Hyperfine-induced effects on the linear polarization of the magnetic-quadrupole lines of spin-1/2 Be-like ions excited by electron impact

The linear polarization of magnetic-quadrupole emission lines 1s22s2p3/23P2→1s22s21S0 and 1s2s22p3/23P2→1s22s21S0 following electron-impact excitation of Be-like ions with nuclear spin I=1/2 is studied by employing the density-matrix theory and the relativistic distorted-wave theory. To explore the effects of the hyperfine interaction, detailed calculations are performed for the polarization of the magnetic-quadrupole lines emitted from AXe50+ (A = 125, 127, and 129) and ATl77+ (A = 187, 205, and 207) ions with different nuclear magnetic dipole moments μI at a series of impact electron energies. It is shown that the hyperfine interaction strongly lowers the polarization of the 1s22s2p3/23P2→1S0 line at all considered impact energies, while its effects behave less and less prominent with increasing impact energy for the 1s2s22p3/23P2→1S0 line. In addition, we also find that the polarization of the 1s22s2p3/23P2→1S0 line is much more sensitive to μI than that of the 1s2s22p3/23P2→1S0 line. In particular, for the 1s22s2p3/23P2→1S0 line of spin-1/2 Xe50+ ions, the differences in the polarization among the isotopes are significant. These findings indicate that precise polarization measurements of magnetic-quadrupole lines of Be-like ions are expected to be used for exploring the hyperfine interaction and even the nuclear magnetic dipole moment of nonzero-spin isotopes.