shelton_1985_sf6 ================ D\. P\. Shelton and V\. Mizrahi, Chem\. Phys\. Lett\. 120, 318 \(1985\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1016/0009\-2614\(85\)87065\-2 `__ **Source kind:** measurement **Recorded technique:** Electric\-field\-induced second\-harmonic generation \(ESHG\) with periodic phase matching\: a cw dye or argon\-ion laser \(0\.3\-2\.0 W\) weakly focused through a cell whose electrodes \(spacing 2\.69 mm\) reverse the static field every coherence length, the gas density being adjusted to phase match \(1\-6 atm\); sample SF6 \(99\.99 %\) and reference N2 \(99\.9995 %\); densities from pressure and temperature by the virial equation of state \(virial corrections about 2 % for SF6, Dymond and Smith\) \(pp\. 1\-2\)\. **Materials in structured entries:** N2, SF6 **Dataset quantities:** hyperpolarizability, hyperpolarizability\_ratio, phase\_match\_density\_ratio **Contents:** 4 datasets; 1 formula. Curation notes -------------- The paper's aim is the hyperpolarizability gamma; its by\-product, the ratio Delta alpha\_SF6 / Delta alpha\_N2 with Delta alpha = alpha\(2 omega\) \- alpha\(omega\), 'is just proportional to the phase match density rho measured' \(table note a\), i\.e\. it is the phase\-match density ratio rho\_N2 / rho\_SF6\. As in shelton\_1990 the printed number is filed under N2 as gas with SF6 as reference\_material \(the package's quantity is rho\_gas / rho\_reference\); parameters\.sample\_gas and shelton\_reference\_gas keep the paper's roles\. Wavelengths\: the fundamental, 670\.0, 650\.0, 620\.0 nm \(dye laser\) and 514\.5, 488\.0, 457\.9 nm \(argon\-ion lines as usually quoted in air\); the paper does not say, and standard air is assumed \(as the later papers of the series state, shelton\_1986\_ch4 and shelton\_1986\_co2\)\. Uncertainty\: \+\-0\.003 per ratio \(level not stated\); 'the accuracy of the overall measurement is chiefly determined by photon\-counting statistics' \(p\. 2\)\. The gamma values \(Table 1, fit gamma = A\(1 \+ B nu^2\), A = 8\.21e\-62 C^4 m^4 J^\-3, B = 8\.44e\-10 cm^2\) are hyperpolarizabilities and are not extracted\. The 694\.3 nm row holds only Ward and Miller's gamma\. The same ratio at 1064 and 1319 nm is in shelton\_1990 \(density\_N2\_over\_SF6\)\. THIRD\-ORDER DATA \(added 2026\-09\-26; supersedes the remark above that the gamma values are not extracted\)\. gamma\(\-2 omega; omega, omega, 0\), the ESHG gamma of Shelton's series \(Taylor\-series convention, SI C^4 m^4 J^\-3; shelton\_1990 and shelton\_1994 reproduce these values\), measured relative to N2 and put on an absolute scale with Mizrahi & Shelton's smoothed N2 curve \(ref \[10\]\)\. The authors note \(p\. 319\)\: 'The values at lambda = 514\.5 nm in ref\. \[6\] \[shelton\_1982\] are systematically low by 1\.5% \[10\]; when corrected, gamma\_SF6 from ref\. \[6\] coincides with the value reported here\.' Fit \(p\. 319\)\: gamma = A \(1 \+ B nu^2\), formula below \(nu the fundamental wavenumber, not nu\_L^2\)\. Relations between processes \(pp\. 319\-320\)\: gamma^elec = gamma\_0^elec \[1 \+ C \(omega/omega\_0\)^2\] \(Eq\. 2\) with C^THG \: C^ESHG \: C^Kerr = 6 \: 3 \: 1 \(Eq\. 3, Dawes; Finn\); the measured gamma^THG/gamma^ESHG of SF6 at 694\.3 nm is 1\.14 \+\- 0\.07 \(Elliott & Ward; Ward & Elliott\) against 1\.15 predicted from this dispersion, while gamma^ESHG/gamma^Kerr is measured 0\.65 \+\- 0\.06 against 1\.11 predicted, attributed to vibrational contributions to the Kerr gamma \(ratios between processes\: no quantity; recorded here only\)\. For H2 gamma\_0^vib/gamma\_0^elec = 0\.28 is quoted from Mizrahi & Shelton \(to be published\)\. **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\_1985\_sf6/density\_N2\_over\_SF6 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "density_N2_over_SF6", "material": "N2", "file": "N2/shelton_1985_sf6__density_N2_over_SF6.csv", "table": "tbl_72ec8b2e57c2", "quantity": "phase_match_density_ratio", "abscissa_unit": "nm", "wavelength_medium": "standard_air", "density": "real", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "SF6", "harmonic": 2, "process": "ESHG (electric-field-induced second-harmonic generation), periodic phase matching", "definition": "rho_gas / rho_reference_gas at equal wave-vector mismatch |Delta k| = (4 pi / lambda) |n(2w) - n(w)|; to first order in density = [alpha_ref(2w) - alpha_ref(w)] / [alpha_gas(2w) - alpha_gas(w)]; lambda = fundamental", "sample_gas": "SF6", "shelton_reference_gas": "N2", "printed_as": "Delta alpha_SF6 / Delta alpha_N2" } } Table 1, Delta alpha\_SF6 / Delta alpha\_N2 = rho\_N2 / rho\_SF6 as printed, six fundamental wavelengths 457\.9\-670\.0 nm\. shelton\_1985\_sf6/gamma\_SF6\_over\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_SF6_over_N2", "material": "SF6", "file": "SF6/shelton_1985_sf6__gamma_SF6_over_N2.csv", "table": "tbl_72ec8b2e57c2", "quantity": "hyperpolarizability_ratio", "unit": "1", "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "N2", "process": "eshg", "convention": "T", "part": "total" } } Table 1 \(p\. 319\)\: gamma\_SF6/gamma\_N2 by ESHG, as printed \(Eq\. 1\: gamma\_A/gamma\_B = \(S\_A/S\_B\)^\(1/2\) \(rho\_A n\_A / rho\_B n\_B\)^\-1, n = \(n\_0^4 n\_omega^\(2\+zeta\) n\_2omega\)^\(1/6\)\)\. The raw measurement behind gamma\_SF6\. 'The accuracy of the overall measurement is chiefly determined by photon\-counting statistics'; the 457\.9 nm error is large for lack of a filter \(p\. 319\)\. shelton\_1985\_sf6/gamma\_SF6 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_SF6", "material": "SF6", "file": "SF6/shelton_1985_sf6__gamma_SF6.csv", "table": "tbl_72ec8b2e57c2", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-62, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "total" } } Table 1 \(p\. 319\)\: gamma\_SF6 in 1e\-62 C^4 m^4 J^\-3, 'Obtained using the smoothed results given in ref\. \[10\]' for gamma\_N2 \(Mizrahi & Shelton, then to be published; the N2 ESHG curve of mizrahi\_1985\_arn2o2, itself calibrated against He\); 'The error bars given for gamma\_SF6 include allowance for \+\-0\.4% uncertainty in the calibration values of gamma\_N2' \(p\. 319\)\. Total ESHG gamma; 'The nu^2 dependence seen in these experiments substantiates the usual assumption that vibrational contributions to gamma are negligible at optical frequencies for ESHG' \(pp\. 319\-320; shelton\_1988 later finds gamma^v\_ESHG ~ \-3e\-62, not negligible\)\. shelton\_1990 Table III\(b\) reproduces these on its new He calibration \(e\.g\. 98\.2e\-63 against 9\.75e\-62 at 670 nm\)\. shelton\_1985\_sf6/gamma\_SF6\_ward\_miller ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_SF6_ward_miller", "material": "SF6", "file": "SF6/shelton_1985_sf6__gamma_SF6_ward_miller.csv", "table": "tbl_72ec8b2e57c2", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-62, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "ward_1979" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "total" } } Table 1 row 694\.3 nm, note c\)\: 'From ref\. \[12\]' \(Ward & Miller 1979\), ESHG, as converted by the authors\. Formulas -------- shelton\_1985\_sf6/fit ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "fit", "material": "SF6", "equation": "text, p. 319", "printed": "gamma = A (1 + B nu^2); A = (8.21 +- 0.09) x 10^-62 C^4 m^4 J^-3 and B = (8.44 +- 0.03) x 10^-10 cm^2, where nu is in cm^-1", "variable": "nu: vacuum wavenumber of the fundamental in cm^-1 (not nu_L^2: for ESHG nu_L^2 = 6 nu^2, so B corresponds to Shelton & Rice's A = B/6 = 1.41e-10 cm^2)", "process": "eshg", "convention": "T", "part": "total", "range": "457.9-694.3 nm (Table 1, including Ward & Miller's 694.3 nm point: 'the results are also presented graphically in fig. 1')", "coefficients": { "A": "8.21e-62", "B": "8.44e-10" }, "coefficient_units": { "A": "C^4 m^4 J^-3", "B": "cm^2" }, "calibration": "N2: Mizrahi & Shelton's smoothed gamma_N2 (ref [10]), on the old He calibration", "check": "Gives 9.753e-62 at 670.0 nm (14921 cm^-1 from the air wavelength) and 10.826e-62 at 514.5 nm against 9.75 +- 0.07 and 10.84 +- 0.04. Checked 2026-09-26." } Weighted least\-squares straight line against nu^2; A and B uncertainties as printed\. Superseded by shelton\_1990's refit \(gamma\_0 = 89\.10e\-63, A = 0\.500e\-10, B = 2\.124e\-20 against nu\_L^2, including 1064 and 1319 nm\)\. 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.