golovanov_2020
==============

A\. A\. Golovanov and I\. Yu\. Kostyukov, "Formula for the ionisation rate of an atom or ion in a strong electromagnetic field for numerical simulation", Quantum Electron\. 50, 350 \(2020\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/golovanov_2020.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1070/qel17309 <https://doi.org/10.1070/qel17309>`__

**Source kind:** theory

**Recorded technique:** A piecewise static\-field ionisation rate for particle\-in\-cell codes\: the tunnelling \(PPT/ADK\) rate at low field, Bauer and Mulser's quadratic rate in the transition region and the barrier\-suppression \(BSI\) linear rate at high field, joined where they cross \(Eq\. \(6\)\); compared with published one\-electron TDSE rates for H, He, Ne and Ar \(Fig\. 2\)\.

**Materials in structured entries:** None recorded.

**Dataset quantities:** None recorded.

**Contents:** 0 datasets; 0 formulas.

Curation notes
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Pages are pdf pages\: pdf page 1 is the IOPscience download cover, so pdf pp\. 2\-5 are journal pp\. 350\-353 \(translation of Kvantovaya Elektronika 50 \(4\) 350\-353\)\. Identity checked against pdf p\. 2\. Gaussian units\.

WHY NOTHING IS TAKEN\. No table; the comparison is Fig\. 2 \(p\. 4\)\: w\_i \(arb\. units\) against E/E\_cr from 1 to 100 \(static fields\) for \(a\) H, \(b\) He, \(c\) Ne, \(d\) Ar, with TDSE points of Bauer and Mulser, Phys\. Rev\. A 59, 569 \(1999\) \[21\] \(squares\) and Zhang, Lan and Lu, Phys\. Rev\. A 90, 043410 \(2014\) \[22\] \(circles\), and curves 1 = Eq\. \(6\), 2 = Eq\. \(3\), 3 = Eq\. \(1\), 4 = Eq\. \(5\), 5 = the formula of Tong and Lin 2005 \[20\], 6 = Eq\. \(3\) with 1\.4 in place of 0\.8\. The Ip, l and m used for He, Ne and Ar are not given\. \(The library's unlabelled figure on p\. 4 is a duplicate crop of Fig\. 2 panels \(a\) and \(c\)\.\) Zhang, Lan and Lu's points are curated as zhang\_2014 \(Tables IX and X, the static rates of Ar and Ar\+\); Bauer and Mulser's paper is not in the library\.

KEY FORMULAS \(p\. 3, checked against the equation image eq\_38c11320ba48\.jpg; for review\)\: \- Eq\. \(1\), tunnelling \[14\-16\]\: w\_TI\(F\) = w\_a k^2 C\_kl^2 \(2l \+ 1\) \(2/F\)^\(2n\*\) \(F/2\)^\(m\+1\) \(l \+ m\)\!/\(2^m m\! \(l \- m\)\!\) exp\(\-2/\(3F\)\), C\_kl^2 = 2^\(2n\*\)/\(n\* Gamma\(n\* \+ l\* \+ 1\) Gamma\(n\* \- l\*\)\); F = E/\(k^3 E\_a\) the instantaneous normalised field, k^2 = I\_i/I\_H, n\* = Z/k, l\* = n\* \- 1, Z the charge number of the ion, l and m the orbital and magnetic quantum numbers; I\_H = m\_e e^4/\(2 hbar^2\) ~ 13\.6 eV, E\_a = m\_e^2 e^5 hbar^\-4 ~ 5\.1 x 10^9 V/cm, w\_a = m\_e e^4 hbar^\-3 ~ 4\.1 x 10^16 s^\-1\. Valid for gamma\_K \<\< 1, E \<\< E\_cr, the instantaneous \(not cycle\-averaged\) field\. FINDING \(computed 2026\-09\-26\)\: with k^2 = I\_i/I\_H, w\_a k^2 = 2 I\_p in atomic units, where the quasistatic ADK rate with the same coefficients A = C\_kl^2 and B \(yudin\_2001 Eq\. \(1\) at cos phi = 1\) has I\_p\: Eq\. \(1\) as printed is twice that rate \(for atomic hydrogen, k = n\* = 1, l = m = 0, it gives 8/F exp\(\-2/\(3F\)\) w\_a\)\. Whether the factor 2 is intended is not said\. \- Eq\. \(2\)\: W\_i\(t\) = 1 \- exp{\-int\_\-inf^t w\_i\[E\(t'\)\] dt'}\. \- Barrier suppression sets in above E\_cr = E\_a k^4/\(16 Z\); for hydrogen E\_a/16 ~ 3\.2 x 10^8 V/cm, 1\.4 x 10^14 W/cm^2 \(p\. 3\)\. \- Eq\. \(3\), BSI high\-field limit \(E \>\> E\_cr\), from classical \[10\] and quantum \[18\] calculations\: w\_BSI\(E\) ~ 0\.8 w\_a \(E/E\_a\) sqrt\(I\_H/I\_i\)\. \- Eq\. \(4\), the earlier piecewise rate of \[18\]\: w\_TI for E \<= E0, w\_BSI for E \> E0, with w\_TI\(E0\) = w\_BSI\(E0\); 'small accuracy in the transition region' \(p\. 3\)\. \- Eq\. \(5\), Bauer and Mulser \[21\]\: w\_BM ~ 2\.4 w\_a \(E/E\_a\)^2 \(I\_H/I\_i\)^2, 'verified approximation only for a hydrogen atom and hydrogen\-like ions' \(I\_i = Z^2 I\_H\); its use for other atoms by substituting I\_i is the authors' assumption \(p\. 3\)\. \- Eq\. \(6\), the proposed rate\: w\_TI for E \<= E1, w\_BM for E1 \< E \<= E2, w\_BSI for E \> E2, with w\_TI\(E1\) = w\_BM\(E1\) and w\_BM\(E2\) = w\_BSI\(E2\)\. Curves 3 and 4 of Fig\. 2 cross twice \(near E/E\_cr ~ 1\-2 and ~10\-20\); the paper does not say which crossing is E1\.

ACCURACY \(qualitative only\)\: for H the formula and the numerics 'agree fairly well', linear at high field but with different coefficients \(p\. 4\); Eq\. \(5\) is 'a fairly good approximation' in the transition region for He, Ne and Ar \(p\. 4\); the \[22\] data do not reach E \>\> E\_cr, so the linear branch is tested for H only \(p\. 4\); 'good agreement \.\.\. hydrogen, helium, neon and argon; however, additional studies are needed' for other species \(p\. 5\)\. In the BSI regime the rate depends on the field history, so w\_i\(E\) is an approximation \(p\. 4\)\. Keldysh\: E\_K = omega\_las \(2 m\_e I\_i\)^\(1/2\)/e, gamma\_K = E\_K/E\_max \(p\. 2\)\. References 9 and 29 are printed identically \(Tamburini et al\. 2017\)\.

**Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets
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No datasets are recorded.

Formulas
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No formulas are recorded.

Corrections
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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 </register>` for the checks and decisions.