Angle-resolved x-ray spectroscopic scheme to determine overlapping hyperfine splittings in highly charged heliumlike ions

An angle-resolved x-ray spectroscopic scheme is presented for determining the hyperfine splitting of highly charged ions. For heliumlike ions, in particular, we propose to measure either the angular distribution or polarization of the $1s2p{}^{3}P_1,F\to 1s^2{}^{1}S_0,F_f$ emission following the stimulated decay of the initial $1s2s{}^{1}S_0,F_i$ level. It is found that both the angular and polarization characteristics of the emitted x-ray photons strongly depend on the (relative) splitting of the partially overlapping hyperfine $1s2p{}^{3}P_1,F$ resonances and may thus help resolve their hyperfine structure. The proposed scheme is feasible with present-day photon detectors and allows a measurement of the hyperfine splitting of heliumlike ions with a relative accuracy of about ${10}^{-4}$.

Figure 1

Schema (left panel) and geometry (right panel) for measuring the two-step radiative decay (1) of heliumlike ${}^{71}\mathrm{Ga}^{29+}$ ions. While the first-step decay is stimulated by laser photons ${\gamma }_1$ with energy $\hslash {\omega }_1$, the fast subsequent spontaneous decay to the $1s^2{}^{1}S_0,F_f$ ground level gives rise to an emission of the ${\gamma }_2$ fluorescence photons. As distinguished in black solid and gray dashed lines, the angular distribution and polarization of the ${\gamma }_2$ photons depend sensitively on the hyperfine constant of the intermediate levels.

Figure 2

Anisotropy parameter $\beta$ (left panel) and degree of linear polarization $P_1$ (right panel) of the hyperfine $1s2p{}^{3}P_1,F=1/2,3/2,5/2\to 1s^2{}^{1}S_0,F_f=3/2$ fluorescence emission from heliumlike ${}^{71}\mathrm{Ga}^{29+}$ ions as functions of photon energy $\hslash {\omega }_1$ of the incident photons ${\gamma }_1$. Results are shown for the calculated hyperfine constant $A_J=0.0274$ eV (black solid lines) as listed in Table 1 as well as for two assumed values, $0.8A_J$ (red dash-dotted lines) and $1.2A_J$ (blue dash-dot-dotted lines), which differ by just 20%.

Figure 3

Same as in Fig. 2 but for ${}^{141}\mathrm{Pr}^{57+}$ (left panel) and ${}^{209}\mathrm{Bi}^{81+}$ (right panel) ions.