Molecular Siegert states in an electric field. II. Transverse momentum distribution of the ionized electrons

Abstract

This paper completes our previous studies of atomic [P. A. Batishchev, O. I. Tolstikhin, and T. Morishita, Phys. Rev. A 82, 023416 (2010)] and molecular [L. Hamonou, T. Morishita, and O. I. Tolstikhin, Phys. Rev. A 86, 013412 (2012)] Siegert states (SSs) in an electric field by presenting illustrative calculations of the transverse momentum distribution (TMD) for a molecular potential. The method of adiabatic expansion in parabolic coordinates developed in this series for calculating the SSs is summarized. Its implementation is extended to the calculation of the normalized molecular SS eigenfunction, which is required for calculating the TMD. We consider a soft-core potential modeling the hydrogen molecular ion ${{\mathrm{H}}_{2}}^{+}$. The behavior of the parabolic adiabatic potentials, channel functions and the total SS eigenfunction is illustrated, which was not included in the previous publications. The TMDs for the $1s\ensuremath{\sigma}$ and $2p{\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$ states are calculated. Their dependence on field and orientation of the molecule with respect to the field is compared with the predictions of the weak-field asymptotic theory. On the example of the even $2p{\ensuremath{\pi}}^{+}$ state, it is shown that TMD can rapidly change its shape in situations where there is no a single dominant ionization channel.