# Angular Distribution of Characteristic Radiation Following the Excitation of He-Like Uranium in Relativistic Collisions

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## Abstract

**:**

## 1. Introduction

## 2. Experiment

## 3. Results and Discussion

#### 3.1. Experimental Data and Evaluation

#### 3.2. Theoretical Background

#### 3.3. Comparison with Theory

## 4. Summary

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**X-ray spectrum recorded for 218 MeV/u U${}^{90+}$→H${}_{2}$ collisions with a Ge(i) detector at the observation angle of 35${}^{\circ}$ with respect to the ion beam. The radiative electron capture (REC) transitions into L, M and higher shells are clearly visible together with the characteristic transitions into the K-shell.

**Figure 2.**K- and L-shell levels of He-like uranium along with the transitions contributing to the observed K${\alpha}_{1}$ and K${\alpha}_{2}$ lines.

**Figure 3.**Angular distributions of K${\alpha}_{2}$ line intensity measured for K-shell excitation of He-like uranium in collisions with argon (

**left**) and hydrogen (

**right**) targets at 218 MeV/u. In addition, fits of Equation (1) to the experimental data are shown by solid lines. The clear change of shape between the two targets is due to the contribution of the electron-impact excitation (EIE) process. For details see text.

**Table 1.**Theoretical values for the alignment parameters ${A}_{2}$, the relative populations N, and the resulting effective anisotropy parameters ${\beta}_{2}^{eff}$ for ${[1{s}_{1/2},2{p}_{3/2}]}^{1}{P}_{1}$ and ${[1{s}_{1/2},2{p}_{3/2}]}^{3}{P}_{2}$ states contributing to the K${\alpha}_{1}$ line. For details see text.

Beam Energy | Process | ${\mathit{A}}_{2}{(}^{1}{\mathit{P}}_{1})$ | $\mathit{N}{(}^{1}{\mathit{P}}_{1})$ | ${\mathit{A}}_{2}{(}^{3}{\mathit{P}}_{2})$ | $\mathit{N}{(}^{3}{\mathit{P}}_{2})$ | ${\mathit{\beta}}_{2}^{\mathit{eff}}$ |
---|---|---|---|---|---|---|

218 MeV/u | PIE | −0.1694 | 0.9864 | 0.4473 | 0.0135 | −0.1218 |

PIE + EIE | −0.2161 | 0.7861 | −0.3517 | 0.2138 | −0.0751 | |

300 MeV/u | PIE | −0.0359 | 0.9843 | 0.4969 | 0.01567 | −0.0296 |

PIE + EIE | −0.1367 | 0.8773 | −0.2874 | 0.1226 | −0.0637 |

**Table 2.**Theoretical values for the alignment parameters ${A}_{2}$, the relative populations N, and the resulting effective anisotropy parameters ${\beta}_{2}^{eff}$ for ${[1{s}_{1/2},2{s}_{1/2}]}^{3}{S}_{1}$ and ${[1{s}_{1/2},2{p}_{1/2}]}^{3}{P}_{1}$ states contributing to the K${\alpha}_{2}$ line. For details see text.

Beam Energy | Process | ${\mathit{A}}_{2}{(}^{3}{\mathit{S}}_{1})$ | $\mathit{N}{(}^{3}{\mathit{S}}_{1})$ | ${\mathit{A}}_{2}{(}^{3}{\mathit{P}}_{1})$ | $\mathit{N}{(}^{3}{\mathit{P}}_{1})$ | ${\mathit{\beta}}_{2}^{\mathit{eff}}$ |
---|---|---|---|---|---|---|

218 MeV/u | PIE | 0.1729 | 0.0442 | 0.1082 | 0.9557 | 0.0785 |

PIE + EIE | 0.0361 | 0.2555 | −0.0731 | 0.7444 | −0.0320 | |

300 MeV/u | PIE | 0.1352 | 0.0449 | 0.2279 | 0.9550 | 0.1582 |

PIE + EIE | 0.0658 | 0.1843 | 0.0227 | 0.8156 | 0.0217 |

**Table 3.**Experimental values in comparison with theoretical predictions for the effective anisotropy parameters for the K${\alpha}_{1}$ and K${\alpha}_{2}$ lines of helium-like uranium ions produced by $K\to L$ excitation in collisions with argon atoms. PIE calculations were performed for the screened potential.

Beam Energy | Line | PIE Screened | Experiment |
---|---|---|---|

218 MeV/u | K${\alpha}_{1}$ | −0.1201 | −0.12 ± 0.07 [12] |

K${\alpha}_{2}$ | 0.0805 | 0.07 ± 0.02 | |

300 MeV/u | K${\alpha}_{1}$ | −0.0273 | 0.02 ± 0.02 |

K${\alpha}_{2}$ | 0.1606 | 0.16 ± 0.03 |

**Table 4.**Experimental values in comparison with theoretical predictions for the effective anisotropy parameters for the K${\alpha}_{1}$ and K${\alpha}_{2}$ lines of helium-like uranium ions produced by $K\to L$ excitation in collisions with hydrogen molecules. For details see text.

Beam Energy | Line | PIE | PIE + EIE | Experiment |
---|---|---|---|---|

218 MeV/u | K${\alpha}_{1}$ | −0.1218 | −0.0751 | −0.11 ± 0.04 |

K${\alpha}_{2}$ | 0.0785 | −0.0319 | −0.07 ± 0.03 | |

300 MeV/u | K${\alpha}_{1}$ | −0.0296 | −0.0637 | −0.02 ± 0.05 |

K${\alpha}_{2}$ | 0.1582 | 0.0217 | 0.04 ± 0.02 |

**Table 5.**Partial cross sections for the excitation into magnetic sub-levels of the ${}^{3}{P}_{1}$ state for U${}^{90+}$ in collision with an H${}_{2}$ target at 218 MeV/u. The results are given in barns.

$\mathit{m}=0$ | $\left|\mathit{m}\right|=1$ | |
---|---|---|

EIE | 0.7898 | 0.5319 |

PIE | 0.3423 | 0.4407 |

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**MDPI and ACS Style**

Gumberidze, A.; Thorn, D.B.; Surzhykov, A.; Fontes, C.J.; Banaś, D.; Beyer, H.F.; Chen, W.; Grisenti, R.E.; Hagmann, S.; Hess, R.;
et al. Angular Distribution of Characteristic Radiation Following the Excitation of He-Like Uranium in Relativistic Collisions. *Atoms* **2021**, *9*, 20.
https://doi.org/10.3390/atoms9020020

**AMA Style**

Gumberidze A, Thorn DB, Surzhykov A, Fontes CJ, Banaś D, Beyer HF, Chen W, Grisenti RE, Hagmann S, Hess R,
et al. Angular Distribution of Characteristic Radiation Following the Excitation of He-Like Uranium in Relativistic Collisions. *Atoms*. 2021; 9(2):20.
https://doi.org/10.3390/atoms9020020

**Chicago/Turabian Style**

Gumberidze, Alexandre, Daniel B. Thorn, Andrey Surzhykov, Christopher J. Fontes, Dariusz Banaś, Heinrich F. Beyer, Weidong Chen, Robert E. Grisenti, Siegbert Hagmann, Regina Hess,
and et al. 2021. "Angular Distribution of Characteristic Radiation Following the Excitation of He-Like Uranium in Relativistic Collisions" *Atoms* 9, no. 2: 20.
https://doi.org/10.3390/atoms9020020