Atomic ionization by twisted photons: Angular distribution of emitted electrons

We investigate the angular distribution of electrons that are emitted in the ionization of hydrogen-like ions by twisted photons. Analysis is performed based on the first-order perturbation theory and the non-relativistic Schr\"odinger equation. Special attention is paid to the dependence of the electron emission pattern on the impact parameter b of the ion with respect to the centre of the twisted wave front. In order to explore such a dependence, detailed calculations were carried out for the photoionization of the 1s ground and 2 py excited states of neutral hydrogen atoms. Based on these calculations, we argue that for relatively small impact parameters the electron angular distributions may be strongly affected by altering the position of the atom within the wave front. In contrast, if the atom is placed far from the front centre, the emission pattern of the electrons is independent on the impact parameter b and resembles that observed in the photoionization by plane wave photons.