Hyperfine-induced effects on the Kα1 angular distribution following electron-impact excitation of heliumlike spin- 1/2 Tl<

Hyperfine-induced effects on Kα1 linear polarization following electron-impact excitation of heliumlike Tl79+ ions with nuclear spin I=1/2

“…For this purpose, we take heliumlike spin-1/2 207 81 Tl 79+ ions as an example and detailed calculations are performed with the use of the multi-configurational Dirac-Fock (MCDF) method and the relativistic distorted-wave (RDW) theory. Similar to the results for the angular distribution of the Kα 1 line [48], the hyperfine-induced effect upon its linear polarization is found to be dependent dominantly on the impact electron energy. In contrast to the results for zero-spin Tl 79+ ions, the hyperfine interaction makes the Kα 1 line of the 207 81 Tl 79+ ions more polarized at low impact energies, especially for the photons radiated perpendicularly to the impact electron beam, while such an effect vanishes at medium and high energies.…”

“…It was discovered that the linear polarization is enhanced by the interference between the leading M2 and hyperfine-induced electric-dipole (E1) decay channels of the hyperfine-resolved 1s2p 3 P 2 , F i = 3/2 → 1s 2 1 S 0 , F f = 1/2 transition. Just very recently, we investigated the angular distribution of both the M2 and Kα 1 (1s2p 1,3 P 1,2 → 1s 2 1 S 0 ) lines following the same EIE of heliumlike spin-1/2 Tl 79+ ions [47,48]. The hyperfine-induced effect on the angular distribution was found to be very different from the results obtained for the Kα 1 line populated by REC of initially hydrogenlike ions [49][50][51].…”

“…P 2 (cos θ) is the second-order Legendre polynomial. Note that the angular distribution W hf E1 (θ) of the E1 component 1s2p 1 P 1 → 1s 2 1 S 0 remains the same as for zero-spin Tl 79+ ions [48,51], whereas the one W hf M2 (θ) of the M2 component 1s2p 3 P 2 → 1s 2 1 S 0 depends upon the reduced hyperfine amplitudes a hf E1 (µ I ) and a M2 . With P hf E1 (θ) and P hf M2 (θ) ready, the linear polarization P hf Kα1 (θ) of the Kα 1 line can be given by a weighted sum over both of them as follows,…”

“…To obtain the linear polarization P hf Kα1 (θ) of the Kα 1 line, both the angular distributions W hf E1 (θ) and W hf M2 (θ) of the fine-structure components 1s2p 1 P 1 → 1s 2 1 S 0 and 1s2p 3 P 2 → 1s 2 1 S 0 are also required. As these two angular distributions have been derived in detail in our previous work [48], here we just present their explicit expressions for reference,…”

“…In the past decades and especially after the first polarization measurements for x-ray lines of heliumlike Sc 19+ ions [41], which demonstrated that high-precision polarization measurements can be used to study the hyperfine interaction in highly charged ions, many studies were performed for exploring hyperfine-induced effects on angular and polarization properties of x-ray lines [42][43][44][45][46][47][48][49][50][51][52]. For example, Inal et al investigated the circular polarization of x-ray lines of Sc 19+ ions excited by impact with polarized electrons and found that it is drastically reduced due to the hyperfine interaction [43].…”