shelton_1982 ============ D\. P\. Shelton and A\. D\. Buckingham, Phys\. Rev\. A 26, 2787 \(1982\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/physreva\.26\.2787 `__ **Source kind:** measurement **Recorded technique:** Electric\-field\-induced second\-harmonic generation \(ESHG\) with periodic phase matching, cw argon\-ion laser \(about 1 W\), 158 electrode pairs \(N = 79, spacing l = 1\.27 mm\) in a stainless\-steel cell, confocal parameter z0 = 9\.2 cm; the gas density is adjusted to the peak of the phase\-matching curve, located to better than 0\.1 % in density; density from pressure \(Budenberg dead\-weight tester, or mercury manometer\) and temperature \(platinum resistance thermometer\) by the virial equation of state with second and third virial coefficients \(Dymond and Smith\); measurements near 20 C \(pp\. 2789\-2792\)\. **Materials in structured entries:** Ar, CH4, CO2, H2, He, N2, SF6 **Dataset quantities:** hyperpolarizability **Contents:** 9 datasets; 0 formulas. Curation notes -------------- NO DATASETS\: the linear\-dispersion content is the optimum phase\-matching density rho\_opt at a fixed wave\-vector mismatch \|Delta k\|\_opt = 2465\.0 \+\- 0\.5 m^\-1 \(Table II note b, Table III note b\), with Delta k = \(4 pi/lambda\_w\)\(n\_w \- n\_2w\) = \-\(2 pi/\(lambda\_w eps0\)\)\(alpha\_2w \- alpha\_w\) rho \(Eq\. \(5\)\), so \(alpha\_2w \- alpha\_w\) is proportional to 1/rho\_opt\. The vocabulary has no quantity for a phase\-match density at a stated \|Delta k\| \(FORMAT NEED\: e\.g\. 'phase\_match\_density', unit mol/m3, with parameters\.delta\_k\_per\_m and harmonic; phase\_mismatch\_per\_density would need 1/rho, not the printed number, and no ratio is printed\)\. The values are transcribed here from the library tables \(CSV cells; the images agree\)\. Table II \(tbl\_09cd9a18fa27\), at 514\.5 nm, rho\_opt \(mol m^\-3\) at \|Delta k\|\_opt = 2465\.0 \+\- 0\.5 m^\-1\: He 4690 \+\- 3, Ar 236\.8 \+\- 0\.2, H2 322\.7 \+\- 0\.2, N2 220\.7 \+\- 0\.2, CO2 125\.32 \+\- 0\.02, CH4 98\.97 \+\- 0\.02, SF6 127\.7 \+\- 0\.4 \(CH3F 121\.6, CHF3 174\.9, CF4 220\.8\: not curated species\); rho\_3K \(third spatial harmonic of the electrode field, Eq\. \(12\)\) at \|Delta k\_3K\|\_opt = 7412\.4 \+\- 1\.5 m^\-1\: CH4 297\.9 \+\- 0\.2 \(CH3F 367 \+\- 1\)\. Table III \(tbl\_e6603d44b34e\), rho\_He and rho\_CH4 \(mol m^\-3\) at \|Delta k\|\_opt = 2465\.0 m^\-1\: 694\.3 nm He 11620 \+\- 12 \(note d\: 'From Ref\. 1'\), CH4 270 \+\- 3 \(note e\: 'From Ref\. 4'\); 514\.5 nm He 4690 \+\- 3, CH4 98\.97 \+\- 0\.02; 501\.7 nm 4346 \+\- 2, 90\.71 \+\- 0\.08; 496\.5 nm 4205 \+\- 2, 87\.51 \+\- 0\.02; 488\.0 nm 3987 \+\- 2, 82\.26 \+\- 0\.04; 476\.5 nm 3698 \+\- 2, 75\.75 \+\- 0\.07; 457\.9 nm 3265 \+\- 2, 65\.58 \+\- 0\.07\. The 694\.3 nm values are other authors' \(Ref\. 1\: R\. S\. Finn and J\. F\. Ward, Phys\. Rev\. Lett\. 26, 285 \(1971\); Ref\. 4\: C\. K\. Miller and J\. F\. Ward, Phys\. Rev\. A 16, 1179 \(1977\)\), apparently converted to this \|Delta k\|; the paper does not say how\. Wavelengths\: the argon\-ion lines are printed at their standard air wavelengths \(514\.5, 501\.7, 496\.5, 488\.0, 476\.5, 457\.9 nm; ruby 694\.3 nm\), although Eq\. \(1\) defines lambda\_w as a vacuum wavelength \(shelton\_1986 prints the vacuum values 514\.7, 496\.6, 488\.1, 476\.6\)\. Accuracy\: the phase\-match density limited 'by the accuracy of the virial corrections, the gauge calibration, the sample purity, and the reproducibility of the peak\-position determination' \(p\. 2792\); the \+\- are those of the tables, level not stated\. The ratios of these densities between two gases at one wavelength \(e\.g\. rho\_He/rho\_CH4\) would be phase\_match\_density\_ratio data; they are not printed, so they are not stored\. Not extracted\: Table I \(phase\-matching peak parameters, theory\), the hyperpolarizabilities gamma, beta and gamma rho\_opt \(Tables II, III\)\. THIRD\-ORDER DATA \(added 2026\-09\-26; the "NO DATASETS" and "Not extracted" remarks above predate it and concern the linear data\)\. Definitions \(p\. 2788\)\: the second\-harmonic power is Eq\. \(3\), with the nonlinear susceptibility of the gas chi\_NL = \(1/4\) \[\(n\_omega^2 \+ 2\)/3\]^2 \[\(n\_2omega^2 \+ 2\)/3\] \[mu^\(0\) beta/3 k\_B T \+ gamma\] rho \(Eq\. 4\), rho the number density, beta and gamma 'the appropriate components of the first and second hyperpolarizability tensors' \(all fields parallel\), the static field E^\(0\) cos\(Kz\); the same gamma \(Taylor\-series convention, SI C^4 m^4 J^\-3\) as shelton\_1990\. Ratios\: R = \[gamma \+ mu beta/3kT\]\_A / \[\.\.\.\]\_B = \(S\_A/S\_B\)^\(1/2\) \(n\_B rho\_B\)/\(n\_A rho\_A\) \(Eq\. 13, p\. 2792; the printed Eq\. 13 shows no square root on the signal ratio, but Eq\. \(6\) makes the power quadratic in chi\_NL and the text says 'only the phase\-matching density and the square root of the second\-harmonic signal need to be measured' \(p\. 2792\); the tabulated gammas are unaffected\)\. Calibration\: gamma\_He of Sitz & Yaris \(ref 18\), 2\.950e\-63 C^4 m^4 J^\-3 at 514\.5 nm \(Table II note d\) and Table III's values at the other lines; 'the correct values of the hyperpolarizabilities could be recovered from the values in Table II by multiplying by the ratio of the new and old values of gamma\_He' \(p\. 2792\)\. Uncertainties exclude the He calibration \(~1 %\)\. Nondipolar molecules measured near 20 C; CH3F and CHF3 \(dipolar, 20\-170 C\) are not curated\. Parts\: the atoms electronic; the molecules total ESHG gamma\. Datasets\: table2\_\ \(Ar, H2, N2, CO2, SF6 at 514\.5 nm; CH4's Table II value is table3\_CH4's 514\.5 nm row\), table3\_CH4 \(six lines\), table3\_CH4\_miller\_ward \(694\.3 nm, reproduced\), table3\_He\_calc \(the calibrant, reproduced\), and text\_He\_absolute \(the direct absolute measurement, 2\.7 \+\- 0\.5e\-63 at 514\.5 nm, p\. 2791\)\. Also from the text \(p\. 2791\)\: the illustrative He parameters omega\_1 = 3\.9e16 rad/s, alpha\_0 = 2\.3e\-41 C^2 m^2 J^\-1, gamma\_0 = 2\.8e\-63 C^4 m^4 J^\-3 \(from Bogaard & Orr, ref 15; not extracted\)\. A text slip\: p\. 2797 prints \|Delta k\|\_opt = 0\.9965 \(pi/l\) = 2456\.0 \+\- 0\.5 m^\-1 while Tables II and III give 2465\.0 \+\- 0\.5 m^\-1; 0\.9965 pi / 1\.27 mm = 2465\.0 m^\-1, so the text's 2456\.0 transposes two digits \(the tables are right\)\. Later correction by the same group \(shelton\_1985\_sf6, p\. 319\)\: 'The values at lambda = 514\.5 nm in ref\. \[6\] \[this paper\] are systematically low by 1\.5% \[10\]' \(ref \[10\]\: Mizrahi & Shelton, then to be published\); not applied here \(the Table II values are as printed\)\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- shelton\_1982/table2\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_Ar", "material": "Ar", "file": "Ar/shelton_1982__table2_Ar.csv", "table": "tbl_09cd9a18fa27", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "electronic" } } Table II \(p\. 2793\)\: 10^63 gamma \(C^4 m^4 J^\-3\) measured by ESHG at 514\.5 nm, the ratio to He times the calibrant, near 20 C\. Calibrated against gamma\_He = 2\.950e\-63 C^4 m^4 J^\-3 at 514\.5 nm, 'Calculated value from Ref\. 18' \(Sitz & Yaris 1968; Table II note d\); 'Error estimates exclude the uncertainty of gamma\_He used for calibration' \(note a\), 'thought to be about 1%' \(p\. 2792\)\. Shelton & Rice 1994 rescale such values to Bishop & Pipin's He\. shelton\_1982/table2\_H2 ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_H2", "material": "H2", "file": "H2/shelton_1982__table2_H2.csv", "table": "tbl_09cd9a18fa27", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "total" } } Table II \(p\. 2793\)\: 10^63 gamma \(C^4 m^4 J^\-3\) measured by ESHG at 514\.5 nm, the ratio to He times the calibrant, near 20 C\. Calibrated against gamma\_He = 2\.950e\-63 C^4 m^4 J^\-3 at 514\.5 nm, 'Calculated value from Ref\. 18' \(Sitz & Yaris 1968; Table II note d\); 'Error estimates exclude the uncertainty of gamma\_He used for calibration' \(note a\), 'thought to be about 1%' \(p\. 2792\)\. Shelton & Rice 1994 rescale such values to Bishop & Pipin's He\. Total ESHG gamma \(vibration included; gamma = gamma \+ mu beta/3kT with mu = 0 for this molecule\)\. shelton\_1982/table2\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_N2", "material": "N2", "file": "N2/shelton_1982__table2_N2.csv", "table": "tbl_09cd9a18fa27", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "total" } } Table II \(p\. 2793\)\: 10^63 gamma \(C^4 m^4 J^\-3\) measured by ESHG at 514\.5 nm, the ratio to He times the calibrant, near 20 C\. Calibrated against gamma\_He = 2\.950e\-63 C^4 m^4 J^\-3 at 514\.5 nm, 'Calculated value from Ref\. 18' \(Sitz & Yaris 1968; Table II note d\); 'Error estimates exclude the uncertainty of gamma\_He used for calibration' \(note a\), 'thought to be about 1%' \(p\. 2792\)\. Shelton & Rice 1994 rescale such values to Bishop & Pipin's He\. Total ESHG gamma \(vibration included; gamma = gamma \+ mu beta/3kT with mu = 0 for this molecule\)\. shelton\_1982/table2\_CO2 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_CO2", "material": "CO2", "file": "CO2/shelton_1982__table2_CO2.csv", "table": "tbl_09cd9a18fa27", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "total" } } Table II \(p\. 2793\)\: 10^63 gamma \(C^4 m^4 J^\-3\) measured by ESHG at 514\.5 nm, the ratio to He times the calibrant, near 20 C\. Calibrated against gamma\_He = 2\.950e\-63 C^4 m^4 J^\-3 at 514\.5 nm, 'Calculated value from Ref\. 18' \(Sitz & Yaris 1968; Table II note d\); 'Error estimates exclude the uncertainty of gamma\_He used for calibration' \(note a\), 'thought to be about 1%' \(p\. 2792\)\. Shelton & Rice 1994 rescale such values to Bishop & Pipin's He\. Total ESHG gamma \(vibration included; gamma = gamma \+ mu beta/3kT with mu = 0 for this molecule\)\. shelton\_1982/table2\_SF6 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_SF6", "material": "SF6", "file": "SF6/shelton_1982__table2_SF6.csv", "table": "tbl_09cd9a18fa27", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "total" } } Table II \(p\. 2793\)\: 10^63 gamma \(C^4 m^4 J^\-3\) measured by ESHG at 514\.5 nm, the ratio to He times the calibrant, near 20 C\. Calibrated against gamma\_He = 2\.950e\-63 C^4 m^4 J^\-3 at 514\.5 nm, 'Calculated value from Ref\. 18' \(Sitz & Yaris 1968; Table II note d\); 'Error estimates exclude the uncertainty of gamma\_He used for calibration' \(note a\), 'thought to be about 1%' \(p\. 2792\)\. Shelton & Rice 1994 rescale such values to Bishop & Pipin's He\. Total ESHG gamma \(vibration included; gamma = gamma \+ mu beta/3kT with mu = 0 for this molecule\)\. shelton\_1982/table3\_CH4 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table3_CH4", "material": "CH4", "file": "CH4/shelton_1982__table3_CH4.csv", "table": "tbl_e6603d44b34e", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "total" } } Table III \(p\. 2793\)\: gamma\_CH4 by ESHG at the six argon\-ion lines 514\.5\-457\.9 nm \(the 514\.5 nm value is also Table II's\)\. Calibrated against gamma\_He = 2\.950e\-63 C^4 m^4 J^\-3 at 514\.5 nm, and at each wavelength the calculated gamma\_He of the same table \(table3\_He\_calc\), 'Calculated value from Ref\. 18' \(Sitz & Yaris 1968; Table II note d\); 'Error estimates exclude the uncertainty of gamma\_He used for calibration' \(note a\), 'thought to be about 1%' \(p\. 2792\)\. Shelton & Rice 1994 rescale such values to Bishop & Pipin's He\. Note c\: 'Error estimates exclude the uncertainty of gamma\_He'\. The authors see a resonance\-like feature at 20140 cm^\-1 \(width ~200 cm^\-1, Fig\. 5\), attributed tentatively to the Delta v = 8 CH\-stretch overtone \(20520 cm^\-1 expected\)\: measured Delta gamma^res/gamma^nonres = \+5e\-2 against a calculated 1e\-10 \(pp\. 2795\-2796\)\. Later ESHG work \(shelton\_1986\_ch4\) is the reference for CH4's dispersion\. shelton\_1982/table3\_CH4\_miller\_ward ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table3_CH4_miller_ward", "material": "CH4", "file": "CH4/shelton_1982__table3_CH4_miller_ward.csv", "table": "tbl_e6603d44b34e", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "C. K. Miller and J. F. Ward, Phys. Rev. A 16, 1179 (1977)" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "total" } } Table III note e\: the 694\.3 nm gamma\_CH4 = 196 \+\- 2 is 'From Ref\. 4' \(Miller & Ward 1977\), presumably rescaled to the same He calculation \(not stated\)\. shelton\_1982/table3\_He\_calc ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table3_He_calc", "material": "He", "file": "He/shelton_1982__table3_He_calc.csv", "table": "tbl_e6603d44b34e", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "P. Sitz and R. Yaris, J. Chem. Phys. 49, 3546 (1968)" ], "uncertainty": { "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "electronic" } } Table III note a\: 10^63 gamma\_He for ESHG, 'Calculated values from Ref\. 18 \[Sitz & Yaris 1968\]; assumed in calibrating the gamma\_CH4 measurements' \(694\.3\-457\.9 nm\)\. The old He calibration\: Bishop & Pipin's later curve \(shelton\_1990 Table II in SI, with its C corrected\) gives 2\.990e\-63 at 514\.5 nm \(19431 cm^\-1\), 1\.3 % above Sitz & Yaris's 2\.950 \(computed here, not a statement of the paper\)\. shelton\_1982/text\_He\_absolute ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "text_He_absolute", "material": "He", "table": "text", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-63, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "electronic" } } 1 inline points in the source record. p\. 2791\: 'Our experimentally determined value of gamma\_He at 514\.5 nm is 2\.7 \+\- 0\.5 x 10^\-63 C^4 m^4 J^\-3 in agreement with the computed value of 2\.95 \+\- 0\.03 x 10^\-63' \(Sitz & Yaris\)\. An absolute ESHG measurement from Eqs\. \(4\) and \(6\), with the factors \(2m \- 1\)/m ~ 2 for the ~30 longitudinal laser modes and 1\.14^2 for the cos Kz component of the electrode field \(Eq\. 12\)\. 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.