Cooper minima in photoionization of H2+

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

Paris, Francia

Conferencia; International Conference on Many Particle Spectroscopy of atoms, molecules clusters and surfaces; 2008

It is well known that the photoionization spectra of atoms present Cooper mimima in \ell \to \ell +1 transitions provided that the initial radial wavefunction has at least one node. Theses minima arise when the transition matrix vanishes and at this particular energy there is not photon absorption \cite{Cooper62}. The molecular case is different because there are Cooper-like minima even when the ground state has no nodes. This was attributed to the non-spherical shape of the molecular potential \cite{Semenov03} and thus we can expect that  the minima depend not only on the photon energy but on the internuclear distance too.To analize in more detail these features we present here a thorought investigation of the photoionization partial cross sections for H2+. We calculate it for parallel alignment of the internuclear direction and the polarization vector, and for different values of \ell in a wide range of internuclear distances R and electron momenta ke. We find that the minima follow approximately the empirical formula ke R=\ell \pi proposed in \cite{Fernandez07}, which we show to be valid only for high enough photoelectron energy \cite{DellaPicca08}. Interestingly, as can be seen from the figure, we find that the Cooper minima are associated to a maximun in the corresponding phase shifts and that the transtition matrix is exactly zero at the particular value of electron momentum. This results implies therefore that the minima are clearly associated to zero absoption as in the atomic case.