shelton_1989 ============ D\. P\. Shelton, Phys\. Rev\. Lett\. 62, 2660 \(1989\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/physrevlett\.62\.2660 `__ **Source kind:** measurement **Recorded technique:** Gas\-phase electric\-field\-induced second\-harmonic generation \(ESHG\) with periodic phase matching, as in Shelton and Lu \(1988\), with a cw Nd\:YAG laser Q\-switched at 5 kHz \(1 kW pulses\) at 1064 and 1319 nm; electrode spacing increased 6 or 9 times to keep the phase\-match pressures below 60 atm \(Ne\) and 110 atm \(He reference\); Ne measured against He \(pp\. 2660\-2661\)\. **Materials in structured entries:** He, Ne **Dataset quantities:** hyperpolarizability, hyperpolarizability\_ratio, phase\_match\_density\_ratio **Contents:** 11 datasets; 2 formulas. Curation notes -------------- Table I gives, besides hyperpolarizability ratios, the linear\-dispersion ratios Delta alpha\_Ne / Delta alpha\_He with Delta alpha = alpha\(2 nu\) \- alpha\(nu\), 'determined from phase\-match density measurements, except for the result given by Ref\. 18 which was calculated from refractive index data in the literature' \(caption\)\. At equal phase mismatch, rho\_He / rho\_Ne = Delta alpha\_Ne / Delta alpha\_He to first order in density, so the printed ratio is stored as phase\_match\_density\_ratio of He with reference gas Ne without inversion \(the convention of shelton\_1990, TC\-27\)\. The second\-harmonic process is ESHG \(harmonic 2\)\. Densities from pressure and temperature by the virial equation of state \(as in Shelton's other work; not restated here\)\. Abscissa\: the vacuum wavenumber nu of the fundamental \(cm^\-1\), printed beside lambda\. The lambda column's '488\.8' is inconsistent with nu = 20487 cm^\-1 and nu\_L^2 = 25\.183e8 \(= 6 nu^2\), which belong to the 488\.0 nm argon line \(lambda in air\); the wavenumbers are used, so no correction of the data is needed\. The other lambdas \(1319, 1064, 694\.3, 594\.5, 514\.5\) are consistent with nu as air wavelengths\. The present\-work values \(1319 and 1064 nm\) are identical to Shelton \(1990\) Table I \(shelton\_1990/density\_He\_over\_Ne, 1\.853\(4\) and 1\.850\(7\)\), the 'more complete account' announced here as Ref\. 16\: the same measurements\. They are kept here as a check so as not to count them twice \(the other record could be made primary\)\. The Shelton and Lu \(1988\) values are reproduced \(the original, Phys\. Rev\. A 37, 3813, is not in the library, so this copy is the best available\)\. The Finn and Ward \(1971\) value is calculated from literature refractive indices, not measured\: excluded\. Uncertainties\: the \+\- of Table I, level not stated\. The ratio 'shows the expected slow monotonic increase with nu' and rules out significant sample impurities \(p\. 2661\)\. Not extracted \(not refractive data\)\: the gamma\_Ne/gamma\_He ratios and the fit A = 2\.753, B = \-2\.251e\-10 cm^2, C = 6\.609e\-20 cm^4 \(Fig\. 1 caption\), gamma\_Ne = 115\.8 a\.u\. static\. THIRD\-ORDER DATA \(added 2026\-09\-26; supersedes the "Not extracted" paragraph above\)\. The gamma\_Ne/gamma\_He ratios of Table I by source and process, the Fig\. 1 fits \(formulas\) and the static values of the text\. THE ANOMALY IS SPURIOUS\: shelton\_1992 shows that the Shelton & Lu \(1988\) visible ESHG ratios behind the non\-monotonic curve were corrupted by an unnoticed electrical breakdown in neon; they are excluded here, and the fits and the static 116 au are kept for the record only\. gamma is the ESHG gamma of Shelton's series \(Taylor convention\); gamma\_Ne in au uses 1 au = 6\.23538e\-65 C^4 m^4 J^\-3 \(Fig\. 1 caption\) and Bishop & Lam's ab initio gamma\_He \(Ref\. 8\: Phys\. Rev\. A 37, 464 \(1988\)\)\. The processes are compared at nu\_L^2 = nu\_s^2 \+ nu\_1^2 \+ nu\_2^2 \+ nu\_3^2 \(4\.992 for dc Kerr at 632\.8 nm, 6 nu^2 for ESHG, 12 nu^2 for THG, as printed\)\. Parts\: atoms, electronic\. **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\_1989/present\_He\_over\_Ne ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "present_He_over_Ne", "material": "He", "file": "He/shelton_1989__present_He_over_Ne.csv", "table": "tbl_96462ca3eb80", "quantity": "phase_match_density_ratio", "abscissa_unit": "cm-1", "density": "real", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "Ne", "harmonic": 2, "process": "ESHG (electric-field-induced second-harmonic generation), periodic phase matching", "definition": "rho_gas / rho_reference_gas at equal wave-vector mismatch; to first order in density = [alpha_ref(2w) - alpha_ref(w)] / [alpha_gas(2w) - alpha_gas(w)] = Delta alpha_Ne / Delta alpha_He as printed; wavenumber = fundamental (vacuum)", "sample_gas": "Ne", "shelton_reference_gas": "He" } } Table I, present work \(a\)\: Delta alpha\_Ne / Delta alpha\_He = rho\_He / rho\_Ne at 7581 cm^\-1 \(1319 nm\) and 9395 cm^\-1 \(1064 nm\)\. Identical to shelton\_1990/density\_He\_over\_Ne \(same measurements, source notes\)\: a check\. shelton\_1989/shelton\_lu\_1988\_He\_over\_Ne ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "shelton_lu_1988_He_over_Ne", "material": "He", "file": "He/shelton_1989__shelton_lu_1988_He_over_Ne.csv", "table": "tbl_96462ca3eb80", "quantity": "phase_match_density_ratio", "abscissa_unit": "cm-1", "density": "real", "use": "reproduced", "reproduced_from": [ "D. P. Shelton and Z. Lu, Phys. Rev. A 37, 3813 (1988)" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "Ne", "harmonic": 2, "process": "ESHG (electric-field-induced second-harmonic generation), periodic phase matching", "definition": "rho_gas / rho_reference_gas at equal wave-vector mismatch; to first order in density = [alpha_ref(2w) - alpha_ref(w)] / [alpha_gas(2w) - alpha_gas(w)] = Delta alpha_Ne / Delta alpha_He as printed; wavenumber = fundamental (vacuum)", "sample_gas": "Ne", "shelton_reference_gas": "He" } } Table I, Ref\. 15\: Delta alpha\_Ne / Delta alpha\_He at 16817, 19430 and 20487 cm^\-1 \(594\.5, 514\.5 and 488\.0 nm; the last printed '488\.8', see source notes\), ESHG phase\-match densities\. The original is not in the library\. shelton\_1989/finn\_ward\_1971\_He\_over\_Ne ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "finn_ward_1971_He_over_Ne", "material": "He", "file": "He/shelton_1989__finn_ward_1971_He_over_Ne.csv", "table": "tbl_96462ca3eb80", "quantity": "phase_match_density_ratio", "abscissa_unit": "cm-1", "use": "excluded", "reproduced_from": [ "R. S. Finn and J. F. Ward, Phys. Rev. Lett. 26, 285 (1971)" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "Ne", "harmonic": 2, "definition": "Delta alpha_Ne / Delta alpha_He computed from literature refractive indices" } } Table I, Ref\. 18\: 1\.87 \+\- 0\.01 at 14399 cm^\-1 \(694\.3 nm\), 'calculated from refractive index data in the literature' \(caption\), not a phase\-match measurement\: excluded\. shelton\_1989/gamma\_Ne\_over\_He\_present ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_Ne_over_He_present", "material": "Ne", "file": "Ne/shelton_1989__gamma_Ne_over_He_present.csv", "table": "tbl_96462ca3eb80", "quantity": "hyperpolarizability_ratio", "unit": "1", "abscissa_unit": "cm-1", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "He", "process": "eshg", "convention": "T", "part": "electronic" } } Table I \(p\. 2660\)\: gamma\_Ne/gamma\_He as printed; abscissa and row\: the vacuum wavenumber\. Present work \(a\), ESHG at 1319 and 1064 nm \(Nd\:YAG Q\-switched, periodic phase matching; Ne at up to 60 atm, He up to 110 atm\)\. The same measurements and numbers as shelton\_1990 Table I \(gamma\_Ne\_over\_He there, also a check\)\: not independent\. 'The collision\-induced contributions \.\.\. are found to increase gamma\_Ne/gamma\_He by 0\.6% at the highest sample densities employed' \(not corrected\)\. shelton\_1989/gamma\_Ne\_over\_He\_buckingham\_dunmur\_kerr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_Ne_over_He_buckingham_dunmur_kerr", "material": "Ne", "file": "Ne/shelton_1989__gamma_Ne_over_He_buckingham_dunmur_kerr.csv", "table": "tbl_96462ca3eb80", "quantity": "hyperpolarizability_ratio", "unit": "1", "abscissa_unit": "cm-1", "use": "reproduced", "reproduced_from": [ "buckingham_1968" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "He", "process": "dc_kerr", "convention": "T", "part": "electronic" } } Table I \(p\. 2660\)\: gamma\_Ne/gamma\_He as printed; abscissa and row\: the vacuum wavenumber\. dc Kerr \(Ref\. 17, Buckingham & Dunmur 1968\) at 632\.8 nm, two evaluations of one gamma\_Ne \(caption\)\: row 'He measured', 'dividing gamma\_Ne by the experimental value for gamma\_He also measured in the same experiments' \(1\.91\); row 'He ab initio', 'dividing gamma\_Ne by the accurate ab initio value of gamma\_He \(Ref\. 8\)' \(2\.38\)\. 'The wide discrepancy between these two numbers reflects the fact that the dc\-Kerr experimental value for gamma\_He is 30% larger than the accurate ab initio result\.' shelton\_1989/gamma\_Ne\_over\_He\_finn\_ward\_1971 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_Ne_over_He_finn_ward_1971", "material": "Ne", "file": "Ne/shelton_1989__gamma_Ne_over_He_finn_ward_1971.csv", "table": "tbl_96462ca3eb80", "quantity": "hyperpolarizability_ratio", "unit": "1", "abscissa_unit": "cm-1", "use": "reproduced", "reproduced_from": [ "R. S. Finn and J. F. Ward, Phys. Rev. Lett. 26, 285 (1971)" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "He", "process": "eshg", "convention": "T", "part": "electronic" } } Table I \(p\. 2660\)\: gamma\_Ne/gamma\_He as printed; abscissa and row\: the vacuum wavenumber\. ESHG, Ref\. 18 \(Finn & Ward 1971\), 694\.3 nm\. shelton\_1989/gamma\_Ne\_over\_He\_shelton\_lu\_1988 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_Ne_over_He_shelton_lu_1988", "material": "Ne", "file": "Ne/shelton_1989__gamma_Ne_over_He_shelton_lu_1988.csv", "table": "tbl_96462ca3eb80", "quantity": "hyperpolarizability_ratio", "unit": "1", "abscissa_unit": "cm-1", "use": "excluded", "reproduced_from": [ "D. P. Shelton and Z. Lu, Phys. Rev. A 37, 3813 (1988)" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "He", "process": "eshg", "convention": "T", "part": "electronic" } } Table I \(p\. 2660\)\: gamma\_Ne/gamma\_He as printed; abscissa and row\: the vacuum wavenumber\. ESHG, Ref\. 15 \(Shelton & Lu 1988\) at 594\.5, 514\.5 and 488\.0 nm \(the table prints 488\.8; the wavenumber 20487 cm^\-1 is the 488\.0 nm line\)\. EXCLUDED\: shown spurious by shelton\_1992 \(unnoticed electrical breakdown in Ne\)\. These points produced the 'anomalous' dispersion reported here\. shelton\_1989/gamma\_Ne\_over\_He\_lehmeier\_thg ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_Ne_over_He_lehmeier_thg", "material": "Ne", "file": "Ne/shelton_1989__gamma_Ne_over_He_lehmeier_thg.csv", "table": "tbl_96462ca3eb80", "quantity": "hyperpolarizability_ratio", "unit": "1", "abscissa_unit": "cm-1", "use": "reproduced", "reproduced_from": [ "lehmeier_1985" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "He", "process": "thg", "convention": "T", "part": "electronic" } } Table I \(p\. 2660\)\: gamma\_Ne/gamma\_He as printed; abscissa and row\: the vacuum wavenumber\. THG, Ref\. 19 \(Lehmeier, Leupacher & Penzkofer 1985\), 1055 nm \(9480 cm^\-1\)\: the ratio of their Ne and He values \(a ratio needs no convention factor\)\. shelton\_1989/gamma\_Ne\_over\_He\_ward\_new\_thg ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_Ne_over_He_ward_new_thg", "material": "Ne", "file": "Ne/shelton_1989__gamma_Ne_over_He_ward_new_thg.csv", "table": "tbl_96462ca3eb80", "quantity": "hyperpolarizability_ratio", "unit": "1", "abscissa_unit": "cm-1", "use": "reproduced", "reproduced_from": [ "ward_1969" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "reference_material": "He", "process": "thg", "convention": "T", "part": "electronic" } } Table I \(p\. 2660\)\: gamma\_Ne/gamma\_He as printed; abscissa and row\: the vacuum wavenumber\. THG, Ref\. 20 \(Ward & New 1969\), 694\.3 nm\. shelton\_1989/text\_static\_expt ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "text_static_expt", "material": "Ne", "table": "text", "quantity": "hyperpolarizability", "unit": "au", "abscissa_unit": "nm", "use": "excluded", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "static", "convention": "T", "part": "electronic" } } 1 inline points in the source record. p\. 2662\: 'the present experimental result of 116 \+\- 2 a\.u\.' for the static gamma\_Ne \(A\* of the Fig\. 1 fit, 115\.8 au\), 'probably reliable to about \+\-2%'\. EXCLUDED\: extrapolated with the spurious Shelton & Lu data; superseded by shelton\_1992 \(108 \+\- 2 au\)\. shelton\_1989/text\_static\_abinitio ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "text_static_abinitio", "material": "Ne", "table": "text", "quantity": "hyperpolarizability", "unit": "au", "abscissa_unit": "nm", "use": "reproduced", "reproduced_from": [ "I. Cernusak, G. H. F. Diercksen and A. J. Sadlej, Phys. Rev. A 33, 814 (1986)", "G. Maroulis and A. J. Thakkar, Chem. Phys. Lett. 156, 87 (1989)" ], "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "static", "convention": "T", "part": "electronic" } } 2 inline points in the source record. p\. 2662\: 'The MBPT calculation \(complete to fourth order in the electron\-correlation perturbation but still incompletely converged\) gives gamma\_Ne = 105 a\.u\. \.\.\. The CCD calculation gives gamma\_Ne = 114 \+\- 9 a\.u\.' SCF values 'fall in the range 42\-84 a\.u\.'; 'The HF limit probably lies near 70 a\.u\.' \(not tabulated per reference here; see shelton\_1994 Table V\)\. Formulas -------- shelton\_1989/ratio\_fit ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "ratio_fit", "material": "Ne", "equation": "Fig. 1 caption, p. 2661", "printed": "gamma_Ne/gamma_He = A[1 + B nu_L^2 + C nu_L^4]; A = 2.753, B = -2.251 x 10^-10 cm^2, and C = 6.609 x 10^-20 cm^4, where nu_L is given in cm^-1", "variable": "nu_L^2 = nu_s^2 + nu_1^2 + nu_2^2 + nu_3^2 in cm^-2 (6 nu^2 for ESHG)", "process": "eshg", "convention": "T", "part": "electronic", "range": "the five ESHG measurements of the author's laboratory (1319 nm to 488.0 nm)", "coefficients": { "A": "2.753", "B": "-2.251e-10", "C": "6.609e-20" }, "coefficient_units": { "A": "1", "B": "cm^2", "C": "cm^4" }, "check": "Gives 2.561 (1319 nm, nu_L^2 = 3.448e8) and 2.476 (1064 nm, 5.296e8) against 2.534 +- 0.019 and 2.487 +- 0.011 (1.4 and 1.0 sigma), and 2.225, 2.283, 2.346 at the three Shelton & Lu points (2.20, 2.28, 2.36). Checked 2026-09-26." } SUPERSEDED \(spurious anomaly, see the record notes\)\: fitted to the present infrared points and Shelton & Lu's three visible points, which shelton\_1992 discards\. shelton\_1989/gamma\_fit ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_fit", "material": "Ne", "equation": "Fig. 1 caption, p. 2661", "printed": "gamma_Ne = A*[1 + B* nu_L^2 + C* nu_L^4], where A* = 115.8 a.u., B* = -1.923 x 10^-10 cm^2, and C* = 6.924 x 10^-20 cm^4 (one atomic unit equals 6.23538 x 10^-65 C^4 m^4 J^-3 for gamma). The curve for gamma_Ne has a minimum of 100.4 a.u. at nu_L^2 = 13.9 x 10^8 cm^-2", "variable": "nu_L^2 in cm^-2 (6 nu^2 for ESHG)", "process": "eshg", "convention": "T", "part": "electronic", "range": "as ratio_fit", "coefficients": { "gamma0": "115.8", "B": "-1.923e-10", "C": "6.924e-20" }, "coefficient_units": { "gamma0": "au", "B": "cm^2", "C": "cm^4" }, "calibration": "He: Bishop & Lam (Phys. Rev. A 37, 464 (1988))", "check": "Minimum at nu_L^2 = 1.923e-10/(2 x 6.924e-20) = 13.89e8 cm^-2, value 115.8 (1 - 0.1335) = 100.3 au, as stated (100.4). Checked 2026-09-26." } SUPERSEDED \(spurious anomaly\)\: shelton\_1992's refit gives gamma\_0 = 108\.1 au with positive dispersion\. 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.