Interference effects in the photoionizatin of the hydrogen molecular ion

DELLA PICCA, RENATA; FAINSTEIN, PABLO DANIEL; MARTIARENA, MARÍA LUZ; DUBOIS, ALAIN

Bariloche, Argentina

Jornada; Jornadas de Física Bariloche 2005, Conmemorando los 50 años del IB; 2005

Instituto Balseiro

Recent experiments have found for the first time evidence of interference effects in the electron emission spectra produced in collisions between fast highly charged ions with H$_2$. These results have been confirmed by new evidence obtained using fast protons and electrons as projectiles. With the aid of theoretical models these oscillations have been now identified as a Young-type interference effect due to the multicenter character of the molecular target. More recent experimental and theoretical studies have shown that this process is dominant at electron energies larger than 1~a.u. while close to the ionization threshold the autoionization of excited states of H$_2$ plays a main role.The theoretical study of the single ionization process is very complicated. Even though the experiments have been performed at high impact energies several features must be taken into account accurately. The most important are: the effect of long-range interactions and the geometrical structure of the target. At present it is very difficult to take both into account and it is therefore convenient to consider a system where at least one can be neglected. For this purpose we have chosen the photoionization of H$_2^+$. In this case we must only take into account accurately the electronic states of the molecule.The main problem is to obtain the two-center continuum wavefunctions. In previous studies the continuum state was represented by a product of two single-center atomic-continuum wave functions centered on each nuclei of the target. This is the wellknown 2C wavefunction which has been used with great success to study the single ionization process in ion-atom and electron-atom collisions. The results from these calculations show important discrepancies with respect to calculations in which the emitted electron wavefunction is represented by a plane wane. In particular both calculations show a very different angular distribution of the photoelectron.For the hydrogen molecular ion two-center bound and continuum wavefunctions can be obtained exactly solving numerically the corresponding Schr\"odinger equation in prolate spheroidal coordinates. We have developed methods to calculate the transition matrix, in the dipolar approximation, using these wavefunctions. The whole calculation is much more complicated with respect to the plane wave or 2C calculations because it must be done numerically.A detailed comparison of the angular distributions shows that the2C wavefunction only agrees with the exact calculation at very largeelectron energies. This is compatible with the fact that the 2C wavefunction is the exact asymptotic solution. On the contrary,in a large range of electron energies very large discrepancies appear.