Radiative recombination into high-$Z$ few-electron ions: Cross sections and angular distributions

The radiative electron capture into high-$Z$, few-electron ions is studies in the framework of the density matrix, based on Dirac’s equation. In this formalism, all the properties of the photons and the (remaining) ions can be described, independent from their initial shell structure or polarization. Detailed computations have first been carried out for the total and angle-differential cross sections, following the capture of an electron into hydrogen-${\mathrm{U}}^{91+}$ and lithiumlike ${\mathrm{U}}^{89+}$ ions. From these calculations, which were performed in two different approximations, it is shown that many-electron interactions affect the angular distribution at low projectile energies by about 5%. Apart from describing the (angular-dependent) capture cross sections, our formalism is also appropriate to explore the subsequent $K\alpha ,\beta$ photon emission, if the electron is captured into an excited state of the ion, the polarization of the photons and ions as well as the interplay of the radiative with other, nonradiative capture processes in the future.

Figure 1

(Color online) The unit vector $\mathbf{u}\left(\chi \right)$ of the linear polarization is defined in the plane, which perpendicular to the photon momentum $\mathbf{k}$, and is characterized by an angle $\chi$ with respect to the reaction plane.

Figure 2

(Color online) Angle-differential cross sections for the radiative electron capture into the $1s^2{}^{1}S_0$ ground state of (initially) hydrogenlike uranium ions ${\mathrm{U}}^{91+}$ with projectile energies $T_p=2.18$, 21.8, and $218\mathrm{MeV}∕u$. Results are presented for an effective one-particle model with $Z_{\mathrm{eff}}=92$ (– – –) and for the MCDF method (—) using Babushkin gauge.

Figure 3

(Color online) Angle-differential cross sections for the radiative electron capture into the $1s^{2}2s^2$ state of (initially) lithiumlike uranium ions ${\mathrm{U}}^{89+}$ with projectile energies of 2.18, 21.8, and $218\mathrm{MeV}∕u$. Results from an independent particle model with an effective charge $Z_{\mathrm{eff}}=91$. (– – –) are compared with those from MCDF calculations in Coulomb (—) and Babushkin gauge (– –).

Figure 4

(Color online) Angle-differential cross sections for the radiative electron capture into the $1s^{2}2s2p_{3∕2}$ states of (initially) lithiumlike uranium ions ${\mathrm{U}}^{89+}$ with projectile energies of 2.18, 21.8, and $218\mathrm{MeV}∕u$. Results from MCDF calculations are shown in Coulomb (—) and Babushkin gauge (– –).

Figure 5

(Color online) Angle-differential cross sections for the radiative electron capture into the $1s^{2}2s3s$ states of (initially) lithiumlike uranium ions ${\mathrm{U}}^{89+}$ with projectile energies of 2.18, 21.8, and $218\mathrm{MeV}∕u$. Results from MCDF calculations are shown in Coulomb (—) and Babushkin gauge (– –).