e+ AND e- COLLISIONS WITH ATOMS AND MOLECULES 

O. A. Fojón

Instituto de Física Rosario (CONICET-Escuela de Ciencias Exactas, UNR)
Pellegrini 250, (2000) Rosario, Argentina

ABSTRACT

Collisions of positrons and electrons with atoms and molecules at intermediate and high impact energies are studied. In particular, the positronium formation reaction is analyzed in the case of fast positrons impigning on alkali atoms. The ionization of hydrogen molecules by electron impact in a coplanar asymmetric geometry is studied by using a simple two-effective center approximation.

Collision processes at intermediate and high impact (although non relativistic)  energies involving electrons and positrons are briefly studied. The experimental research with positrons has developed rather slowly in comparison with electrons. Only recently, positrons beams with the required intensity and stability to perform experiments were developed. For positron impact, not only excitation and ionization of the target is possible as for electron impact but also positronium (Ps) formation1.
The Ps atom is a bound system consisting of an electron and a positron. In the Ps formation reaction, an electron is transferred from the target to the projectile. This reaction is of fundamental importance as transfer of mass is a quasiforbidden process. A full quantum formalism is required to study the impact of positrons. This is contrast with the impact of heavy particles where the relative motion of the ions may be described by a classical straight-line trajectory. 
At sufficiently high impact energies, perturbation methods are suitable to describe Ps formation. In particular, distorted wave methods are adequate as they may incorporate easily higher order terms in the transition amplitude. A Continumm Distorted Wave-Final State (CDW-FS) approximation including distortions in the final channel of the reaction was applied to study Ps formation with alkali targets. In Fig. 1, Ps(1s)  formation CDW-FS total cross sections (TCS) with K targets are shown. At low impact energies, TCS are dominated by capture of the valence electron. As the impact energy increases, capture from the n=3 shell becomes dominant increasing the TCS after reaching a relative minimum at about 30 eV. This may be explained in terms of matching velocity arguments. As the impact energy increases, electron capture is more favorable 

Figure 1.  Ps formation TCS with K targets. CDW-FS, full line. CCA3, open squares. Experiments4: upper limit, open circles; lower limit, full circles. 
Figure 2. 3DCS as a function of the ejection angle for ionization of H2 molecules. TEC, full line. CWVA7, dashed line. CWLA7, dot-dashed line. Experiments6, full circles. 

for inner electrons as they have higher mean orbital velocities. TCS obtained with a Close Coupling Approximation (CCA) (usually adequate at low and intermediate impact energies) and experiments are also included in the figure.
The ionization reaction of atomic and molecular species by electron impact is a fundamental process in which one electron from the target is ejected leading to three unbounded charged  bodies interacting through Coulomb potentials. In Fig. 2, Triply Differential Cross Sections (3DCS) for ionization of H2 molecules in a coplanar asymmetric geometry are shown. 3DCS were obtained by means of a first order model within the frame of a two-effective center  (TEC) approximation5. The impact and ejection energies are EI=4168 eV and Ee=100 eV, respectively, and the scattering angle is s=8.9. The kinematical situation corresponds to the Bethe condition in which the target recoil is zero being all the momentum transfer given to the ejected electron.  The agreement of the TEC results with experiments is good. TEC results are also in good agreement with more elaborated theoretical ones based on a factorised first Born approximation in its velocity (CWVA) and wavelength (CWLA) forms. This shows that the simple TEC approximation may be useful in studying more complex diatomic molecules.