Inelastic scattering of vortex electrons beyond the Born approximation

Abstract We present a theoretical study of the inelastic scattering of vortex electrons by a hydrogen atom. In our study, special emphasis is placed on the effects of the Coulomb interaction between a projectile electron and a target atom. To understand these effects, we construct vortex electron wave functions both from free space and distorted solutions of the Schrödinger equation. These wave functions give rise to the first Born and distorted wave scattering amplitudes, respectively. The derived theory has been employed to investigate the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mi>s</mml:mi> <mml:mo stretchy="false">→</mml:mo> <mml:mn>2</mml:mn> <mml:mi>p</mml:mi> </mml:mrow> </mml:math> transition of a hydrogen atom induced by electrons with the kinetic energies in the range from 20 to 100 eV. The results of the calculations have clearly indicated that the Coulomb interaction can significantly affect the phase pattern and probability density of a vortex electron beam as well as the squared transition amplitudes. For the latter, the most pronounced effect was found for the excitation to the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mo fence="false" stretchy="false">|</mml:mo> <mml:mn>2</mml:mn> <mml:mi>p</mml:mi> <mml:mstyle scriptlevel="0"/> <mml:msub> <mml:mi>m</mml:mi> <mml:mi>f</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> <mml:mo fence="false" stretchy="false">⟩</mml:mo> </mml:mrow> </mml:math> sublevel and large scattering angles.