Physical Review A

Inelastic Raman scattering of light by hydrogenlike ions

Thorsten Jahrsetz, S. Fritzsche, A. Surzhykov

Published Apr 7, 2014• 7 citations

Abstract

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 $1{s}_{1/2}\ensuremath{\rightarrow}2{s}_{1/2}$, $1{s}_{1/2}\ensuremath{\rightarrow}2{p}_{1/2}$, and $1{s}_{1/2}\ensuremath{\rightarrow}2{p}_{3/2}$ 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.

DOI: 10.1103/physreva.89.042501

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Physical Review A

Inelastic Raman scattering of light by hydrogenlike ions

Thorsten Jahrsetz, S. Fritzsche, A. Surzhykov

Published Apr 7, 2014• 7 citations

Publisher

Abstract

1{s}_{1/2}\ensuremath{\rightarrow}2{s}_{1/2}

1{s}_{1/2}\ensuremath{\rightarrow}2{p}_{1/2}

, and

1{s}_{1/2}\ensuremath{\rightarrow}2{p}_{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.

DOI: 10.1103/physreva.89.042501

Related papers

Angular correlations in the two-photon decay of hydrogenlike ions: Relativistic Green’s-function approach

A. Surzhykov, Peter Koval, S. Fritzsche

The angular correlations in the two-photon decay of hydrogenlike ions are studied within the framework of second-order perturbation theory, based on Dirac's equation. Particular attention has been paid to the effects which arise from the higher (nondipole) terms in the expansion of the electron-photon interaction. It is shown that the photon-photon angular correlation function, which is found symmetric with respect to the angle $\ensuremath{\theta}=90\ifmmode^\circ\else\textdegree\fi{}$ in the electric dipole approximation, becomes asymmetric because of the nondipole contributions, and that this effect is enhanced as the nuclear charge $Z$ increases. Detailed computations on the photon-photon angular distribution have been carried out for the $2{s}_{1∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ and $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transitions in neutral hydrogen (H) as well as for hydrogenlike xenon $({\mathrm{Xe}}^{53+})$ and uranium $({\mathrm{U}}^{91+})$ ions, and are compared with previous nonrelativistic results by Au [Phys. Rev. A 14, 531 (1976)]).The angular correlations in the two-photon decay of hydrogenlike ions are studied within the framework of second-order perturbation theory, based on Dirac's equation. Particular attention has been paid to the effects which arise from the higher (nondipole) terms in the expansion of the electron-photon interaction. It is shown that the photon-photon angular correlation function, which is found symmetric with respect to the angle $\ensuremath{\theta}=90\ifmmode^\circ\else\textdegree\fi{}$ in the electric dipole approximation, becomes asymmetric because of the nondipole contributions, and that this effect is enhanced as the nuclear charge $Z$ increases. Detailed computations on the photon-photon angular distribution have been carried out for the $2{s}_{1∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ and $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transitions in neutral hydrogen (H) as well as for hydrogenlike xenon $({\mathrm{Xe}}^{53+})$ and uranium $({\mathrm{U}}^{91+})$ ions, and are compared with previous nonrelativistic results by Au [Phys. Rev. A 14, 531 (1976)]).

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arXiv:0908.2498Physical Review ANov 30, 200918 citations

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Lesya Borowska, A. Surzhykov, Th. Stöhlker +1 more

The two-photon decay of highly charged hydrogenlike ions is studied within the framework of second-order perturbation theory, based on Dirac's equation. Attention has been paid to the angle-angle correlations between the two emitted photons. In particular, the density matrix theory is applied in order to explore how these angle-angle correlations are affected by the alignment of the excited states of the ions. Detailed computations have been carried out for the $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transition in hydrogenlike uranium ${\mathrm{U}}^{91+}$ ions for different (degrees of) initial alignment. It is shown that the angular correlation function is very sensitive to the alignment of the $3{d}_{5∕2}$ state, an effect which has to be accounted for in the analysis of all (future) two-photon decay experiments, for which the excited state of the ions is produced by relativistic ion-atom collisions.The two-photon decay of highly charged hydrogenlike ions is studied within the framework of second-order perturbation theory, based on Dirac's equation. Attention has been paid to the angle-angle correlations between the two emitted photons. In particular, the density matrix theory is applied in order to explore how these angle-angle correlations are affected by the alignment of the excited states of the ions. Detailed computations have been carried out for the $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transition in hydrogenlike uranium ${\mathrm{U}}^{91+}$ ions for different (degrees of) initial alignment. It is shown that the angular correlation function is very sensitive to the alignment of the $3{d}_{5∕2}$ state, an effect which has to be accounted for in the analysis of all (future) two-photon decay experiments, for which the excited state of the ions is produced by relativistic ion-atom collisions.

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L. Safari, Pedro Manuel Duarte Gonçalves Amaro, José Paulo Santos +1 more

The amplitude of two-photon transitions between hyperfine states in hydrogenlike ions is derived based on the relativistic Dirac equation and second-order perturbation theory. We study angular and linear polarization properties of the photon pair emitted in the decay of $2s$ states, where spin-flip and non-spin-flip transitions are highlighted. We pay particular attention to hydrogenlike uranium, since it is an ideal candidate for investigating relativistic and high-multipole effects, such as spin-flip transitions. Two types of emission patterns are identified: (i) non-spin-flip transitions are found to be characterized by an angular distribution of the type $W(\ensuremath{\theta})\ensuremath{\sim}1+{cos}^{2}\ensuremath{\theta}$ while the polarizations of the emitted photons are parallel; and (ii) spin-flip transitions have somewhat smaller decay rates and are found to be characterized by an angular distribution of the type $W(\ensuremath{\theta})\ensuremath{\sim}1\ensuremath{-}1/3{cos}^{2}\ensuremath{\theta}$ while the polarizations of the emitted photons are orthogonal, where $\ensuremath{\theta}$ is the angle between photons directions. Deviations due to nondipole and relativistic contributions are evaluated for both types of transitions. This work is the first step toward exploring the effect of the nucleus over the angular and polarization properties of the photon pairs emitted by two-photon transitions.The amplitude of two-photon transitions between hyperfine states in hydrogenlike ions is derived based on the relativistic Dirac equation and second-order perturbation theory. We study angular and linear polarization properties of the photon pair emitted in the decay of $2s$ states, where spin-flip and non-spin-flip transitions are highlighted. We pay particular attention to hydrogenlike uranium, since it is an ideal candidate for investigating relativistic and high-multipole effects, such as spin-flip transitions. Two types of emission patterns are identified: (i) non-spin-flip transitions are found to be characterized by an angular distribution of the type $W(\ensuremath{\theta})\ensuremath{\sim}1+{cos}^{2}\ensuremath{\theta}$ while the polarizations of the emitted photons are parallel; and (ii) spin-flip transitions have somewhat smaller decay rates and are found to be characterized by an angular distribution of the type $W(\ensuremath{\theta})\ensuremath{\sim}1\ensuremath{-}1/3{cos}^{2}\ensuremath{\theta}$ while the polarizations of the emitted photons are orthogonal, where $\ensuremath{\theta}$ is the angle between photons directions. Deviations due to nondipole and relativistic contributions are evaluated for both types of transitions. This work is the first step toward exploring the effect of the nucleus over the angular and polarization properties of the photon pairs emitted by two-photon transitions.

arXiv:1407.4063Physical Review AJul 29, 20149 citations

1{s}_{1/2}\ensuremath{\rightarrow}2{s}_{1/2}

1{s}_{1/2}\ensuremath{\rightarrow}2{p}_{1/2}

, and

1{s}_{1/2}\ensuremath{\rightarrow}2{p}_{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.

Z

increases. Detailed computations on the photon-photon angular distribution have been carried out for the $2{s}_{1∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ and $3{d}_{5∕2}\ensuremath{\rightarrow}1{s}_{1∕2}$ transitions in neutral hydrogen (H) as well as for hydrogenlike xenon

({\mathrm{Xe}}^{53+})

and uranium

({\mathrm{U}}^{91+})

ions, and are compared with previous nonrelativistic results by Au [Phys. Rev. A 14, 531 (1976)]).

{\text{Xe}}^{53+}

and uranium

{\text{U}}^{91+}

ions. We found that for a correct evaluation of the total and energy-differential decay rates, summation over the negative-energy part of Dirac's spectrum should be properly taken into account both for high-

Z

and low-

Z

atomic systems.

{\mathrm{U}}^{91+}

ions for different (degrees of) initial alignment. It is shown that the angular correlation function is very sensitive to the alignment of the

3{d}_{5∕2}

state, an effect which has to be accounted for in the analysis of all (future) two-photon decay experiments, for which the excited state of the ions is produced by relativistic ion-atom collisions.

2s

states, where spin-flip and non-spin-flip transitions are highlighted. We pay particular attention to hydrogenlike uranium, since it is an ideal candidate for investigating relativistic and high-multipole effects, such as spin-flip transitions. Two types of emission patterns are identified: (i) non-spin-flip transitions are found to be characterized by an angular distribution of the type $W(\ensuremath{\theta})\ensuremath{\sim}1+{cos}^{2}\ensuremath{\theta}$ while the polarizations of the emitted photons are parallel; and (ii) spin-flip transitions have somewhat smaller decay rates and are found to be characterized by an angular distribution of the type $W(\ensuremath{\theta})\ensuremath{\sim}1\ensuremath{-}1/3{cos}^{2}\ensuremath{\theta}$ while the polarizations of the emitted photons are orthogonal, where $\ensuremath{\theta}$ is the angle between photons directions. Deviations due to nondipole and relativistic contributions are evaluated for both types of transitions. This work is the first step toward exploring the effect of the nucleus over the angular and polarization properties of the photon pairs emitted by two-photon transitions.