# X-ray Spectroscopy Based on Micro-Calorimeters at Internal Targets of Storage Rings

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## Abstract

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## 1. Introduction

## 2. Experiment

## 3. Detector Performance

## 4. Experimental Data and Results

#### 4.1. Transitions into the L-Shell

#### 4.2. Transitions within the L-Shell

## 5. Conclusions and Outlook

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**The two photos show the positioning of the MMC detector at the internal target of the ESR for the ${\mathrm{U}}^{89+}$ on ${\mathrm{N}}_{2}$ collision experiment from different viewing angles. On the left, the cryostat, which is required to operate the calorimeters, is visible. On the right, the helium-filled tube can be seen, which bridges the air gap to the ESR gas jet target chamber, which is also visible in the bottom photo.

**Figure 2.**The spectrum contains X-ray transitions from the M- to the L-shell, resulting from the impact excitation of ${\mathrm{U}}^{89+}$ (red text) as well as the electron capture into excited states of ${\mathrm{U}}^{88+}$ (black text). For simplicity, the $1{\mathrm{s}}^{2}$ term has been omitted from all given electronic configurations of ${\mathrm{U}}^{88+}$ ions. Overlaid is a fit to a model containing all identified lines (red line).

**Figure 3.**Shown is a spectrum that contains X-ray transitions of ${\mathrm{U}}^{89+}$ (red text) and ${\mathrm{U}}^{88+}$ (black text) from the N- and M-shells. Furthermore, a fit to a model consisting of all identified lines (red line) is presented. As an example, for the $3{\mathrm{d}}_{3\phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}2}\to 2{\mathrm{p}}_{1\phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}2}$ line, the individual fitting result is plotted (yellow, dashed line) in order to illustrate the discussed model function (Equation (1)) that takes into account the different operation points of the detector.

**Figure 4.**This spectrum contains X-ray transitions within the L-shell of ${\mathrm{U}}^{89+}$ (red text) as well as ${\mathrm{U}}^{88+}$ (black text). Additionally, a fit to a model containing all identified lines is plotted (red line).

**Figure 5.**The two level schemes show the energy of the bound states of lithium-like (

**left**) and beryllium-like uranium (

**right**). Additionally, the X-ray transitions observed during the experiment are marked in the level schemes.

**Table 1.**This table lists the measured and Doppler-corrected L-shell-transitions used for the estimation of the 2s Lamb shift of uranium. The given errors represent the approximated statistical uncertainty of the lines (see the text for details). An additional systematic uncertainty of $\Delta {E}_{\mathrm{syst}}/E\approx 8e-4$ has to be taken into account. For comparison, the corresponding energy value calculated by FAC is given as well.

Transition | $\mathbf{\Delta}{\mathit{E}}_{\mathbf{exp}}\left[\mathbf{eV}\right]$ | $\mathbf{\Delta}{\mathit{E}}_{\mathbf{theo}}\left[\mathbf{eV}\right]$ |
---|---|---|

${\mathbf{U}}^{89+}$ | Emitter-System | Calculation FAC |

$3{\mathrm{d}}_{3\phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}2}\to 2{\mathrm{p}}_{3\phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}2}$ | $\mathrm{15,660.6}\pm 6.4$ | $\mathrm{15,657.7}$ |

$3{\mathrm{d}}_{3\phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}2}\to 2{\mathrm{p}}_{1\phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}2}$ | $\mathrm{19,844.1}\pm 3.4$ | $\mathrm{19,841.7}$ |

$3{\mathrm{p}}_{3\phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}2}\to 2{\mathrm{s}}_{1\phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}2}$ | $\mathrm{20,117.6}\pm 3.8$ | $\mathrm{20,113.1}$ |

$3{\mathrm{p}}_{1\phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}2}\to 2{\mathrm{s}}_{1\phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}2}$ | $\mathrm{18,868.7}\pm 3.5$ | $\mathrm{18,862.7}$ |

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**MDPI and ACS Style**

Herdrich, M.O.; Hengstler, D.; Fleischmann, A.; Enss, C.; Gumberidze, A.; Hillenbrand, P.-M.; Indelicato, P.; Fritzsche, S.; Stöhlker, T.
X-ray Spectroscopy Based on Micro-Calorimeters at Internal Targets of Storage Rings. *Atoms* **2023**, *11*, 13.
https://doi.org/10.3390/atoms11010013

**AMA Style**

Herdrich MO, Hengstler D, Fleischmann A, Enss C, Gumberidze A, Hillenbrand P-M, Indelicato P, Fritzsche S, Stöhlker T.
X-ray Spectroscopy Based on Micro-Calorimeters at Internal Targets of Storage Rings. *Atoms*. 2023; 11(1):13.
https://doi.org/10.3390/atoms11010013

**Chicago/Turabian Style**

Herdrich, Marc Oliver, Daniel Hengstler, Andreas Fleischmann, Christian Enss, Alexandre Gumberidze, Pierre-Michel Hillenbrand, Paul Indelicato, Stephan Fritzsche, and Thomas Stöhlker.
2023. "X-ray Spectroscopy Based on Micro-Calorimeters at Internal Targets of Storage Rings" *Atoms* 11, no. 1: 13.
https://doi.org/10.3390/atoms11010013