# Mixed-State Ionic Beams: An Effective Tool for Collision Dynamics Investigations

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Production of Metastable States

## 3. Lifetimes of Metastable States

## 4. Mixed-State Ionic Beams—Content Determination

#### 4.1. $1s2s{\phantom{\rule{0.166667em}{0ex}}}^{3}\phantom{\rule{-0.166667em}{0ex}}S$

#### 4.2. $1{s}^{2}2s2p{\phantom{\rule{0.166667em}{0ex}}}^{3}\phantom{\rule{-0.166667em}{0ex}}P$

## 5. Case Studies: Results and Discussion

#### 5.1. Doubly and Triply Excited Li-Like States

#### 5.2. Doubly Excited He-Like States

## 6. Summary

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

APAPES | Atomic Physics with Accelerators: Projectile Electron Spectroscopy |

AOCC | Atomic Orbital Close Coupling |

ZAPS | Zero-degree Auger Projectile Spectroscopy |

TANDEM | The two-stage (tandem) Van de Graaff accelerator |

FPS | Foil Post-Stripping |

FTS | Foil Terminal Stripping |

GPS | Gas Post-Stripping |

GTS | Gas Terminal Stripping |

RTE | Resonant Transfer and Excitation |

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**Figure 1.**The surviving fraction of the $1s2s{\phantom{\rule{0.166667em}{0ex}}}^{1}\phantom{\rule{-0.166667em}{0ex}}S$ metastable state as a function of the ion beam traveling distance s for various elements with $4\le {Z}_{p}\le 9$ and typical projectile energies of 0.25–2 MeV/u. Lifetimes are from Ref. [66]. For these He-like ions the survival of the much longer lived $1s2s{\phantom{\rule{0.166667em}{0ex}}}^{3}\phantom{\rule{-0.166667em}{0ex}}S$ metastable state (not shown) is practically 100% over the same distances.

**Figure 2.**Auger KLL spectra obtained in collisions of 4.5 MeV B${}^{3+}$ with H${}_{2}$, as reported in Ref. [64], and of 6.0 MeV C${}^{4+}$ with He. The B${}^{3+}$ and C${}^{4+}$ beams were produced: [Red squares] After post-stripping the incident B${}^{2+}$ and C${}^{3+}$ beams in thin carbon foils (FPS). [Blue dots] After post-stripping the incident B${}^{2+}$ beam in Ar gas (GPS). [Green triangles] after stripping the incident C${}^{-}$ beam in the accelerator terminal in N${}_{2}$ gas (GTS). A smaller ratio of ${}^{4}\phantom{\rule{-0.166667em}{0ex}}P$ to ${}^{2}\phantom{\rule{-0.166667em}{0ex}}D$ yields implies a smaller metastable fraction.

**Figure 3.**(

**Top**) Li-like Auger spectra obtained in collisions of 4 MeV B${}^{3+}$ with H${}_{2}$ targets. The red squares correspond to the mixed-state ($1{s}^{2}{\phantom{\rule{0.166667em}{0ex}}}^{1}\phantom{\rule{-0.166667em}{0ex}}S,1s2s{\phantom{\rule{0.166667em}{0ex}}}^{3}\phantom{\rule{-0.166667em}{0ex}}S$) beam, while the blue dots to the almost pure ground state $1{s}^{2}{\phantom{\rule{0.166667em}{0ex}}}^{1}\phantom{\rule{-0.166667em}{0ex}}S$, as evident by the very small contribution of the ${}^{4}\phantom{\rule{-0.166667em}{0ex}}P$ peak. The high fraction spectrum was obtained with FPS, while the low fraction with GTS. (

**Middle**) Same as in the top graph, but here the ground state spectrum was convoluted with the slightly larger energy resolution of the mixed-state spectrum and then normalized to the $1s2{p}^{2}{\phantom{\rule{0.166667em}{0ex}}}^{2}\phantom{\rule{-0.166667em}{0ex}}D$ line. (

**Bottom**) Li-like Auger spectrum corresponding just to the $1s2s{\phantom{\rule{0.166667em}{0ex}}}^{3}\phantom{\rule{-0.166667em}{0ex}}S$ metastable state. The spectrum resulted from the subtraction of the two normalized spectra of the middle graph.

**Figure 4.**Auger KLL spectra obtained in collisions of 17.5 MeV O${}^{4+}$ and 6.6 MeV C${}^{2+}$ with H${}_{2}$ targets (from Ref. [89]). SIMION simulations of the ${}^{4}\phantom{\rule{-0.166667em}{0ex}}P$ line distributions are shown by the short dash line in excellent agreement with the measurements. The solid lines correspond to Voigt profile least square fits of the Auger lines.

**Figure 5.**(

**Top**) Li-like Auger spectra obtained in collisions of 15 MeV C${}^{4+}$ with He targets. The red squares correspond to the mixed-state beam with higher value for the $1s2s{\phantom{\rule{0.166667em}{0ex}}}^{3}\phantom{\rule{-0.166667em}{0ex}}S$ metastable fraction, while the blue dots to the lower value. The high fraction spectrum was obtained with FTS, while the low fraction with GTS. (

**Bottom**) The He-like doubly excited $2s2p{\phantom{\rule{0.166667em}{0ex}}}^{1,3}\phantom{\rule{-0.166667em}{0ex}}P$ states obtained in collisions with H${}_{2}$, Ne and Ar gas targets.

**Table 1.**Indicative theoretical lifetimes (in s) of the metastable He-like $1s2s{\phantom{\rule{0.166667em}{0ex}}}^{1}\phantom{\rule{-0.166667em}{0ex}}S$, $1s2s{\phantom{\rule{0.166667em}{0ex}}}^{3}\phantom{\rule{-0.166667em}{0ex}}S$ (from Refs. [66,67]) and Be-like $1{s}^{2}2s2p{\phantom{\rule{0.166667em}{0ex}}}^{3}\phantom{\rule{-0.166667em}{0ex}}{P}_{1}$ states (from Refs. [68,69]) for $3\le {Z}_{p}\le 10$.

${\mathit{Z}}_{\mathit{p}}$ | $1\mathit{s}2\mathit{s}{\phantom{\rule{0.166667em}{0ex}}}^{1}\phantom{\rule{-0.166667em}{0ex}}\mathit{S}$ | $1\mathit{s}2\mathit{s}{\phantom{\rule{0.166667em}{0ex}}}^{3}\phantom{\rule{-0.166667em}{0ex}}\mathit{S}$ | $1{\mathit{s}}^{2}2\mathit{s}2\mathit{p}{\phantom{\rule{0.166667em}{0ex}}}^{3}\phantom{\rule{-0.166667em}{0ex}}{\mathit{P}}_{1}$ |
---|---|---|---|

3 | $5.1\times {10}^{-4}$ | $4.9\times {10}^{1}$ | - |

4 | $5.5\times {10}^{-5}$ | $1.8\times {10}^{0}$ | - |

5 | $1.1\times {10}^{-5}$ | $1.5\times {10}^{-1}$ | $9.8\times {10}^{-2}$ |

6 | $3.0\times {10}^{-6}$ | $2.1\times {10}^{-2}$ | $9.7\times {10}^{-3}$ |

7 | $1.1\times {10}^{-6}$ | $3.9\times {10}^{-3}$ | $1.7\times {10}^{-3}$ |

8 | $4.3\times {10}^{-7}$ | $9.6\times {10}^{-4}$ | $4.4\times {10}^{-4}$ |

9 | $2.0\times {10}^{-7}$ | $2.8\times {10}^{-4}$ | $1.4\times {10}^{-4}$ |

10 | $1.0\times {10}^{-7}$ | $9.2\times {10}^{-5}$ | $5.3\times {10}^{-5}$ |

**Table 2.**Results of the experimental determination (using Equation (1)) of the $1s2s{\phantom{\rule{0.166667em}{0ex}}}^{3}\phantom{\rule{-0.166667em}{0ex}}S$ metastable fraction ${f}_{{}^{3}\phantom{\rule{-0.166667em}{0ex}}S}$ on target. FPS: foil post-stripping, GPS: gas post-stripping, GTS: gas terminal stripping. The uncertainties of the fractions are given in the adjacent parentheses.

Stripping | Incident | Stripping Energy | Final Energy | ${\mathit{f}}_{{}^{3}\phantom{\rule{-0.166667em}{0ex}}\mathit{S}}$ |
---|---|---|---|---|

Method | Ion | MeV | MeV | % |

FPS | B${}^{2+}$ | 4.5 | 4.5 | 42 (10) |

GPS | B${}^{2+}$ | 4.5 | 4.5 | 18 (5) |

FPS | C${}^{3+}$ | 6.0 | 6.0 | 16 (3) |

GTS | C${}^{-}$ | 1.2 | 6.0 | 7 (2) |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Benis, E.P.; Madesis, I.; Laoutaris, A.; Nanos, S.; Zouros, T.J.M. Mixed-State Ionic Beams: An Effective Tool for Collision Dynamics Investigations. *Atoms* **2018**, *6*, 66.
https://doi.org/10.3390/atoms6040066

**AMA Style**

Benis EP, Madesis I, Laoutaris A, Nanos S, Zouros TJM. Mixed-State Ionic Beams: An Effective Tool for Collision Dynamics Investigations. *Atoms*. 2018; 6(4):66.
https://doi.org/10.3390/atoms6040066

**Chicago/Turabian Style**

Benis, Emmanouil P., Ioannis Madesis, Angelos Laoutaris, Stefanos Nanos, and Theo J. M. Zouros. 2018. "Mixed-State Ionic Beams: An Effective Tool for Collision Dynamics Investigations" *Atoms* 6, no. 4: 66.
https://doi.org/10.3390/atoms6040066