We present a theoretical investigation of the resonant elastic scattering of twisted light, carrying angular momentum, by partially stripped ions. Special emphasis is placed on a question of whether the scattered radiation is also twisted. In order to investigate such an "angular momentum transfer,"we develop an approach that allows us to find a quantum state of the final photon without projecting it onto a detector state. A general expression for this so-called evolved state of outgoing radiation is derived, and it can be used to analyze the resonant scattering by any ion, independently of its shell structure. Here we illustrate our approach with the strong electric dipole nS0→n′P1→nS0 transitions, which play an important role for the Gamma Factory project at CERN. For the incident Bessel light, the scattered radiation is shown to be in a superposition of twisted modes with the projections of the total angular momentum mf=0,±1. The larger values of mf can be efficiently generated by inducing transitions of higher multiplicity. This angular momentum transfer, together with a remarkable cross section that is many orders of magnitude larger than that of the backward Compton scattering, makes the resonant photon scattering an effective tool for the production of twisted x rays and even γ rays at the Gamma Factory facility.
- 1.03 PHYSICAL SCIENCES AND ASTRONOMY
- 1.03.SY OPTICS