#
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

- Connerade, J. Highly Exited Atoms; Cambridge University Press: Cambridge, UK, 1998. [Google Scholar]
- Baig, M.A. Measurement of Photoionization Cross-Section for the Excited States of Atoms: A Review. Atoms
**2022**, 10, 39. [Google Scholar] [CrossRef] - Avdonina, N.B.; Amusia, M.Y. Characteristic features in photoionisation of excited atomic states. J. Phys. B At. Mol. Phys.
**1983**, 16, L543–L545. [Google Scholar] [CrossRef] - Cooper, J.W. Interaction of Maxima in the Absorption of Soft X Rays. Phys. Rev. Lett.
**1964**, 13, 762–764. [Google Scholar] [CrossRef] - Fano, U.; Cooper, J.W. Spectral Distribution of Atomic Oscillator Strengths. Rev. Mod. Phys.
**1968**, 40, 441–507. [Google Scholar] [CrossRef] - Msezane, A.; Manson, S.T. New Minima in Photoionization Cross Section. Phys. Rev. Lett.
**1975**, 35, 364–366. [Google Scholar] [CrossRef] - Mamsom, S.T.; Cooper, J.W. Photo-Ionization in the Soft x-Ray Range: 1Z Dependence in a Central-Potential Model. Phys. Rev.
**1968**, 165, 126–138. [Google Scholar] [CrossRef] - McGuire, E.J. Photo-Ionization Cross Sections of the Elements Helium to Xenon. Phys. Rev.
**1968**, 175, 20–30. [Google Scholar] [CrossRef] - Amusia, M.; Chernysheva, L.; Yarzhemsky, V. Handbook of Theoretical Atomic Physics: Data for Photon Absorption, Electron Scattering, and Vacancies Decay; Springer Science & Business Media: Berlin/Heidelberg, Germany, 2012. [Google Scholar]
- Amusia, M.; Kheifets, A. The influence of “two-electron-two-hole excitation”s on the 3s
^{−1}4p autoionization profile in Ar atoms. Phys. Lett. A**1981**, 82, 407–411. [Google Scholar] [CrossRef] - Amusia, M.Y.; Ivanov, V.K.; Cherepkov, N.A.; Chernysheva, L.V. Interference effects in photoionization of noble gas atoms outer s-shells. Phys. Lett.
**1972**, 40A, 361–362. [Google Scholar] [CrossRef] - Toffoli, D.; Stener, M.; Fronzoni, G.; Decleva, P. Convergence of the multicenter B-spline DFT approach for the continuum. Chem. Phys.
**2002**, 276, 25–43. [Google Scholar] [CrossRef] - Marante, C.; Klinker, M.; Corral, I.; González-Vázquez, J.; Argenti, L.; Martín, F. Hybrid-Basis Close-Coupling Interface to Quantum Chemistry Packages for the Treatment of Ionization Problems. J. Chem. Theory Comput.
**2017**, 13, 499–514. [Google Scholar] [CrossRef] - Moitra, T.; Ponzi, A.; Koch, H.; Coriani, S.; Decleva, P. Accurate Description of Photoionization Dynamical Parameters. J. Phys. Chem. Lett.
**2020**, 11, 5330–5337. [Google Scholar] [CrossRef] - Kheifets, A.S. Time delay in valence-shell photoionization of noble-gas atoms. Phys. Rev. A
**2013**, 87, 063404. [Google Scholar] [CrossRef] - Palatchi, C.; Dahlstrom, J.M.; Kheifets, A.S.; Ivanov, I.A.; Canaday, D.M.; Agostini, P.; DiMauro, L.F. Atomic delay in helium, neon, argon and krypton. J. Phys. B At. Mol. Opt. Phys.
**2014**, 47, 245003. [Google Scholar] [CrossRef] - Alexandridi, C.; Platzer, D.; Barreau, L.; Busto, D.; Zhong, S.; Turconi, M.; Neoričić, L.; Laurell, H.; Arnold, C.L.; Borot, A.; et al. Attosecond photoionization dynamics in the vicinity of the Cooper minima in argon. Phys. Rev. Res.
**2021**, 3, L012012. [Google Scholar] [CrossRef] - Saha, S.; Mandal, A.; Jose, J.; Varma, H.R.; Deshmukh, P.C.; Kheifets, A.S.; Dolmatov, V.K.; Manson, S.T. Relativistic effects in photoionization time delay near the Cooper minimum of noble-gas atoms. Phys. Rev. A
**2014**, 90, 053406. [Google Scholar] [CrossRef] - Fano, U. Effects of Configuration Interaction on Intensities and Phase Shifts. Phys. Rev.
**1961**, 124, 1866–1878. [Google Scholar] [CrossRef] - Arimondo, E.; Clark, C.W.; Martin, W.C. Colloquium: Ettore Majorana and the birth of autoionization. Rev. Mod. Phys.
**2010**, 82, 1947–1958. [Google Scholar] [CrossRef] - Madden, R.P.; Codling, K. New Autoionizing Atomic Energy Levels in He, Ne, and Ar. Phys. Rev. Lett.
**1963**, 10, 516–518. [Google Scholar] [CrossRef] - Baig, M.A.; Connerade, J.P. Centrifugal barrier effects in the high Rydberg states and autoionising resonances of neon. J. Phys. B At. Mol. Phys.
**1984**, 17, 1785–1796. [Google Scholar] [CrossRef] - Maeda, K.; Ueda, K.; Ito, K. High-resolution measurement for photoabsorption cross sections in the autoionization regions of Ar, Kr and Xe. J. Phys. B At. Mol. Opt. Phys.
**1993**, 26, 1541–1555. [Google Scholar] [CrossRef] - Kabachnik, N.M.; Sazhina, I.P. Angular distribution and polarization of photoelectrons in the region of resonances. J. Phys. B At. Mol. Opt. Phys.
**1976**, 9, 1681–1697. [Google Scholar] [CrossRef] - Pratt, S.T.; Dehmer, P.M.; Dehmer, J.L. Three-photon excitation of autoionizing states of atomic xenon between the
^{2}∘_{3/2}and^{2}∘_{1/2}fine-structure thresholds. Phys. Rev. A**1987**, 35, 3793–3798. [Google Scholar] [CrossRef] - Blazewicz, P.R.; Stockdale, J.A.D.; Miller, J.C.; Efthimiopoulos, T.; Fotakis, C. Four-photon excitation of even-parity Rydberg states in krypton and xenon. Phys. Rev. A
**1987**, 35, 1092–1098. [Google Scholar] [CrossRef] - Koeckhoven, S.M.; Buma, W.J.; de Lange, C.A. Three-photon excitation of autoionizing states of Ar, Kr, and Xe between the
^{2}P_{3/2}and^{2}P_{1/2}ionic limits. Phys. Rev. A**1994**, 49, 3322–3332. [Google Scholar] [CrossRef] - Moccia, R.; Rahman, N.K.; Rizzo, A. Two-photon ionisation cross section calculations of noble gases: Results for Ne and Ar. J. Phys. B At. Mol. Opt. Phys.
**1983**, 16, 2737–2751. [Google Scholar] [CrossRef] - Saenz, A.; Lambropoulos, P. Theoretical two-, three- and four-photon ionization cross sections of helium in the XUV range. J. Phys. B At. Mol. Opt. Phys.
**1999**, 32, 5629–5637. [Google Scholar] [CrossRef] - Aloïse, S.; O’Keeffe, P.; Cubaynes, D.; Meyer, M.; Grum-Grzhimailo, A.N. Photoionization of Synchrotron-Radiation-Excited Atoms: Separating Partial Cross Sections by Full Polarization Control. Phys. Rev. Lett.
**2005**, 94, 223002. [Google Scholar] [CrossRef] - Petrov, I.; Peters, T.; Halfmann, T.; Aloıse, S.; O’Keeffe, P.; Meyer, M.; Sukhorukov, V.; Hotop, H. Lineshapes of the even ${\mathit{mp}}_{1/2}^{5}5n({p}^{\prime}/{f}^{\prime})$ autoionizing resonances of Ar, Kr and Xe. Eur. Phys. J. D
**2006**, 40, 181–193. [Google Scholar] [CrossRef] - O’Keeffe, P.; Bolognesi, P.; Mihelic, A.; Moise, A.; Richter, R.; Cautero, G.; Stebel, L.; Sergo, R.; Pravica, L.; Ovcharenko, E.; et al. Photoelectron angular distributions from polarized Ne
^{*}atoms near threshold. Phys. Rev. A**2010**, 82, 052522. [Google Scholar] [CrossRef] - O’Keeffe, P.; Gryzlova, E.V.; Cubaynes, D.; Garcia, G.A.; Nahon, L.; Grum-Grzhimailo, A.N.; Meyer, M. Isotopically Resolved Photoelectron Imaging Unravels Complex Atomic Autoionization Dynamics by Two-Color Resonant Ionization. Phys. Rev. Lett.
**2013**, 111, 243002. [Google Scholar] [CrossRef] [PubMed] - Bartschat, K.; Madison, D.H. Electron impact excitation of rare gases: Differential cross sections and angular correlation parameters for neon, argon, krypton and xenon. J. Phys. B At. Mol. Opt. Phys.
**1987**, 20, 5839–5863. [Google Scholar] [CrossRef] - Knight, R.D.; guo Wang, L. One-photon laser spectroscopy of the np and nf Rydberg series in xenon. J. Opt. Soc. Am. B
**1985**, 2, 1084–1087. [Google Scholar] [CrossRef] - L’Huillier, A.; Lompré, L.A.; Normand, D.; Morellec, J.; Ferray, M.; Lavancier, J.; Mainfray, G.; Manus, C. Spectroscopy of the np and nf even-parity Rydberg series in xenon by two-photon excitation. J. Opt. Soc. Am. B
**1989**, 6, 1644–1647. [Google Scholar] [CrossRef] - McCann, K.J.; Flannery, M.R. Photoionization of metastable rare-gas atoms (He
^{*},Ne^{*},Ar^{*},Kr^{*},Xe^{*}). Appl. Phys. Lett.**1977**, 31, 599–601. [Google Scholar] [CrossRef] - Kau, R.; Petrov, I.D.; Sukhorukov, V.L.; Hotop, H. Experimental and theoretical cross sections for photoionization of metastable atoms near threshold. J. Phys. B At. Mol. Opt. Phys.
**1996**, 29, 5673–5698. [Google Scholar] [CrossRef] - Kopeika, N.S.; Shuker, R.; Yerachmiel, Y.; Gabai, Y.; Ih, C.S. Observation of Cooper minima in excited-s-state photoionization cross sections in neon and argon. Phys. Rev. A
**1983**, 28, 1517–1526. [Google Scholar] [CrossRef] - Petrov, I.D.; Lagutin, B.M.; Sukhorukov, V.L.; Knie, A.; Ehresmann, A. Correlation and polarization effects in two-photon photoionization of Ar. Phys. Rev. A
**2016**, 93, 033408. [Google Scholar] [CrossRef] - Petrov, I.D.; Sukhorukov, V.L.; Hotop, H. Photoionization of excited Ne
^{*}(2p^{5}3p, J = 3) atoms near threshold. J. Phys. B At. Mol. Opt. Phys.**2008**, 41, 065205. [Google Scholar] [CrossRef] - Sukhorukov, V.L.; Petrov, I.D.; Schafer, M.; Merkt, F.; Ruf, M.W.; Hotop, H. Photoionization dynamics of excited Ne, Ar, Kr and Xe atoms near threshold. J. Phys. B At. Mol. Opt. Phys.
**2012**, 45, 092001. [Google Scholar] [CrossRef] [Green Version] - Gallagher, T.F. Quantum defect theory. In Rydberg Atoms; Cambridge Monographs on Atomic, Molecular and Chemical Physics; Cambridge University Press: Cambridge, UK, 1994; pp. 415–428. [Google Scholar] [CrossRef]
- Ojha, P.C.; Burke, P.G. Photoionisation of the 3p
^{5}4s excited states of argon. J. Phys. B At. Mol. Opt. Phys.**1983**, 16, 3513–3529. [Google Scholar] [CrossRef] - Petrov, I.D.; Sukhorukov, V.L.; Hollenstein, U.; Kaufmann, L.J.; Merkt, F.; Hotop, H. Autoionization dynamics of even Ar (3${p}_{1/2}^{5}{\mathit{np}}^{\prime},{\mathit{nf}}^{\prime}$) resonances: Comparison of experiment and theory. J. Phys. B At. Mol. Opt. Phys.
**2011**, 44, 025004. [Google Scholar] [CrossRef] - Gryzlova, E.V.; O’Keeffe, P.; Cubaynes, D.; Garcia, G.A.; Nahon, L.; Grum-Grzhimailo, A.N.; Meyer, M. Isotope effects in resonant two-color photoionization of Xe in the region of the 5p
^{5}(^{2}P_{1/2})4f[5/2]_{2}autoionizing state. N. J. Phys.**2015**, 17, 043054. [Google Scholar] [CrossRef] - McKenna, C.; van der Hart, H.W. Multiphoton ionization cross sections of neon and argon. J. Phys. B At. Mol. Opt. Phys.
**2003**, 37, 457–470. [Google Scholar] [CrossRef] - van der Hart, H.W.; Greene, C.H. Multichannel photoionization spectroscopy of Ar: Total cross section and threshold photoelectrons. Phys. Rev. A
**1998**, 58, 2097–2105. [Google Scholar] [CrossRef] - Hamonou, L.; Lysaght, M.A.; van der Hart, H.W. Influence of autoionizing states on the pulse-length dependence of strong-field Ne
^{+}photoionization at 38.4 eV. J. Phys. B At. Mol. Opt. Phys.**2010**, 43, 045601. [Google Scholar] [CrossRef] - Zhou, Z.; Chu, S.I. Time-dependent localized Hartree-Fock density-functional linear response approach for photoionization of atomic excited states. Phys. Rev. A
**2009**, 79, 053412. [Google Scholar] [CrossRef] - Edwards, A.K.; Rudd, M.E. Excitation of Auto-Ionizing Levels in Neon by Ion Impact. Phys. Rev.
**1968**, 170, 140–144. [Google Scholar] [CrossRef] - Olsen, J.O.; Anderson, N. Autoionizing levels in neon excited by low-energy heavy-ion impact. J. Phys. B At. Mol. Opt. Phys.
**1977**, 10, 101–110. [Google Scholar] [CrossRef] - Jureta, J.J.; Marinković, B.P.; Milosavljević, A.R.; Avaldi, L. Singly and doubly excited states in ejected electron spectra of neon at high incident electron energies. Eur. Phys. J. D
**2015**, 69, 74. [Google Scholar] [CrossRef] - Prince, K.C.; Allaria, E.; Callegari, C.; Cucini, R.; Ninno, G.D.; Mitri, S.D.; Diviacco, B.; Ferrari, E.; Finetti, P.; Gauthier, D.; et al. Coherent control with a short-wavelength free-electron laser. Nat. Photonics
**2016**, 10, 176. [Google Scholar] [CrossRef] - You, D.; Ueda, K.; Gryzlova, E.V.; Grum-Grzhimailo, A.N.; Popova, M.M.; Staroselskaya, E.I.; Tugs, O.; Orimo, Y.; Sato, T.; Ishikawa, K.L.; et al. New Method for Measuring Angle-Resolved Phases in Photoemission. Phys. Rev. X
**2020**, 10, 031070. [Google Scholar] [CrossRef] - Gryzlova, E.V.; Carpeggiani, P.; Popova, M.M.; Kiselev, M.D.; Douguet, N.; Reduzzi, M.; Negro, M.; Comby, A.; Ahmadi, H.; Wanie1, V.; et al. Influence of an atomic resonance on the coherent control of the photoionization process. Phys. Rev. Res.
**2022**, 4, 033231. [Google Scholar] [CrossRef] - Gryzlova, E.V.; Ma, R.; Fukuzawa, H.; Motomura, K.; Yamada, A.; Ueda, K.; Grum-Grzhimailo, A.N.; Kabachnik, N.M.; Strakhova, S.I.; Rouzée, A.; et al. Doubly resonant three-photon double ionization of Ar atoms induced by an EUV free-electron laser. Phys. Rev. A
**2011**, 84, 063405. [Google Scholar] [CrossRef] - Zatsarinny, O. BSR: B-spline atomic R-matrix codes. Comput. Phys. Commun.
**2006**, 174, 273–356. [Google Scholar] [CrossRef] - Fischer, C.F. Towards B-Spline Atomic Structure Calculations. Atoms
**2021**, 9, 50. [Google Scholar] [CrossRef] - Zatsarinny, O.; Bartschat, K. B-spline calculations of oscillator strengths in noble gases. Phys. Scr.
**2009**, T134, 014020. [Google Scholar] [CrossRef] - Zatsarinny, O.; Tayal, S.S. Photoionization of potassium atoms from the ground and excited states. Phys. Rev. A
**2010**, 81, 043423. [Google Scholar] [CrossRef] - Fischer, C.F.; Brage, T.; Johnsson, P. Computational Atomic Structure. An MCHF Approach; IOP Publishing: Bristol, UK, 1997. [Google Scholar]
- Zatsarinny, O.; Fischer, C.F. A general program for computing angular integrals of the Breit–Pauli Hamiltonian with non-orthogonal orbitals. Comput. Phys. Commun.
**2000**, 124, 247–289. [Google Scholar] [CrossRef] - Wilden, D.G.; Hicks, P.J.; Comer, J. Electron impact studies of resonances and autoionizing states of neon. J. Phys. B At. Mol. Phys.
**1977**, 10, 1477–1486. [Google Scholar] [CrossRef] - NIST Atomic Spectra Database (Version 5.8); National Institute of Standards and Technology: Gaithersburg, MD, USA, 2020. Available online: https://physics.nist.gov/asd (accessed on 18 May 2020).
- Zeman, V.; Bartschat, K. Electron-impact excitation of the and states of neon. J. Phys. B At. Mol. Opt. Phys.
**1997**, 30, 4609–4622. [Google Scholar] [CrossRef] - Khakoo, M.A.; Wrkich, J.; Larsen, M.; Kleiban, G.; Kanik, I.; Trajmar, S.; Brunger, M.J.; Teubner, P.J.O.; Crowe, A.; Fontes, C.J.; et al. Differential cross sections and cross-section ratios for the electron-impact excitation of the neon 2p
^{5}3s configuration. Phys. Rev. A**2002**, 65, 062711. [Google Scholar] [CrossRef] - Kheifets, A. Revealing the Target Electronic Structure with Under-Threshold RABBITT. Atoms
**2021**, 9, 66. [Google Scholar] [CrossRef] - Baier, S.; Grum-Grzhimailo, A.N.; Kabachnik, N.M. Angular distribution of photoelectrons in resonant photoionization of polarized atoms. J. Phys. B At. Mol. Opt. Phys.
**1994**, 27, 3363–3388. [Google Scholar] [CrossRef]

**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 $ |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

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