Hyperfine-induced effects on angular emission of the magnetic-quadrupole line 1 s 2 p 3 / 2 P 2 3 → 1 s 2 S 0 1 following electron-impact excitation of Tl 79 + ions

The electron-impact excitation from the ground state to the excited $1s2{p}_{3/2}$ $^{3}P_{2}$ energy level and the subsequent magnetic-quadrupole radiative decay $1s2{p}_{3/2}\phantom{\rule{0.16em}{0ex}}^{3}P_{2}\ensuremath{\rightarrow}1{s}^{2}\phantom{\rule{0.16em}{0ex}}^{1}S_{0}$ of heliumlike ${\mathrm{Tl}}^{79+}$ ions with nuclear spin $I=1/2$ have been investigated by employing the multiconfigurational Dirac-Fock method and the relativistic distorted-wave theory. Special attention has been paid to the effects of the hyperfine interaction on the angular distribution of the emitted magnetic-quadrupole line. To this end, we considered heliumlike spin-1/2 $_{81}^{187}\mathrm{Tl}^{79+}$, $_{81}^{205}\mathrm{Tl}^{79+}$, and $_{81}^{207}\mathrm{Tl}^{79+}$ ions with rather large nuclear magnetic dipole moment ${\ensuremath{\mu}}_{I}$. It is found that the hyperfine interaction lowers significantly the anisotropy of the angular distribution of the magnetic-quadrupole line emitted from these spin-1/2 ions for all considered impact electron energies, compared with the results for ${\mathrm{Tl}}^{79+}$ ions with zero nuclear spin. In particular, the angular distribution becomes first less and less anisotropic as the impact energy increases up to about 4.4 times the excitation threshold, for which it becomes fully isotropic. For even higher impact energies, the angular distribution becomes again anisotropic, although with inverse emission pattern. We also find that the angular distribution is quite sensitive to the magnetic moment ${\ensuremath{\mu}}_{I}$ with a more isotropic distribution for spin-1/2 ions with larger ${\ensuremath{\mu}}_{I}$. This ${\ensuremath{\mu}}_{I}$ sensitivity of the angular distribution may therefore (help) probe important information about the nuclear magnetic dipole moment of spin-1/2 isotopes.