Application of Radiative Electron Capture for the Diagnostics of Spin-Polarized Ion Beams at Storage Rings

It is proposed to apply the radiative electron capture into high-$Z$ projectiles as a probe process for measuring the spin polarization of the hydrogenlike ions at storage rings. We argue that such polarization measurements are possible since the linear polarization of emitted x-ray photons is greatly sensitive to the spin states of incoming ions with nuclear spin $I>1/2$. In particular, for $K$-shell electron capture into the hydrogenlike ions, the linear polarization of light as measured out of the reaction plane is found to be proportional to the degree of ion polarization. Detailed computations for the dependence of the photon polarization on the ion spin states and projectile energies are carried out for the electron recombination into hydrogenlike ${\mathrm{Bi}}^{82+}$ ions.

Figure 1

The Stokes parameters $P_1$ and $P_2$ of the recombination photons which are emitted in the electron capture into the $K$ shell of hydrogenlike bismuth ions with projectile energy $T_p=420\mathrm{MeV}/\mathrm{u}$. The Stokes parameter $P_2$ is shown for four degrees of ion polarization: ${\lambda }_F=1$ (solid line), ${\lambda }_F=0.7$ (dashed line), ${\lambda }_F=0.3$ (dash-dotted line), and ${\lambda }_F=0.0$ (dotted line). The Stokes parameter $P_1$ (solid line) is independent of the ion polarization. Calculations are presented in the laboratory frame (i.e., rest frame of the electron target).

Figure 2

Definition of the polarization ellipse; its principal axis is characterized by ${\chi }_0$, the angle with respect to the reaction plane which is formed by the directions of incoming ion beam and emitted photons.

Figure 3

Rotation angle ${\chi }_0$ of the polarization ellipse (top row) and the Stokes parameters (middle row) of the emitted photons following the capture of unpolarized electrons into the $K$ shell of hydrogenlike bismuth ions. In the bottom row, the REC angle-differential cross sections are shown. Calculations are presented for completely polarized projectile ions (${\lambda }_F=1$) and in the laboratory frame.