Radiative electron capture into high-$Z$ few-electron ions: Alignment of the excited ionic states

We lay out a unified formalism for the description of radiative electron capture into excited states of heavy, few-electron ions and their subsequent decay, including a full account of many-electron effects and higher-order multipoles of the radiation field. In particular, the density-matrix theory is applied to explore the magnetic sublevel population of the residual ions, as described in terms of alignment parameters. For the electron capture into the initially hydrogenlike ${\mathrm{U}}^{91+}$ and lithiumlike ${\mathrm{U}}^{89+}$ uranium projectiles, the alignment parameters are calculated, within the multiconfiguration Dirac-Fock approach, as a function of the collision energy and for different ionic states. From these calculations, we find that the many-electron interactions may result in a small enhancement of the alignment, and that this effect becomes more pronounced for highly excited levels.

Figure 1

Alignment parameters ${\mathcal{A}}_{20}$ of the $2p_{3∕2}$ state of hydrogenlike (left panel) and the $1s2p_{3∕2}J=1,2$ states of heliumlike (right panel) ions following the radiative electron capture of uranium projectiles. The results of MCDF calculations in Coulomb and Babushkin gauges yield consistent results which are plotted as a single curve.

Figure 2

Alignment parameters ${\mathcal{A}}_{20}$ of the $3d_{3∕2}$ state of hydrogenlike (left panel) and the $1s^{2}2s3d_{3∕2}J=1,2$, states of berylliumlike (right panel) ions following the radiative electron capture into uranium projectiles. Again, the results of MCDF calculations in Coulomb and Babushkin gauges yield consistent results which are plotted as a single curve.

Figure 3

Alignment parameter ${\mathcal{A}}_{40}$ of the $1s^{2}2s_{1∕2}3d_{3∕2}{}^{3}D_{J=2}$ state following the radiative electron capture of (initially) lithiumlike uranium ions ${\mathrm{U}}^{89+}$ (finally berylliumlike). For the corresponding capture into the $3d_{3∕2}$ state of initially bare uranium, the alignment parameter ${\mathcal{A}}_{40}$ identically vanishes. Results from MCDF calculations are shown in Coulomb (dotted line) and Babushkin gauges (dashed line).

Figure 4

Alignment parameters ${\mathcal{A}}_{20}$ and ${\mathcal{A}}_{40}$ of the $3d_{5∕2}$ state of hydrogenlike (left panels) and the $1s^{2}2s_{1∕2}3d_{5∕2}{}^{1,3}D_{J=2,3}$ states of berylliumlike (right panels) ions following the radiative electron capture into uranium projectiles. Results from MCDF calculations are shown in Coulomb (dotted line) and Babushkin gauges (dashed line).

Figure 5

Angular distribution of the $1s^{2}2s_{1∕2}3d_{3∕2}{}^{3}D_{J=2}\to 1s^{2}2s_{1∕2}2p_{3∕2}{}^{1}P_{J=1}$ decay following REC into the (initially) lithiumlike projectile ions with energies $T_p=10\mathrm{MeV}∕u$ (left panel), $T_p=200\mathrm{MeV}∕u$ (middle panel), and $T_p=400\mathrm{MeV}∕u$ (right panel). Results are presented within the laboratory frame for the exact relativistic theory (solid line) and the electric dipole approximation (dashed line). Following the experimental technique applied in Ref. 21, the angular distribution is normalized to the intensity of the isotropic Lyman-${\alpha }_2$ radiation in hydrogen like ${\mathrm{U}}^{91+}$ ions.

Figure 6

Angular distribution of the $1s^{2}2s_{1∕2}3d_{3∕2}{}^{3}D_{J=2}\to 1s^{2}2s_{1∕2}3s_{1∕2}{}^{3}S_{J=1}$ decay following REC into the (initially) lithiumlike projectile ions with energies $T_p=10\mathrm{MeV}∕u$ (left panel), $T_p=200\mathrm{MeV}∕u$ (middle panel), and $T_p=400\mathrm{MeV}∕u$ (right panel). Results are presented within the laboratory frame for the exact relativistic theory (solid line) and the magnetic dipole approximation (dashed line). Following the experimental technique applied in Ref. 21, the angular distribution is normalized to the intensity of the isotropic Lyman-${\alpha }_2$ radiation in hydrogenlike ${\mathrm{U}}^{91+}$ ions.