In this paper, we report our calculations of the triple-differential cross section (TDCS) for the relativistic $(e,2e)$ process with a twisted electron beam on Cu and Ag atomic targets in coplanar asymmetric geometry mode. The theoretical formalism has been developed in the first Born approximation, in which we use the Dirac plane wave as well as the twisted electron wave for the incident electron beam to study the effect of various parameters of the twisted electron beam on the $(e,2e)$ process. We use a Dirac plane-wave function, semirelativistic Coulomb wave function, and Darwin wave function for the scattered, ejected, and K-shell electron, respectively. We compare the angular profiles of the TDCS of the twisted electron impact $(e,2e)$ process with that of the plane wave. We segregate the TDCS for charge-charge interaction and current-current interaction with their interference term and study the effect of different parameters of the twisted electron beam on them. The study is also extended to the macroscopic Cu and Ag targets to further investigate the effect of the opening angle of the twisted electron beam on TDCS. The spin asymmetry in TDCS caused by the polarized incident electron beam is also studied to elucidate the effects of the twisted electron beam on the $(e,2e)$ process.

• Received 3 July 2021
• Accepted 26 October 2021

DOI:https://doi.org/10.1103/PhysRevA.104.052818