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 · Catalogue · 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#
{
"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#
{
"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+#
{
"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+#
{
"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+#
{
"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 review register for the checks and decisions.