#
Collinear Laser Spectroscopy of Helium-like ^{11}B^{3+}

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

^{11}B

^{3+}was produced inside the SPARC-EBIT using the metal-ion from volatile compounds (MIVOC) method. The volume above a small amount of liquid trimethylborate (TMB) is evacuated until a substantial fraction of the liquid is evaporated and the atmosphere above the remaining substance is dominated by TMB molecules. This vapor is then fed into the center of the EBIT via a feedback-loop controlled needle-valve that stabilizes the pressure inside the EBIT during operation to $2\xb7{10}^{-9}$ mbar (standby pressure $\approx {10}^{-10}$ mbar). Once the molecule is broken up by the impact of the dense electron beam, its constituents are ionized subsequently. The final distribution of charge states depends on the confinement time, the electron current, and the depth of the axial potential well.

^{11}B

^{3+}with 282 nm light, a diode-pumped frequency-doubled Nd:Yag continuous wave (cw) laser (Millennia 20 eV, Spectra Physics) was used to pump a tunable ring-cavity dye laser (Matisse DS 2, Sirah) with about 5 W. The dye solution was Rhodamine 110 dissolved in ethylene–glycol with a concentration of 1.93 g/L. Approximately 400 mW of fundamental power produced by the dye laser was fed into a second-harmonic generation (SHG) unit (Wavetrain 2, Spectra Physics), generating an output power of approximately 30 mW at 282 nm. The beam is directed through a pinhole to obtain a pure TEM00 spatial mode and is then transported to the ODR. We used a commercial beam stabilization system from MRC systems consisting of two piezo-actuated mirrors (PAM) and position-sensitive detectors (PSD) for spacial beam stabilization and to establish a reproducible superposition of laser and ion beam in vertical direction through the SPECTRAP magnet and the ODR.

## 3. Results

^{11}B

^{3+}hyperfine-multiplet, due to the reduced S/N ratio in this geometry. This line therefore served as a reference line and its transition frequency was measured in collinear–anticollinear geometry. All other transitions, indicated by dashed lines in Figure 3, were investigated only in anticollinear geometry. Spectra of the reference line obtained in anticollinear and collinear geometry are depicted in Figure 4a,b, respectively.

## 4. Discussion

^{11}B

^{3+}were taken from [35,36], respectively. Since no hyperfine transitions of the $2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1}\to 2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{1}$ multiplet were measured, its corresponding fine-structure transition frequency parameter was fixed to the theoretical value provided by Yerokhin et al. [37]. The fine-structure splitting obtained by this procedure is given in Table 1 and is compared to former experimental and theoretical values.

^{11}B

^{3+}ions in an EBIT. Second, experimental conditions at the EBIT should be improved to obtain a more symmetric lineshape and—if possible—to reduce the linewidth. One possibility could be the so-called leakage mode of the EBIT, where the potential at the exit electrode is lowered such that some ions can escape from the trap and are continuously accelerated into the beamline. The investigation of this mode was not possible under the conditions at the HITRAP beamline but are currently ongoing with a dedicated electron beam ion source (EBIS) at COALA, where, especially, a much lower background rate is achieved. Furthermore, a careful analysis of systematic effects on the extracted fine-structure transition frequencies due to uncertainties in the theoretical predictions for the mixing amplitudes is missing and must be conducted before the all-optical approach can be applied to those isotopes.

## 5. Conclusions

^{12}C does not exhibit a hyperfine structure. Additionally, the odd isotope

^{13}C can be used to characterize uncertainties arising from the hyperfine mixing. These are the first steps planned at the COALA beamline.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic drawing of the HITRAP low-energy beamline (

**right**) and a more detailed figure of the modified SPECTRAP beamline (

**left**).

**Figure 2.**Schematic drawing of the optical detection region (

**left**) and photo of the assembled vacuum system (

**right**).

**Figure 3.**Level scheme of

^{11}B

^{3+}. All transitions, which were measured during the measurement campaign, are indicated by straight arrows: The strongest hyperfine transition that was used as reference line is the solid line, while all others are indicated by the dashed lines. The M1-transition from the metastable 2s2p ${}^{3}{\mathrm{S}}_{1}$ to the ground state 1s${}^{2}$${}^{1}{\mathrm{S}}_{0}$ is depicted with its lifetime $\tau =149$ ms taken from [32].

**Figure 4.**Anticollinear and collinear measurements of the reference transition $2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1}\phantom{\rule{0.166667em}{0ex}}(F=5\phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}2)\to 2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{2}\phantom{\rule{0.166667em}{0ex}}(F=7\phantom{\rule{-1.111pt}{0ex}}/\phantom{\rule{-0.55542pt}{0ex}}2)$ evaluated with the asymmetric Gaussian fit-model. In the collinear setup (

**b**), the laser passed the optical detection region twice, but only one way contributes to the signal. Hence, the signal-to-noise ratio is worse compared to the anticollinear geometry (

**a**). The anticollinear measurement was performed subsequently to the collinear measurement. Only the mirror on top of the vertical SPECTRAP beamline was removed. The difference between the main and the satellite peak in the asymmetric Gaussian profile was fixed, but with opposite sign for the two geometries.

**Figure 5.**Complete hyperfine spectrum of the $2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1}\to 2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{0}$ and $2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{S}}_{1}\to 2{\phantom{\rule{0.166667em}{0ex}}}^{3}{\mathrm{P}}_{2}$ fine-structure transitions including the fit of the hyperfine transitions, including hyperfine-induced fine-structure mixing, as discussed in the text. The individual transitions are indicated at the resonances.

**Table 1.**Preliminary result for the 2 ${}^{3}{\mathrm{P}}_{2}$ – 2 ${}^{3}{\mathrm{P}}_{0}$ fine-structure splitting in

^{11}B

^{3+}. Numbers are given in ${\mathrm{cm}}^{-1}$, and $1\sigma $ uncertainty is indicated in parentheses if available. The final analysis is expected to provide an even more accurate value.

2 ${}^{3}{\mathbf{P}}_{2}$ – 2 ${}^{3}{\mathbf{P}}_{0}$ | Ref. | |
---|---|---|

Schiff, 1973 | $36.416\phantom{\rule{0.166667em}{0ex}}$ | [38] |

Drake, 1988 | $36.32\phantom{\rule{0.166667em}{0ex}}\left(11\right)$ | [39] |

Dinnéen (exp.), 1991 | $36.457\phantom{\rule{0.166667em}{0ex}}\left(9\right)$ | [24] |

Chen, 1993 | $36.450\phantom{\rule{0.166667em}{0ex}}\left(40\right)$ | [40] |

Yerokhin, 2010 | $36.460\phantom{\rule{0.166667em}{0ex}}\left(20\right)$ | [37] |

Yerokhin, 2022 | $36.467\phantom{\rule{0.166667em}{0ex}}\left(5\right)$ | [18] |

This work (exp.) | $36.462\phantom{\rule{0.166667em}{0ex}}\left(10\right)$ |

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**MDPI and ACS Style**

Mohr, K.; Buß, A.; Andelkovic, Z.; Hannen, V.; Horst, M.; Imgram, P.; König, K.; Maaß, B.; Nörtershäuser, W.; Rausch, S.;
et al. Collinear Laser Spectroscopy of Helium-like ^{11}B^{3+}. *Atoms* **2023**, *11*, 11.
https://doi.org/10.3390/atoms11010011

**AMA Style**

Mohr K, Buß A, Andelkovic Z, Hannen V, Horst M, Imgram P, König K, Maaß B, Nörtershäuser W, Rausch S,
et al. Collinear Laser Spectroscopy of Helium-like ^{11}B^{3+}. *Atoms*. 2023; 11(1):11.
https://doi.org/10.3390/atoms11010011

**Chicago/Turabian Style**

Mohr, Konstantin, Axel Buß, Zoran Andelkovic, Volker Hannen, Max Horst, Phillip Imgram, Kristian König, Bernhard Maaß, Wilfried Nörtershäuser, Simon Rausch,
and et al. 2023. "Collinear Laser Spectroscopy of Helium-like ^{11}B^{3+}" *Atoms* 11, no. 1: 11.
https://doi.org/10.3390/atoms11010011