#
Spectroscopic Peculiarities at Ionization of Excited 2p^{5}(^{2}P_{Jf})3s[K]_{0,1,2} States of Ne: Cooper Minima and Autoionizing Resonances

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. PhotoIonization of Metastable $\mathbf{2}{\mathit{s}}^{\mathbf{2}}\mathbf{2}{\mathit{p}}^{\mathbf{5}}{(}^{\mathbf{2}}{\mathit{P}}_{\mathbf{1}/\mathbf{2}})\mathbf{3}\mathit{s}{[\mathbf{1}/\mathbf{2}]}_{\mathbf{0}}$ and $\mathbf{2}{\mathit{s}}^{\mathbf{2}}\mathbf{2}{\mathit{p}}^{\mathbf{5}}{(}^{\mathbf{2}}{\mathit{P}}_{\mathbf{3}/\mathbf{2}})\mathbf{3}\mathit{s}{[\mathbf{3}/\mathbf{2}]}_{\mathbf{2}}$ States

## 3. Photoionization of Dipole-Allowed $\mathbf{2}{\mathit{s}}^{\mathbf{2}}\mathbf{2}{\mathit{p}}^{\mathbf{5}}{(}^{\mathbf{2}}{\mathit{P}}_{{\mathit{J}}_{\mathit{f}}})\mathbf{3}\mathit{s}{\left[\mathit{K}\right]}_{\mathbf{1}}$ States

## 4. The Resonance Structures

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Photoionization cross-section of $2{s}^{2}2{p}^{5}\left({P}_{1/2}\right)3s{[1/2]}_{0}$ state of neon to $2{s}^{2}2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ (upper row) and $2{s}^{2}2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ (bottom row). Calculations are performed within $\mathcal{R}$- (

**a**,

**d**), $\mathcal{V}$- (

**b**,

**e**) and $\mathcal{C}$-model (

**c**,

**f**). Solid lines are for calculations in the length gauge and dashed lines in the velocity gauge; different colors mark the number of accounted target states: two (black), six (blue) and ten (red). Experimental data points are taken from [38] and labeled by orange.

**Figure 2.**Photoionization cross-section of $2{s}^{2}2{p}^{5}{(}^{2}{P}_{3/2})3s{[3/2]}_{2}$ state of neon to $2{s}^{2}2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ (upper row) and $2{s}^{2}2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ (bottom row). Calculations are performed within $\mathcal{R}$- (

**a**,

**d**), $\mathcal{V}$- (

**b**,

**e**) and $\mathcal{C}$-model (

**c**,

**f**). Solid lines are for calculations in the length gauge and dashed for the velocity gauge; different colors mark the number of accounted targets: two (black), six (blue) and ten (red). Experimental data points are taken from [38] and labeled by orange.

**Figure 3.**Cross-section calculated within the $\mathcal{V}$- (dash-dotted lines correspond to length gauge, dotted lines to velocity gauge) and $\mathcal{C}$- (solid lines correspond to length gauge, dashed lines to velocity gauge) models with six (cyan and blue) and ten (orange and red) target states for ionization of $2{s}^{2}2{p}^{5}{(}^{2}{P}_{3/2})3s{[3/2]}_{1}$ state to $2{s}^{2}2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ (upper row) and $2{s}^{2}2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ (bottom row) ionic states for unpolarized (

**a**,

**d**), linearly polarized (

**b**,

**e**) and circularly polarized (

**c**,

**f**) fields.

**Figure 4.**Cross-section calculated within the $\mathcal{V}$- (dash-dotted lines correspond to length gauge, dotted lines to velocity gauge) and $\mathcal{C}$- (solid lines correspond to length gauge, dashed lines to velocity gauge) models with six (cyan and blue) and ten (orange and red) target states for ionization of $2{s}^{2}2{p}^{5}{(}^{2}{P}_{1/2})3s{[1/2]}_{1}$ state to $2{s}^{2}2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ (upper row) and $2{s}^{2}2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ (bottom row) ionic states for unpolarized (

**a**,

**d**), linearly polarized (

**b**,

**e**) and circularly polarized (

**c**,

**f**) fields. Within the $\mathcal{V}$-model, orange and cyan lines in panels (

**d**,

**e**,

**f**) practically coincide.

**Figure 5.**Cross-section calculated in the length gauge within the $\mathcal{V}$- (dash-dotted lines) and $\mathcal{C}$- (solid lines) models with six (cyan and blue) and ten (orange and red) thresholds for ionization of $2{s}^{2}2{p}^{5}{(}^{2}{P}_{1/2})3s{[1/2]}_{0}$ (

**a**,

**e**), $2{s}^{2}2{p}^{5}{(}^{2}{P}_{3/2})3s{[3/2]}_{2}$ (

**b**,

**f**) and $2{s}^{2}2{p}^{5}{(}^{2}{P}_{3/2})3s{[3/2]}_{1}$ (

**c**,

**g**), $2{s}^{2}2{p}^{5}{(}^{2}{P}_{1/2})3s{[1/2]}_{1}$ (

**d**,

**h**) states to $2{s}^{2}2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ (upper row) and to $2{s}^{2}2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ (bottom row) ionic states for unpolarized fields. The arrows mark positions of very narrow resonances $2{p}^{4}3{s}^{2}{[}^{2}{P}_{J=1,2}]$ where they would appear within the $LSJ$-coupling scheme.

**Table 1.**Target states (named by the leading term in LSJ approximation), the leading terms in configuration mixing (in percent) and energies according to NIST database [65]. Core $1{s}^{2}$ is omitted for brevity.

Target | Energy | $\mathcal{R}$-Model | $\mathcal{V}$-Model | $\mathcal{C}$-Model |
---|---|---|---|---|

$2{s}^{2}2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ | 21.5645 | 99.92 $2{s}^{2}2{p}^{5}$+0.03 $2{s}^{2}2{p}^{4}3p+$ | 92.80 $2{s}^{2}2{p}^{5}$+3.16 $2{s}^{2}2{p}^{4}3\overline{p}+$ | 98.24 $2{s}^{2}2{p}^{5}$+0.56 $2{s}^{2}2{p}^{3}4{\overline{p}}^{2}+$ |

$2{s}^{2}2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ | 21.6613 | 0.02 $2{s}^{2}2{p}^{3}3{p}^{2}$+0.01 $2{s}^{2}2{p}^{4}4p$ | 2.70 $2s2{p}^{5}3\overline{s}$+0.36 0.37 $2{s}^{2}2{p}^{3}3{\overline{p}}^{2}$ | 0.54 $2{s}^{2}2{p}^{3}3{\overline{d}}^{2}$+0.35 $2s2{p}^{5}3\overline{d}$ |

$2s2{p}^{6}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{S}_{1/2})$ | 48.4750 | 95.39 $2s2{p}^{6}$+4.03 $2{s}^{2}2{p}^{4}3s$+ | 93.58 $2s2{p}^{6}$+2.26 $2{s}^{2}2{p}^{4}3\overline{d}+$ | 94.70 $2s2{p}^{6}$+2.33 $2{s}^{2}2{p}^{4}3\overline{d}+$ |

0.23 $2s{p}^{5}3p$+0.21 $2{s}^{2}2{p}^{4}4s$ | 0.77 $2s2{p}^{4}3{\overline{d}}^{2}$+0.67 $2{s}^{2}2{p}^{4}3s$ | 0.79 $2s2{p}^{4}3{\overline{d}}^{2}$+0.75 $2s2{p}^{4}4{\overline{p}}^{2}$ | ||

$2{s}^{2}2{p}^{4}3s\phantom{\rule{0.166667em}{0ex}}{(}^{4}{P}_{5/2})$ | 48.7333 | 95.13 $2{s}^{2}2{p}^{4}3s$+3.76 $2{s}^{2}2{p}^{4}4s$ | ||

$2{s}^{2}2{p}^{4}3s\phantom{\rule{0.166667em}{0ex}}{(}^{4}{P}_{3/2})$ | 48.7975 | 0.79 $2{s}^{2}2{p}^{3}3s3p$+0.10 $2s2{p}^{5}3p$ | 97.28 $2{s}^{2}2{p}^{4}3s$+1.24 $2s2{p}^{4}3{s}^{2}$+ | 91.68 $2{s}^{2}2{p}^{4}3s$+4.98 $2{s}^{2}2{p}^{4}4\overline{s}$ |

$2{s}^{2}2{p}^{4}3s\phantom{\rule{0.166667em}{0ex}}{(}^{4}{P}_{1/2})$ | 48.8345 | 91.80 $2{s}^{2}2{p}^{4}3s$+3.63 $2{s}^{2}2{p}^{4}4s$ | 0.58 $2s2{p}^{4}3s3\overline{d}$+0.35 $2{s}^{2}2{p}^{2}3s3{\overline{p}}^{2}$ | 0.66 $2{s}^{2}2{p}^{3}3s4\overline{p}$+0.62 $2s2{p}^{4}3s3\overline{d}$ |

3.48 $2s2{p}^{6}$+0.76 $2{s}^{2}2{p}^{3}3s3p$ | ||||

$2{s}^{2}2{p}^{4}3s\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ | 49.3478 | 95.40 $2{s}^{2}2{p}^{4}3s$+3.41 $2{s}^{2}2{p}^{4}4s$+ | 97.70 $2{s}^{2}2{p}^{4}3s$+0.72 $2s2{p}^{4}3{s}^{2}$+ | 94.02 $2{s}^{2}2{p}^{4}3s$+2.50 $2{s}^{2}2{p}^{4}4\overline{s}$+ |

$2{s}^{2}2{p}^{4}3s\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ | 49.4237 | 1.38 $2{s}^{2}2{p}^{3}3s4p$+0.84 $2{s}^{2}2{p}^{3}3s3p$ | 0.59 $2s2{p}^{4}3s3\overline{d}$+0.35 $2{s}^{2}2{p}^{2}3s3{\overline{p}}^{2}$ | 1.38 $2{s}^{2}2{p}^{3}3s4\overline{p}$+0.74 $2{s}^{2}2{p}^{3}3s3p$ |

$2{s}^{2}2{p}^{4}3p\phantom{\rule{0.166667em}{0ex}}{(}^{4}{P}_{5/2})$ | 52.0885 | |||

$2{s}^{2}2{p}^{4}3p\phantom{\rule{0.166667em}{0ex}}{(}^{4}{P}_{3/2})$ | 52.1161 | 94.37 $2{s}^{2}2{p}^{4}3p$+4.70 $2{s}^{2}2{p}^{4}4p$+ | 90.78 $2{s}^{2}2{p}^{4}3p$+6.67 $2{s}^{2}2{p}^{3}3p4\overline{p}$+ | 96.73 $2{s}^{2}2{p}^{4}3p$+1.67 $2{s}^{2}2{p}^{3}3p4\overline{p}$+ |

0.55 $2{s}^{2}2{p}^{3}3{p}^{2}$+0.14 $2{s}^{2}2{p}^{3}3p4p$ | 1.77 $2s2{p}^{4}3p3\overline{s}$+0.48 $2s2{p}^{4}3p3\overline{d}$ | 0.58 $2{s}^{2}2{p}^{4}3p3\overline{d}$+0.49 $2{s}^{2}2{p}^{3}3{p}^{2}$ | ||

$2{s}^{2}2{p}^{4}3p\phantom{\rule{0.166667em}{0ex}}{(}^{4}{P}_{1/2})$ | 52.1388 | |||

$2{s}^{2}2{p}^{4}3s\phantom{\rule{0.166667em}{0ex}}{(}^{2}{D}_{5/2})$ | 52.1135 | 95.30 $2{s}^{2}2{p}^{4}3s$+3.71 $2{s}^{2}2{p}^{4}4s+$ | 97.38 $2{s}^{2}2{p}^{4}3s$+1.01 $2s2{p}^{4}3{s}^{2}+$ | 92.77 $2{s}^{2}2{p}^{4}3s$+4.03 $2{s}^{2}2{p}^{4}4\overline{s}+$ |

$2{s}^{2}2{p}^{4}3s\phantom{\rule{0.166667em}{0ex}}{(}^{2}{D}_{3/2})$ | 52.1139 | 0.73 $2{s}^{2}2{p}^{3}3s3p$+0.16 $2{s}^{2}2{p}^{3}3s4p$ | 0.62 $2s2{p}^{4}3s3\overline{d}$+0.38 $2{s}^{2}2{p}^{2}3s3{\overline{d}}^{2}$ | 1.16 $2{s}^{2}2{p}^{3}3s4\overline{p}$+0.66 $2s2{p}^{4}3s3\overline{d}$ |

**Table 2.**AISs parameters in a model within ten target states: energy position E (eV), width $\Gamma $ (eV) and Fano profile index q at excitation of different initial states for different polarization.

AIS | $2\mathit{s}2{\mathit{p}}^{6}3\mathit{s}\phantom{\rule{0.166667em}{0ex}}{[}^{3}{\mathit{S}}_{1}]$ | $2\mathit{s}2{\mathit{p}}^{6}3\mathit{s}\phantom{\rule{0.166667em}{0ex}}{[}^{1}{\mathit{S}}_{0}]$ | ||
---|---|---|---|---|

Parameter | ||||

E | $\mathcal{C}$-model | 22.03 | 22.13 | |

$\Gamma $ | 0.119 | 0.028 | ||

${q}^{un}$ | ${(}^{2}{P}_{3/2})3s{[3/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ | $-70$ | ∞ | |

${q}^{un}$ | ${(}^{2}{P}_{3/2})3s{[3/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ | $-50$ | $-75$ | |

${q}^{un}$ | ${(}^{2}{P}_{1/2})3s{[1/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ | ∞ | ∞ | |

${q}^{un}$ | ${(}^{2}{P}_{1/2})3s{[1/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ | $-15$ | ∞ | |

${q}^{lin}$ | ${(}^{2}{P}_{3/2})3s{[3/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ | - | ∞ | |

${q}^{lin}$ | ${(}^{2}{P}_{3/2})3s{[3/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ | - | $-80$ | |

${q}^{lin}$ | ${(}^{2}{P}_{1/2})3s{[1/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ | - | $-\infty $ | |

${q}^{lin}$ | ${(}^{2}{P}_{1/2})3s{[1/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ | - | ∞ | |

E | $\mathcal{V}$-model | 22.07 | 22.05 | |

$\Gamma $ | 0.116 | 0.002 | ||

${q}^{un}$ | ${(}^{2}{P}_{3/2})3s{[3/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ | $-75$ | $-\infty $ | |

${q}^{un}$ | ${(}^{2}{P}_{3/2})3s{[3/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ | $-50$ | ∞ | |

${q}^{un}$ | ${(}^{2}{P}_{1/2})3s{[1/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ | 65 | ∞ | |

${q}^{un}$ | ${(}^{2}{P}_{1/2})3s{[1/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ | $-15$ | ∞ | |

${q}^{lin}$ | ${(}^{2}{P}_{3/2})3s{[3/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ | - | $-\infty $ | |

${q}^{lin}$ | ${(}^{2}{P}_{3/2})3s{[3/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ | - | ∞ | |

${q}^{lin}$ | ${(}^{2}{P}_{1/2})3s{[1/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{3/2})$ | - | $-\infty $ | |

${q}^{lin}$ | ${(}^{2}{P}_{1/2})3s{[1/2]}_{1}\to 2{p}^{5}\phantom{\rule{0.166667em}{0ex}}{(}^{2}{P}_{1/2})$ | - | $-\infty $ |

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Popova, M.M.; Kiselev, M.D.; Burkov, S.M.; Gryzlova, E.V.; Grum-Grzhimailo, A.N.
Spectroscopic Peculiarities at Ionization of Excited 2*p*^{5}(^{2}*P*_{Jf})3*s*[*K*]_{0,1,2} States of Ne: Cooper Minima and Autoionizing Resonances. *Atoms* **2022**, *10*, 102.
https://doi.org/10.3390/atoms10040102

**AMA Style**

Popova MM, Kiselev MD, Burkov SM, Gryzlova EV, Grum-Grzhimailo AN.
Spectroscopic Peculiarities at Ionization of Excited 2*p*^{5}(^{2}*P*_{Jf})3*s*[*K*]_{0,1,2} States of Ne: Cooper Minima and Autoionizing Resonances. *Atoms*. 2022; 10(4):102.
https://doi.org/10.3390/atoms10040102

**Chicago/Turabian Style**

Popova, Maria M., Maksim D. Kiselev, Sergei M. Burkov, Elena V. Gryzlova, and Alexei N. Grum-Grzhimailo.
2022. "Spectroscopic Peculiarities at Ionization of Excited 2*p*^{5}(^{2}*P*_{Jf})3*s*[*K*]_{0,1,2} States of Ne: Cooper Minima and Autoionizing Resonances" *Atoms* 10, no. 4: 102.
https://doi.org/10.3390/atoms10040102