Inelastic Raman scattering of light by hydrogenlike ions

The inelastic Raman scattering of light by hydrogenlike ions has been studied by means of second-order perturbation theory and the relativistic Coulomb Green's-function approach. In particular, we investigate the total and angle-differential Raman cross sections as well as the magnetic sublevel population of the residual (excited) ions. Detailed calculations are performed for the inelastic scattering of photons by neutral hydrogen as well as hydrogenlike xenon and uranium ions, accompanied by the $1s_{1/2}\to 2s_{1/2}$, $1s_{1/2}\to 2p_{1/2}$, and $1s_{1/2}\to 2p_{3/2}$ transitions. Moreover, we discuss how the Raman scattering is affected by relativistic and resonance effects as well as the higher-multipole contributions to the electron-photon interaction.

Figure 1

Total cross section (10) for the inelastic Raman scattering of photons on neutral hydrogen as well as hydrogenlike xenon and uranium ions. Results are shown as a function of the incident photon energy ${\omega }_1$ in units of the $|E_{1s}|$ ionization threshold of the ions. Relativistic calculations were performed for the excitation of the targets from their ground state to the $2s_{1/2}$ (black solid line), $2p_{1/2}$ (red dash-dotted line), and $2p_{3/2}$ (green dashed line) levels. Moreover, the nonrelativistic predictions by Sadeghpour and Dalgarno [5] and Zon et al. [6], obtained for the $1s\to 2s$ scattering, are also displayed by closed circles and orange dotted lines, respectively. Positions of the intermediate-state resonances are marked by the vertical dotted lines.

Figure 2

Angle-differential cross section (9) for the inelastic Raman scattering of unpolarized photons by neutral hydrogen (top panels), hydrogenlike xenon (middle panels), and hydrogenlike uranium (bottom panels) ions. Results are displayed for the $1s_{1/2}\to 2s_{1/2}$ (left column), $1s_{1/2}\to 2p_{1/2}$ (middle column), and $1s_{1/2}\to 2p_{3/2}$ (right column) transitions of the ions and for the photon energy ${\omega }_1=0.825\left|E_{1s}\right|$, well below the ionization threshold. Calculations within the leading $E1E1$ approximation for excitations into the $2s_{1/2}$ level and the $E1M1$-$E1E2$ approximation for the $2p_{1/2,3/2}$ levels (dashed line) are compared with those including all of the allowed multipoles (solid line).

Figure 3

Angle-differential cross section (9) for the inelastic Raman scattering of unpolarized photons by hydrogenlike uranium U${}^{91+}$ ions. Results are shown for the $1s_{1/2}\to 2s_{1/2}$ (left column) and $1s_{1/2}\to 2p_{1/2}$ (right column) transitions of the ions and for the photon energies just below and above the $3s_{1/2},3p_{1/2}$ resonances at ${\omega }_1/E_{1s}\simeq 0.8891$, the threshold for the $1s_{1/2}+{\gamma }_1\to 3s_{1/2}/3p_{1/2}\to n_f{j}_f+{\gamma }_2$ scattering.

Figure 4

Alignment $A_{20}$ of the $2p_{3/2}$ state of neutral hydrogen as well as hydrogenlike xenon and uranium ions following the inelastic Raman scattering of unpolarized photons. Calculations, performed within the leading-order approximation $E1M1$ and $E1E2$, are displayed by dashed lines and are compared with those including all of the allowed multipoles (solid lines).