shelton_1989#
D. P. Shelton, Phys. Rev. Lett. 62, 2660 (1989)
Source record · Catalogue · 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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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#
{
"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 review register for the checks and decisions.