mahon_1979 ========== R\. Mahon, T\. J\. McIlrath, V\. P\. Myerscough and D\. W\. Koopman, IEEE J\. Quantum Electron\. 15, 444 \(1979\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1109/jqe\.1979\.1070036 `__ **Source kind:** theory **Recorded technique:** Refractive index of Ar, Kr and Xe from the near infrared to the first ionization limit, summing a Sellmeier term per allowed transition \(oscillator strengths of Natali et al\. for Ar and Kr, Geiger for Xe; r\_e = 2\.818e\-13 cm\) and a principal\-value integral over photoionization cross sections \(Marr and West; West and Morton; Huffman et al\. between the Xe 2P3/2 and 2P1/2 limits, taken as 7\.8e\-17 cm^2\); phase mismatch per atom for frequency tripling, C = Delta k / N = 2 pi \(n\_1 \- n\_3\) / \(lambda N\)\. **Materials in structured entries:** Ar, Kr, Xe **Dataset quantities:** hyperpolarizability, refractivity\_per\_density **Contents:** 7 datasets; 0 formulas. Curation notes -------------- The calculated values are given per atom, \(n \- 1\)/N in cm^3 \(printed as, e\.g\., 'n \- 1 = 1\.417 x 10^\-23 N'\), stored as refractivity per density; state nominal \(0 degrees C, 1 atm\) since the quantity does not depend on it to first order\. The calculation is checked against Leonard's compilation\: 'offset, being 1 percent above the experimental data in Ar, 5 percent below the data in Kr, and in Xe our predictions are 2 percent higher' \(p\. 3\), and 4 % below Smith et al\.'s krypton data to 1680 A\. Wavelengths are vacuum wavelengths in A\. Not extracted as datasets \(the package has no quantity for a phase mismatch per atom, and a negative refractivity cannot be a dataset\)\: Figs\. 1\-3 \(C\_Ar, C\_Kr, C\_Xe against the harmonic wavelength\); Table I \(krypton around 1215\.67 A, \(n\-1\)\_lines x 10^23/N = \-1\.9198 \.\.\. \-2\.4193, \(n\-1\)\_cont x 10^23/N = \+1\.3854 \.\.\. \+1\.3831, total \(n\-1\) x 10^24/N = \-5\.3439, \-6\.5221, \-7\.7486, \-9\.0272, \-10\.362 at 1214\.67, 1215\.17, 1215\.67, 1216\.17, 1216\.67 A; the library lost the caption 'Refractive index contribution for Kr around 1215\.67 A', read from the page\); Table II \(C\_Ar x 10^18 = 4\.330 \.\.\. 4\.279, C\_Kr x 10^17 = \-1\.092 \.\.\. \-1\.352, C\_Xe x 10^17 = 3\.937 \.\.\. 3\.599 over the same wavelengths\)\. Text values of C \(p\. 4\-5\), in cm^2 \(Delta k in cm^\-1 over N in cm^\-3; the unit is printed only once, 'C\_Ar = 2\.38 x 10^\-17 cm^2' at 887 A\)\: measured in pure Kr at 1216 A \(3647 A tightly focused, b = 0\.25 cm, optimum 40 Torr\) C\_Kr = \-1\.13e\-17; from Bjorklund's Xe tripling at 1182\.44 A \(b = 0\.755 cm, 2\.5 Torr\) C\_Xe = \-5\.99e\-17 and, phase\-matched with 77 Torr Ar, C\_Ar = 5\.54e\-18; calculated C\_Xe = \-6\.12e\-17 \(1182\.44 A\), \-6\.71e\-17 \(1181\.95 A\), \-5\.64e\-17 \(1182\.95 A\), C\_Ar = 5\.33e\-18 \(1182\.44 A\)\. The measured C values follow from the optimum pressure through b Delta k = \-2 and constrain n\(lambda\) \- n\(3 lambda\); they would need a phase\-mismatch quantity\. Calculated negative values\: xenon at 1450 A, n \- 1 = \-4\.57e\-23 N \('3 percent more negative than the experiment'\); krypton at 1215\.67 A, \-7\.75e\-24 N\. The text also restates Heddle et al\.'s argon values per atom \(\(2\.08 \+\- 0\.04\)e\-23 at 1210 \+\- 30 A, \(1\.21 \+\- 0\.01\)e\-23 at 1850 A, \(1\.22 \+\- 0\.01\)e\-23 at 1805 A; see heddle\_1963\) and discusses Chopra and Heddle's Xe Rayleigh scattering, dominated by Xe2 \(a cross section 3e5 times the atom's\), and their krypton value's wrong sign\. The library PDF begins with the reference list of the preceding article in the journal\. Third\-order data \(added 2026\-09\-26\)\: only the two calculated THG susceptibilities per atom at 1216 A \(Kr \-1\.1e\-36, Xe 2\.0e\-35 esu, PDF p\. 5\), whose 'details \.\.\. will be reported later'; Ar's is 'sufficiently smaller that we can ignore its contribution'\. They are near\-resonant values for VUV tripling, in Bjorklund's convention \(Eq\. \(1\), PDF p\. 2; Bjorklund's paper is not in the library\), recorded as check\. No measured third\-order values\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- mahon\_1979/theory\_Ar ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "theory_Ar", "material": "Ar", "table": "text", "quantity": "refractivity_per_density", "unit": "cm3", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "unknown", "use": "check" } 5 inline points in the source record. pp\. 3\-4\: calculated n \- 1 per atom for argon\: 1\.417e\-23 at 1500 A \('1\.2 percent above the experimental point of Chashchina'; 3\.4 % at 1140 A, 2\.5 % at 1100 A\), 1\.92e\-23 at 1215\.67 A, and 'over this finite wavelength range' of Heddle et al\.'s detectors \(1\.95 \+\- 0\.16\)e\-23 at 1210 \+\- 30 A, \(1\.26 \+\- 0\.03\)e\-23 at 1850 A, \(1\.25 \+\- 0\.03\)e\-23 at 1805 A; the \+\- \(sigma column, not declared\) is the spread over the band\. At 1850 A the text prints '\(1\.26 \+\- 0\.03\) \+\- 10^\-23', a misprint for 'x 10^\-23'\. mahon\_1979/theory\_Kr ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "theory_Kr", "material": "Kr", "table": "text", "quantity": "refractivity_per_density", "unit": "cm3", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "unknown", "use": "check" } 2 inline points in the source record. p\. 4\: calculated n \- 1 per atom for krypton, 2\.411e\-23 at 1500 A \('5 percent below the experimental data' of Chashchina and Shreider; 2\.5 % at 1350 A\) and 4\.028e\-23 at 1300 A \('0\.5 percent above'\)\. mahon\_1979/theory\_Xe ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "theory_Xe", "material": "Xe", "table": "text", "quantity": "refractivity_per_density", "unit": "cm3", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "unknown", "use": "check" } 1 inline points in the source record. p\. 4\: calculated n \- 1 per atom for xenon at 1500 A, 1\.057e\-22, '2 percent above the experimental value' \(Chashchina and Shreider\)\. At 1400 A the calculation is 7\.5 % higher, 5 % at 1350 A \(no values printed\)\. mahon\_1979/chashchina\_1968\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "chashchina_1968_Ar", "material": "Ar", "table": "text", "quantity": "refractivity_per_density", "unit": "cm3", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "unknown", "use": "reproduced", "reproduced_from": [ "G. I. Chashchina, V. I. Gladushchak and E. Ya. Shreider, Opt. Spektrosk. 24, 1008 (1968)" ] } 1 inline points in the source record. p\. 4\: 'The line displacement work of Chashchina gives n \- 1 = 1\.87 x 10^\-23 N' in the vicinity of 1216 A\. Also quoted by Ferrell et al\. 1987\. The original is not in the library\. mahon\_1979/chopra\_heddle\_1974\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "chopra_heddle_1974_Ar", "material": "Ar", "table": "text", "quantity": "refractivity_per_density", "unit": "cm3", "abscissa_unit": "angstrom", "wavelength_medium": "vacuum", "state": "1atm_0C", "density": "unknown", "use": "reproduced", "reproduced_from": [ "P. D. Chopra and D. W. O. Heddle, J. Phys. B 7, 2421 (1974)" ] } 1 inline points in the source record. p\. 4\: 'The Rayleigh scattering technique used by Chopra and Heddle implies n \- 1 = 1\.90 x 10^\-23 N' for argon at Lyman alpha \(a magnitude; positive for argon\)\. Also quoted by Ferrell et al\. 1987\. The original is not in the library, so this reproduction may be fitted\. mahon\_1979/chi3\_1216\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "chi3_1216_Kr", "material": "Kr", "table": "text", "quantity": "hyperpolarizability", "unit": "esu", "abscissa_unit": "angstrom", "use": "check", "parameters": { "process": "thg", "convention": "bjorklund_1975", "part": "electronic", "beyond_resonance": true } } 1 inline points in the source record. PDF p\. 5 \(journal p\. 448\), and repeated with Figs\. 4\-6 \(PDF p\. 6\)\: 'We have calculated third\-order susceptibilities for Xe and Kr at 1216 A in order to obtain conversion efficiencies; details of the calculations will be reported later\. We will use values chi\_Kr\(3\)\(1216 A\) = \-1\.1 x 10^\-36 ESU and chi\_Xe\(3\)\(1216 A\) = 2\.0 x 10^\-35 ESU\.' The THG susceptibility per atom \(it multiplies N in Eq\. \(1\)\) for tripling 3647 A to 1215\.67 A \(the wavelength column is the fundamental, 3647 A as printed in the abstract; the row is the harmonic, 1216 A\)\. Near\-resonant; the sign is negative\: at 1215\.67 A krypton is negatively dispersive \(n \- 1 = \-7\.75e\-24 N, PDF p\. 4\), i\.e\. the harmonic lies above a Kr resonance\. Convention Bjorklund's \(Eq\. \(1\), PDF p\. 2\: P\_3 = 8\.215e\-2 / \(3 lambda\)^4 \[chi\(3\)\(lambda\)\]^2 N^2 P\_1^3 F\_1, P in W, N in cm^\-3, lambda the harmonic wavelength in cm, chi in esu\); Bjorklund's definition of chi \(IEEE J\. Quantum Electron\. 11, 287 \(1975\)\) is not in the library, so the factor to gamma\_T is not established here\. A calculation used only for relative conversion efficiencies \('our results are not dependent on the accuracy of chi\(3\)'\)\: check\. Electronic\. mahon\_1979/chi3\_1216\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "chi3_1216_Xe", "material": "Xe", "table": "text", "quantity": "hyperpolarizability", "unit": "esu", "abscissa_unit": "angstrom", "use": "check", "parameters": { "process": "thg", "convention": "bjorklund_1975", "part": "electronic" } } 1 inline points in the source record. PDF p\. 5 \(journal p\. 448\), and repeated with Figs\. 4\-6 \(PDF p\. 6\)\: 'We have calculated third\-order susceptibilities for Xe and Kr at 1216 A in order to obtain conversion efficiencies; details of the calculations will be reported later\. We will use values chi\_Kr\(3\)\(1216 A\) = \-1\.1 x 10^\-36 ESU and chi\_Xe\(3\)\(1216 A\) = 2\.0 x 10^\-35 ESU\.' The THG susceptibility per atom \(it multiplies N in Eq\. \(1\)\) for tripling 3647 A to 1215\.67 A \(the wavelength column is the fundamental, 3647 A as printed in the abstract; the row is the harmonic, 1216 A\)\. Near\-resonant; the sign is positive\. Convention Bjorklund's \(Eq\. \(1\), PDF p\. 2\: P\_3 = 8\.215e\-2 / \(3 lambda\)^4 \[chi\(3\)\(lambda\)\]^2 N^2 P\_1^3 F\_1, P in W, N in cm^\-3, lambda the harmonic wavelength in cm, chi in esu\); Bjorklund's definition of chi \(IEEE J\. Quantum Electron\. 11, 287 \(1975\)\) is not in the library, so the factor to gamma\_T is not established here\. A calculation used only for relative conversion efficiencies \('our results are not dependent on the accuracy of chi\(3\)'\)\: check\. Electronic\. 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.