Shape of the cross section for electron ionization of laser-excited atoms

Abstract

Nixon and Murray [K. L. Nixon and A. J. Murray, Phys. Rev. Lett. 112, 023202 (2014)] have measured electron ionization of the $3 {}^{1}{P}_{1}$ state of $^{24}\mathrm{Mg}$. which was excited from the ground state by linearly polarized laser radiation. The direction of laser polarization was parallel to the scattering plane and based on their measurements, they proposed a functional form for the differential cross section as a function of the angle that the polarization direction makes with the incident electron beam. We show that this proposed functional form is exact and express the parameters of this form in terms of the $T$-matrix elements for ionization calculated in the scattering frame. We also show that this form occurs for radiation linearly polarized in an arbitrary direction. Furthermore, we similarly treat the case of excitation by circularly polarized light where a more complex shape is obtained, though this reduces to the form for linearly polarized radiation for ionization in the coplanar geometry. Using the measured results from Nixon and Murray, we calculate the ratio of the magnitudes of the $T$-matrix elements as well as the difference in their phases.