Total and differential cross-section calculations for proton-impact ionization of hydrogen at low energies

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 66, Issue 4, 2002, Pages 427071-4270713

  Zou, Shiyang ^a   Pichl, Lukáš ^b   Kimura, Mineo ^c   Kato, Takako ^d  

^a GRADUATE UNIVERSITY FOR ADVANCED STUDIES   (Japan)

^b UNIVERSITY OF AIZU   (Japan)

^c YAMAGUCHI UNIVERSITY   (Japan)

^d NATIONAL INSTITUTE FOR FUSION SCIENCE   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CHARGE TRANSFER; IONIZATION; MOLECULAR DYNAMICS; PROTONS; SWITCHING FUNCTIONS;

ELASTIC SCATTERING;

HYDROGEN;

EID: 0036818596     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.66.042707     Document Type: Article

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33. The energy of ejected electrons is explicitely included in the equations of motion via the coupling terms in Eq. (2), whilst the total ionization cross section requires a formal integration over the whole continuum. Therefore, we need to revert to a discrete sampling scheme as described further. Our study and also previous works in literature [30,14] find couplings with continuum states to be generally weak, and the full close-coupled equations (2) can be partitioned into separate groups. Each group contains the strongly coupled symmetry allowed discrete states (cf. Table I) and several partial waves for continuum electron with the same energy; these are coupled by weak radial or angular interactions. Truncation in the partial wave expansion of the continuum electron is based on a rapid decrease of the couplings with the increasing angular momentum number (∼3 orders of magnitude for ejected electron with l = 5). Next, we calculate the differential ionization cross sections at a certain set of separate energy points, interpolate these with B splines, and finally integrate the spline function over the whole continuum analytically. Thus the convergence in the number of continuum states can be controlled through the convergence of B-spline interpolation. Ionization cross sections decrease rapidly with the ejected electron energy increase, and the necessary number of interpolation points derives from the number of B-spline terms which can accurately represent this function shape. Logarithm equally spaced mesh points of ejected electron energy were conveniently used in our calculation. The differential cross sections (see Fig. 15) already vary smoothly with free electron energies on the 32 point grid (checked also with 64 and 128 points), yielding converged results with sufficient accuracy from our viewpoint.
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