pan_1990
========

L\. Pan, K\. T\. Taylor and C\. W\. Clark, "Perturbation theory study of high\-harmonic generation", J\. Opt\. Soc\. Am\. B 7, 509 \(1990\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/pan_1990.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1364/josab\.7\.000509 <https://doi.org/10.1364/josab.7.000509>`__

**Source kind:** theory

**Recorded technique:** Lowest\- and next\-lowest\-order perturbation theory for harmonic generation by hydrogenic ions \(Z scaling, Eq\. 10\)\: the q\-th order susceptibility chi\_q\(\-q omega; omega, \.\.\., omega\) as the sum over the q \+ 1 time orderings of the q\-th order perturbed wave functions \(Eqs\. 1\-5\), solved as inhomogeneous equations in a Sturmian basis \(Appendix A\) with complex coordinate rotation above threshold; the next order chi\_q^\(2\) \(coefficient of F^\(q\+2\)\) gives critical intensities\. Hydrogen 1s in a Nd\:YAG \(1064 nm\) field, 3 \<= q \<= 33 \(q \<= 29 at next order\)\.

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

**Dataset quantities:** None recorded.

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

Curation notes
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Pages\: PDF page n is journal page 508 \+ n \(pp\. 509\-516\)\. Identity checked against the first page \(J\. Opt\. Soc\. Am\. B 7, No\. 4, April 1990\)\.

NOTHING TAKEN\. The paper is about atomic hydrogen and harmonic generation; it prints no two\-photon ionisation cross section of any gas\. The 'Pan et al\.' that McKenna and van der Hart cite for argon's two\-photon cross section \('within 20% of 0\.85 x 10^\-50 cm4 s', mckenna\_2004 p\. 465\) is a different paper by different authors\: McKenna's reference list prints 'Pan C, Gao B and Starace A F 1990 Phys\. Rev\. A 41 6271' \(C\. Pan, B\. Gao and A\. F\. Starace; mckenna\_2004's notes\), not in the library\. This paper's first author is Liwen Pan, and it shares the year and the surname only\.

WHAT IT HOLDS\. Table 1 \(p\. 512, tbl\_be7ea64a3db8, checked against the image\)\: for H 1s at 1064 nm, \|chi\_q\| \(a\.u\.\) for q = 3\-33 \(2\.78\(2\) at q = 3 to 3\.01\(51\) at q = 33\), \|chi\_q^\(2\)\| \(a\.u\.\) for q = 3\-29, the critical intensities I\_c\(q\) of Eq\. 15 \(q = 3\-31\) and I\_c'\(q\) of Eq\. 21 \(q = 3\-29\)\. Fig\. 1\: chi\_3 against the energy of the highest virtual state with the fit functions a\(eps\), b\(eps\) of Eqs\. 11\-13 \(no coefficients printed\); Fig\. 2\: \|chi\_21\|^2 against the effective quantum number; Figs\. 3\-4\: relative harmonic yields and I\_c\. Not taken\: these are harmonic\-generation susceptibilities of atomic hydrogen in the paper's own normalisation \(Eq\. 1\: the bare sum over the q \+ 1 time orderings, no prefactor\), not the Taylor\-series gamma the third\-order quantities use, and hydrogen's third\-order response is not curated\. Table 2 \(p\. 513, tbl\_e9d1ec768f53\), 'Ionization Potentials U, Static Polarizabilities alpha, and Low\-Order Susceptibilities chi\_q of Hydrogen and the Noble Gases at the Nd\:YAG Frequency'\: He\-Xe U to 0\.1 eV, alpha \(Miller and Bederson 1977, Ref\. 14\) and the noble\-gas chi\_3, chi\_5, chi\_7 \(esu\) 'reported in Ref\. 2' \(X\. F\. Li, A\. L'Huillier, M\. Ferray, L\. A\. Lompré and G\. Mainfray, Phys\. Rev\. A 39, 5751 \(1989\), not in the library\), with hydrogen's \(chi\_3 1\.4e\-37, chi\_5 1\.5e\-49, chi\_7 1\.2e\-60 esu\)\: all but the hydrogen row reproduced, rounded; not taken\.

INTERNAL INCONSISTENCIES \(text against Table 1, as printed\)\: p\. 512 says 'the highest is I\_c\(31\) = 2\.77 x 10^14 W/cm^2', the table prints 3\.77 \(14\); p\. 513 says 'The lowest value among them is I\_c\(19\) = 1\.66 x 10^11 W/cm^2' of the next\-order I\_c'\(q\), the table prints I\_c'\(19\) = 1\.79 \(11\) and I\_c'\(21\) = 1\.66 \(11\)\. No values taken, so no errata\.

FURTHER TWO\-PHOTON DATA CITED\: M\. Fink and P\. Zoller, Phys\. Rev\. A 39, 2933 \(1989\), 'A quantum defect parameterization of perturbative two photon ionization cross sections' \(Ref\. 12, for the analytic structure of Eq\. 11\), not in the library\.

**Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. 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.