Hyperfine-induced effects on the Kα1 angular distribution following electron-impact excitation of heliumlike spin- 1/2 Tl79+ ions

Abstract

Angular distribution of the $K{\ensuremath{\alpha}}_{1}$ $(1s2p\phantom{\rule{0.16em}{0ex}}^{1,3}P_{1,2}\ensuremath{\rightarrow}1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0})$ emission line following electron-impact excitation of heliumlike spin-1/2 ${\mathrm{Tl}}^{79+}$ ions is studied within the framework of the density-matrix theory and the relativistic distorted-wave theory. In particular, we aim to explore how a (nonzero) nuclear magnetic dipole moment ${\ensuremath{\mu}}_{I}$ affects the $K{\ensuremath{\alpha}}_{1}$ angular distribution due to the hyperfine interactions. To this end, detailed calculations are performed for selected spin-1/2 $_{81}^{A}\mathrm{Tl}^{79+}$ ($A=187$, 205, and 207) ions with large ${\ensuremath{\mu}}_{I}$. It is found that the hyperfine-induced effects on the $K{\ensuremath{\alpha}}_{1}$ angular distribution depend strongly on the impact electron energy. When compared with the case of zero-spin ${\mathrm{Tl}}^{79+}$ ions, the $K{\ensuremath{\alpha}}_{1}$ angular distribution becomes much more anisotropic for low impact energies, whereas this anisotropy decreases quickly at intermediate and high impact energies. Such a behavior is in sharp contrast to the results for the fine-structure-resolved $1s2p\phantom{\rule{0.16em}{0ex}}^{3}P_{2}\ensuremath{\rightarrow}1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$ component [Phys. Rev. A 102, 042813 (2020)]. Therefore, accurate $K{\ensuremath{\alpha}}_{1}$ angular measurements at low impact electron energies could be employed as a sensitive tool to probe the hyperfine interaction in highly charged few-electron ions.