about the convergence of the CP approximation and a factor of 2 difference between the CP and 3DW-EIS predictions. The discord between theory and experiment is even greater with the experiment giving cross sections a factor of 10 larger than the theory. A study of the convergence of the CP approximation shows that it improves rapidly with reducing momentum transfer. As a consequence, lower-order cross sections than the triple are quite well converged and present an opportunity for a more reliable test of the experiment.
We report detailed calculations of the first Born triple-differential cross section for (e, 2e) excitation-ionization of ground state He to He + (n = 2). These are in accord with the very recent work of Kheifets et al (1999 J. Phys. B: At. Mol. Opt. Phys. 32 L433) and confirm that the first Born amplitude is now known very accurately. We illustrate the sensitivity of the first Born cross section to the choice of initial and final state wavefunctions. We combine our accurate first Born amplitude with an estimate of the second Born term evaluated in the closure approximation. As in previous work (Marchalant et al 1998 J. Phys. B: At. Mol. Opt. Phys. 31 1141 we find that second-order effects are significant even up to energies as high as 5.5 keV. Agreement with experiment generally remains not very satisfactory.
We have performed a kinematically complete experiment and
calculations on single ionization in 100 MeV/amu C6+ + He
collisions. For electrons ejected into the
scattering plane (defined by the initial and final projectile
momentum vectors) our first- and higher-order calculations are
in good agreement with the data. In the plane perpendicular to
the scattering plane and containing the initial projectile axis
a strong forward-backward asymmetry is observed. In this plane
both the first-order and the higher-order calculations do not
provide good agreement neither with the data nor amongst each
other.
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