mironov_2025 ============ A\. A\. Mironov, E\. G\. Gelfer, I\. I\. Tupitsyn, A\. Beck, M\. Jirka, O\. Klimo, S\. Meuren, G\. Oberreit, T\. Smorodnikova, R\. Taieb, S\. Weber, C\. Riconda, M\. Grech and S\. V\. Popruzhenko, "Strong\-field ionization in particle\-in\-cell simulations", arXiv\:2501\.11672v2 \(2025\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.48550/arXiv\.2501\.11672 `__ **Source kind:** theory **Recorded technique:** Tunnel \(PPT\) ionisation rates in particle\-in\-cell codes \(SMILEI\) and rate equations\: the m dependence, nonsequential pathways through inner subshells, and barrier\-suppression corrections \(Tong\-Lin, Kostyukov\-Artemenko\-Golovanov\), benchmarked on argon Ar8\+ \-\> Ar16\+; the asymptotic coefficients C\_n\*l of argon's ions from finite\-difference Hartree\-Fock orbitals compared with the Hartree and ADK formulas \(Appendix A\)\. **Materials in structured entries:** Ar, Ar\+ **Dataset quantities:** tunnelling\_structure\_coefficient **Contents:** 5 datasets; 0 formulas. Curation notes -------------- The library copy is the arXiv preprint 2501\.11672v2 \(21 PDF pages\); no journal version is in the library\. Authors as on the first page\. EXTRACTED\. Table III \(Appendix A, p\. 17\)\: C\_n\*l of Ar \(charge 0, 3p^6\: exact and ADK\) and Ar\+ \(charge 1, 3p^5\: exact, Hartree and ADK\)\. Ar2\+ \.\.\. Ar17\+ are not curated materials \(Table III gives them\: exact 0\.842, 0\.876, 0\.772, 0\.689 for 3p^4 \.\.\. 3p^1, 0\.954, 0\.88 for 3s^2, 3s, 0\.652 \.\.\. 0\.623 for 2p^6 \.\.\. 2p, 1\.043, 1\.018 for 2s^2, 2s, 1\.003, 1\.003 for 1s^2, 1s\)\. The neutral atom's Hartree entry '1\.0\*' is 'set manually, as Eq\. \(11\) is not applicable to neutral atoms \[Eq\. \(11\) can take zero or even a complex value in this case\]' \(p\. 17\)\: not a coefficient, not taken\. The relative errors Delta\_rel = \|C^exact \- C\|/C^exact are in the dataset notes\. THE NORMALISATION\. Eq\. \(8\), p\. 4, as printed\: psi\_n\*lm\(r\) ~ 2 C\_n\*l sqrt\(kappa\) \(kappa r\)^\(n\* \- 1\) e^\(\-kappa r\) Y\_lm\(r/r\), kappa = sqrt\(2 I\_p\) \(page image checked\: sqrt\(kappa\)\)\. Eq\. \(6\), the PPT rate\: w = 4 C\_n\*l^2 B\_l\|m\| I\_p \(2/F\(t\)\)^\(2n\* \- \|m\| \- 1\) exp\(\-2/\(3F\(t\)\)\), B\_l\|m\| = \(2l \+ 1\) Gamma\(l \+ \|m\| \+ 1\)/\(2^\|m\| Gamma\(\|m\| \+ 1\) Gamma\(l \- \|m\| \+ 1\)\), n\* = Z\*/sqrt\(2 I\_p\), Z\* = Z \+ 1, F = E/E\_ch, E\_ch = \(2 I\_p\)^\(3/2\) \(Eq\. \(7\)\)\. Eq\. \(11\), Hartree\: C\_n\*l^2 = 2^\(2n\* \- 2\)/\(n\* Gamma\(n\* \+ l \+ 1\) Gamma\(n\* \- l\)\)\. DOUBT\: for a hydrogen\-like ion \(R\_1s = 2 Z^\(3/2\) e^\(\-Z r\)\) Eq\. \(8\) as printed gives C = Z, whereas Eq\. \(6\) gives the exact hydrogen\-like static rate with C = 1 and Table III prints C = 1\.003 and 1\.0 for Ar17\+ \(1s, Z\* = 18\)\: the table's coefficients follow the rate, as if Eq\. \(8\) read kappa^\(3/2\) instead of sqrt\(kappa\)\. With kappa^\(3/2\), 2 C\_n\*l of this paper is ADK's C\_n\*l\* of Eq\. \(3\) of ammosov\_1986 \(Eq\. \(11\) here is ADK's Eq\. \(19\) divided by 4\)\. For Ar \(kappa = 1\.076 with tong\_2005's I\_p = 0\.579 au\) the two readings differ by 8 %, for Ar\+ \(kappa = 1\.426, I\_p = 1\.016 au\) by 43 %; it should be settled before converting to another normalisation\. The exact values are 'stable to 4\-5 significant digits' around the matching point \(p\. 17\); no other accuracy is stated\. OTHER CONTENT \(notes only\)\. Table I \(p\. 9\)\: I\_p \(au\), m and g\_\|m\| for three ionisation pathways of Ar8\+ \-\> Ar15\+ \(not curated charge states\), from the argon levels of ref\. 89\. Table II \(p\. 10\)\: the order of extraction of electrons by \|m\| and the factor g\_\|m\| \(2, 1, 4, 3, 2, 1, \.\.\.\), the number of electrons left with that \|m\|, multiplying the rate \(Eq\. \(19\)\); Nuter et al\.'s alternative, Eq\. \(16\), N/\(2l \+ 1\) sum\_m w, with N the electrons in the l\-shell \(footnote 3\: 'in the original work \[23\] the factor N/\(2l\+1\) is not present'\)\. Barrier suppression\: Tong\-Lin, Eq\. \(14\), w\_TL = w\_PPT exp\(\-\(alpha/8\) \(E/E\_BS\) n\*\), E\_BS = I\_p^2/\(4 Z\*\) \(Eq\. \(10\)\), used with alpha = 6 \(p\. 14; 'the best fit was achieved for hydrogen in the interval alpha = 6\.\.9', p\. 5, a loose reading of tong\_2005, whose alpha 6\-9 spans several atoms\); Kostyukov\-Artemenko\-Golovanov, Eq\. \(15\), with alpha\_1 = 2\.4 and alpha\_2 = 0\.8 'following Refs\. \[64, 83\]' \(p\. 6\)\: model constants, not argon properties\. Figures\: PIC and rate\-equation ion profiles of argon against peak field \(0\.8 um\)\. The rate Eq\. \(6\) is per electron in a given \(l, m\) state; the occupation enters as g\_\|m\| \(Eq\. \(19\)\) or N/\(2l \+ 1\) \(Eq\. \(16\)\), relevant to solprop's occupancy question \(TC\-439\)\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- mironov\_2025/exact\_Ar ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "exact_Ar", "material": "Ar", "file": "Ar/mironov_2025__exact_Ar.csv", "table": "tbl_bcc8c2bd802b", "quantity": "tunnelling_structure_coefficient", "abscissa": "label", "use": "check", "parameters": { "model": "adk", "orbital": "3p", "m": "not stated (the coefficient does not depend on m; Eq. (6) carries it)", "normalisation": "Mironov et al. 2025 Eq. (8), p. 4, as printed: psi_n*lm(r) ~ 2 C_n*l sqrt(kappa) (kappa r)^(n* - 1) exp(-kappa r) Y_lm(r/r), kappa = sqrt(2 I_p), n* = Z*/kappa, atomic units; the coefficient of the PPT rate Eq. (6), w = 4 C_n*l^2 B_l|m| I_p (2/F)^(2n* - |m| - 1) exp(-2/(3F)), F = E/(2 I_p)^(3/2) (see the record's notes on the sqrt(kappa))", "approximation": "exact" } } Table III \(p\. 17\), ion charge 0, configuration 3p^6\: C\_n\*l \(exact\) of the 3p orbital \(row l = 1\)\. 'C\_n\*l^exact is extracted from the numerical solution to the Schrodinger equation for asymptotic electron states' \(caption\)\: the finite\-difference Hartree\-Fock radial function matched to the hydrogen\-like tail \(Eq\. \(8\)\) where P\_nl^2 is 0\.01 of its maximum, stable to 4\-5 significant digits around that point, with the correction A = A\_HF \(gamma\_exp/gamma\)^\(Z\_a/gamma \+ 1/2\) \(Eq\. \(A2\)\) for the difference between the HF and experimental I\_p \(pp\. 16\-17\)\. mironov\_2025/adk\_Ar ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "adk_Ar", "material": "Ar", "file": "Ar/mironov_2025__adk_Ar.csv", "table": "tbl_bcc8c2bd802b", "quantity": "tunnelling_structure_coefficient", "abscissa": "label", "use": "check", "parameters": { "model": "adk", "orbital": "3p", "m": "not stated (the coefficient does not depend on m; Eq. (6) carries it)", "normalisation": "Mironov et al. 2025 Eq. (8), p. 4, as printed: psi_n*lm(r) ~ 2 C_n*l sqrt(kappa) (kappa r)^(n* - 1) exp(-kappa r) Y_lm(r/r), kappa = sqrt(2 I_p), n* = Z*/kappa, atomic units; the coefficient of the PPT rate Eq. (6), w = 4 C_n*l^2 B_l|m| I_p (2/F)^(2n* - |m| - 1) exp(-2/(3F)), F = E/(2 I_p)^(3/2) (see the record's notes on the sqrt(kappa))", "approximation": "ADK" } } Table III \(p\. 17\), ion charge 0, configuration 3p^6\: C\_n\*l \(ADK\) of the 3p orbital \(row l = 1\)\. The ADK variant of Eq\. \(11\), l replaced by l\* = n\* \- 1 \(the B\_l\|m\| factor keeps l; p\. 16\)\. Table III's relative error against the exact value\: 0\.015\. mironov\_2025/exact\_Ar\+ ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "exact_Ar+", "material": "Ar+", "file": "Ar+/mironov_2025__exact_Ar+.csv", "table": "tbl_bcc8c2bd802b", "quantity": "tunnelling_structure_coefficient", "abscissa": "label", "use": "check", "parameters": { "model": "adk", "orbital": "3p", "m": "not stated (the coefficient does not depend on m; Eq. (6) carries it)", "normalisation": "Mironov et al. 2025 Eq. (8), p. 4, as printed: psi_n*lm(r) ~ 2 C_n*l sqrt(kappa) (kappa r)^(n* - 1) exp(-kappa r) Y_lm(r/r), kappa = sqrt(2 I_p), n* = Z*/kappa, atomic units; the coefficient of the PPT rate Eq. (6), w = 4 C_n*l^2 B_l|m| I_p (2/F)^(2n* - |m| - 1) exp(-2/(3F)), F = E/(2 I_p)^(3/2) (see the record's notes on the sqrt(kappa))", "approximation": "exact" } } Table III \(p\. 17\), ion charge 1, configuration 3p^5\: C\_n\*l \(exact\) of the 3p orbital \(row l = 1\)\. 'C\_n\*l^exact is extracted from the numerical solution to the Schrodinger equation for asymptotic electron states' \(caption\)\: the finite\-difference Hartree\-Fock radial function matched to the hydrogen\-like tail \(Eq\. \(8\)\) where P\_nl^2 is 0\.01 of its maximum, stable to 4\-5 significant digits around that point, with the correction A = A\_HF \(gamma\_exp/gamma\)^\(Z\_a/gamma \+ 1/2\) \(Eq\. \(A2\)\) for the difference between the HF and experimental I\_p \(pp\. 16\-17\)\. mironov\_2025/hartree\_Ar\+ ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "hartree_Ar+", "material": "Ar+", "file": "Ar+/mironov_2025__hartree_Ar+.csv", "table": "tbl_bcc8c2bd802b", "quantity": "tunnelling_structure_coefficient", "abscissa": "label", "use": "check", "parameters": { "model": "adk", "orbital": "3p", "m": "not stated (the coefficient does not depend on m; Eq. (6) carries it)", "normalisation": "Mironov et al. 2025 Eq. (8), p. 4, as printed: psi_n*lm(r) ~ 2 C_n*l sqrt(kappa) (kappa r)^(n* - 1) exp(-kappa r) Y_lm(r/r), kappa = sqrt(2 I_p), n* = Z*/kappa, atomic units; the coefficient of the PPT rate Eq. (6), w = 4 C_n*l^2 B_l|m| I_p (2/F)^(2n* - |m| - 1) exp(-2/(3F)), F = E/(2 I_p)^(3/2) (see the record's notes on the sqrt(kappa))", "approximation": "Hartree" } } Table III \(p\. 17\), ion charge 1, configuration 3p^5\: C\_n\*l \(Hartree\) of the 3p orbital \(row l = 1\)\. The Hartree asymptotic formula Eq\. \(11\), C\_n\*l^2 = 2^\(2n\* \- 2\)/\(n\* Gamma\(n\* \+ l \+ 1\) Gamma\(n\* \- l\)\), with the orbital's l\. Table III's relative error against the exact value\: 0\.534\. mironov\_2025/adk\_Ar\+ ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "adk_Ar+", "material": "Ar+", "file": "Ar+/mironov_2025__adk_Ar+.csv", "table": "tbl_bcc8c2bd802b", "quantity": "tunnelling_structure_coefficient", "abscissa": "label", "use": "check", "parameters": { "model": "adk", "orbital": "3p", "m": "not stated (the coefficient does not depend on m; Eq. (6) carries it)", "normalisation": "Mironov et al. 2025 Eq. (8), p. 4, as printed: psi_n*lm(r) ~ 2 C_n*l sqrt(kappa) (kappa r)^(n* - 1) exp(-kappa r) Y_lm(r/r), kappa = sqrt(2 I_p), n* = Z*/kappa, atomic units; the coefficient of the PPT rate Eq. (6), w = 4 C_n*l^2 B_l|m| I_p (2/F)^(2n* - |m| - 1) exp(-2/(3F)), F = E/(2 I_p)^(3/2) (see the record's notes on the sqrt(kappa))", "approximation": "ADK" } } Table III \(p\. 17\), ion charge 1, configuration 3p^5\: C\_n\*l \(ADK\) of the 3p orbital \(row l = 1\)\. The ADK variant of Eq\. \(11\), l replaced by l\* = n\* \- 1 \(the B\_l\|m\| factor keeps l; p\. 16\)\. Table III's relative error against the exact value\: 0\.05\. Formulas -------- No formulas are recorded. Corrections ----------- No dataset errata are recorded in this source record. Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the :doc:`review register ` for the checks and decisions.