liggett_1968#

G. Liggett and J. S. Levinger, J. Opt. Soc. Am. 58, 109 (1968)

Source record · Catalogue · Review register

Source kind: theory

Recorded technique: Kramers-Kronig calculation of delta(E) = Re(n - 1) of neon and argon from photoabsorption cross sections (Ederer and Tomboulian, Samson, Lukerskii, Allen) and calculated discrete oscillator strengths (Cooper, Sewell; for Ar 3p-4s the average 0.28 of Cooper, Knox, Geiger, Stacey and Vaughan), scaled so that the TRK sum rule and the accepted static polarizability are reproduced; x-ray region by Parratt and Hempstead’s integrals over power-law cross sections.

Materials in structured entries: Ar, Ne

Dataset quantities: cauchy_moment, polarizability, refractivity

Contents: 18 datasets; 7 formulas.

Curation notes#

Scaling (pp. 2-3): for neon the discrete strengths were multiplied by 0.85 and the continuum by 0.96; for argon all but the 3p-4s strength by 1.04. The corrected neon oscillator strengths (p. 2) are 2p-3s 0.138, 2p-4s 0.022, 2p-5s 0.008, 2p-3d 0.032, 2s-3p 0.067, 2s-4p 0.024, 2s-5p 0.011; argon (p. 3): 3p-4s 0.28, 3p-3d,5s 0.239, 3p-4d,6s 0.127, 3p-5d,7s 0.071. These are not extracted as datasets because the paper prints no transition wavelengths (the package keys an oscillator strength to its wavelength); they are recorded here. Figures 1-6 (delta(E) from 0.1 to 1000 Ry) are not digitised.

Tables IV and V give delta(E) x 10^8 of neon (302-502 Ry: -1.09 ... -0.40 ‘normal’, -1.13 ... -0.40 this paper, -1.13 ... -0.41 Parratt) and argon (20-4246 Ry: e.g. at 20 Ry -441., -107., -124.; at 1415 Ry -0.090, -0.091, -0.091) in the x-ray region, where n - 1 is negative; the ‘normal’ column is the free-electron term -CZN/E^2 (Eq. (7)). They are not extracted: the package’s refractivity datasets must imply a positive polarizability. Accuracy: the results ‘generally agree with existing theoretical calculations and experimental measurements to within 10 %’ (abstract); the cross sections are ‘known experimentally to an accuracy of about 5 %’. The library marks Table II’s caption as unmatched (CAPTION_UNMATCHED): it is printed in the text above the table.

Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets#

liggett_1968/mu4_cuthbertson_Ne#

{
  "id": "mu4_cuthbertson_Ne",
  "material": "Ne",
  "file": "Ne/liggett_1968__mu4_cuthbertson_Ne.csv",
  "table": "tbl_699c13f7b3b4",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 16,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "reproduced",
  "reproduced_from": [
    "cuthbertson_1910",
    "cuthbertson_1932"
  ]
}

Table II, the negative fourth moment mu_-4 = sum f E^-4 + R int sigma E^-4 dE with energies in rydbergs (Eq. (2)); since E(Ry) = 2 E(hartree), S(-4) in atomic units is 16 mu_-4 (scale 16; e.g. argon’s 1.76 x 16 = 28.16, Langhoff and Karplus’s S(-4)). ‘Determined from the index of refraction, see Refs. 3, 4 and Eq. (3)’ (note a): the Cauchy slope of C. and M. Cuthbertson’s visible data, ‘whose accuracy is about 10 %’ (p. 1).

liggett_1968/mu4_ingersoll_Ne#

{
  "id": "mu4_ingersoll_Ne",
  "material": "Ne",
  "file": "Ne/liggett_1968__mu4_ingersoll_Ne.csv",
  "table": "tbl_699c13f7b3b4",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 16,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "reproduced",
  "reproduced_from": [
    "L. R. Ingersoll and D. H. Liebenberg, J. Opt. Soc. Am. 46, 538 (1956); J. Opt. Soc. Am. 44, 566 (1954)"
  ]
}

Table II, the negative fourth moment mu_-4 = sum f E^-4 + R int sigma E^-4 dE with energies in rydbergs (Eq. (2)); since E(Ry) = 2 E(hartree), S(-4) in atomic units is 16 mu_-4 (scale 16; e.g. argon’s 1.76 x 16 = 28.16, Langhoff and Karplus’s S(-4)). ‘Determined from the Verdet constant’ measured by Ingersoll and Liebenberg (note b).

liggett_1968/mu4_dalgarno_Ne#

{
  "id": "mu4_dalgarno_Ne",
  "material": "Ne",
  "file": "Ne/liggett_1968__mu4_dalgarno_Ne.csv",
  "table": "tbl_699c13f7b3b4",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 16,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "reproduced",
  "reproduced_from": [
    "A. Dalgarno (as quoted by F. Marmo in a private communication); A. Dalgarno and A. E. Kingston, Proc. Roy. Soc. (London) A259, 424 (1960)"
  ]
}

Table II, the negative fourth moment mu_-4 = sum f E^-4 + R int sigma E^-4 dE with energies in rydbergs (Eq. (2)); since E(Ry) = 2 E(hartree), S(-4) in atomic units is 16 mu_-4 (scale 16; e.g. argon’s 1.76 x 16 = 28.16, Langhoff and Karplus’s S(-4)). ‘Calculation by extrapolation from other moments, see Ref. 21’ (note c; Ref. 21 is Dalgarno as quoted by Marmo; the text, p. 3, attributes the value to ‘Dalgarno’s and Kingston’s calculated value’, Ref. 20).

liggett_1968/mu4_theory_Ne#

{
  "id": "mu4_theory_Ne",
  "material": "Ne",
  "file": "Ne/liggett_1968__mu4_theory_Ne.csv",
  "table": "tbl_699c13f7b3b4",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 16,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "check"
}

Table II, the negative fourth moment mu_-4 = sum f E^-4 + R int sigma E^-4 dE with energies in rydbergs (Eq. (2)); since E(Ry) = 2 E(hartree), S(-4) in atomic units is 16 mu_-4 (scale 16; e.g. argon’s 1.76 x 16 = 28.16, Langhoff and Karplus’s S(-4)). ‘This paper’: from the corrected cross sections and oscillator strengths, a check of them (p. 3).

liggett_1968/mu4_cuthbertson_Ar#

{
  "id": "mu4_cuthbertson_Ar",
  "material": "Ar",
  "file": "Ar/liggett_1968__mu4_cuthbertson_Ar.csv",
  "table": "tbl_699c13f7b3b4",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 16,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "reproduced",
  "reproduced_from": [
    "cuthbertson_1910",
    "cuthbertson_1932"
  ]
}

liggett_1968/mu4_ingersoll_Ar#

{
  "id": "mu4_ingersoll_Ar",
  "material": "Ar",
  "file": "Ar/liggett_1968__mu4_ingersoll_Ar.csv",
  "table": "tbl_699c13f7b3b4",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 16,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "reproduced",
  "reproduced_from": [
    "L. R. Ingersoll and D. H. Liebenberg, J. Opt. Soc. Am. 46, 538 (1956); J. Opt. Soc. Am. 44, 566 (1954)"
  ]
}

Table II, the negative fourth moment mu_-4 = sum f E^-4 + R int sigma E^-4 dE with energies in rydbergs (Eq. (2)); since E(Ry) = 2 E(hartree), S(-4) in atomic units is 16 mu_-4 (scale 16; e.g. argon’s 1.76 x 16 = 28.16, Langhoff and Karplus’s S(-4)). ‘Determined from the Verdet constant’ measured by Ingersoll and Liebenberg (note b).

liggett_1968/mu4_dalgarno_Ar#

{
  "id": "mu4_dalgarno_Ar",
  "material": "Ar",
  "file": "Ar/liggett_1968__mu4_dalgarno_Ar.csv",
  "table": "tbl_699c13f7b3b4",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 16,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "reproduced",
  "reproduced_from": [
    "A. Dalgarno (as quoted by F. Marmo in a private communication); A. Dalgarno and A. E. Kingston, Proc. Roy. Soc. (London) A259, 424 (1960)"
  ]
}

Table II, the negative fourth moment mu_-4 = sum f E^-4 + R int sigma E^-4 dE with energies in rydbergs (Eq. (2)); since E(Ry) = 2 E(hartree), S(-4) in atomic units is 16 mu_-4 (scale 16; e.g. argon’s 1.76 x 16 = 28.16, Langhoff and Karplus’s S(-4)). ‘Calculation by extrapolation from other moments, see Ref. 21’ (note c; Ref. 21 is Dalgarno as quoted by Marmo; the text, p. 3, attributes the value to ‘Dalgarno’s and Kingston’s calculated value’, Ref. 20).

liggett_1968/mu4_theory_Ar#

{
  "id": "mu4_theory_Ar",
  "material": "Ar",
  "file": "Ar/liggett_1968__mu4_theory_Ar.csv",
  "table": "tbl_699c13f7b3b4",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 16,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "check"
}

Table II, the negative fourth moment mu_-4 = sum f E^-4 + R int sigma E^-4 dE with energies in rydbergs (Eq. (2)); since E(Ry) = 2 E(hartree), S(-4) in atomic units is 16 mu_-4 (scale 16; e.g. argon’s 1.76 x 16 = 28.16, Langhoff and Karplus’s S(-4)). ‘This paper’: from the corrected cross sections and oscillator strengths, a check of them (p. 3).

liggett_1968/lyman_marmo_Ne#

{
  "id": "lyman_marmo_Ne",
  "material": "Ne",
  "file": "Ne/liggett_1968__lyman_marmo_Ne.csv",
  "table": "tbl_7b2a63bc8b39",
  "quantity": "refractivity",
  "scale": 0.0001,
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "state": "1atm_0C",
  "density": "unknown",
  "use": "reproduced",
  "reproduced_from": [
    "F. Marmo, Bull. Am. Phys. Soc. 9, 626 (1964); 10, 691 (1965), and private communication"
  ]
}

Table III, delta(E) = n - 1 (x 10^4) at the hydrogen Lyman alpha line (the paper names the line, 0.75 Ry; wavelength 1215.67 A as printed by Mahon et al. 1979). The paper does not state the density N of its Eq. (1); taken as NTP, as the measurements compared are. ‘Measurement from Rayleigh scattering, Ref. 7’ (Marmo, unpublished): the original is not available, so this reproduction may be fitted; no uncertainty given. Rayleigh scattering gives |n - 1| (p. 1).

liggett_1968/lyman_marmo_Ar#

{
  "id": "lyman_marmo_Ar",
  "material": "Ar",
  "file": "Ar/liggett_1968__lyman_marmo_Ar.csv",
  "table": "tbl_7b2a63bc8b39",
  "quantity": "refractivity",
  "scale": 0.0001,
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "state": "1atm_0C",
  "density": "unknown",
  "use": "reproduced",
  "reproduced_from": [
    "F. Marmo, Bull. Am. Phys. Soc. 9, 626 (1964); 10, 691 (1965), and private communication"
  ]
}

Table III, delta(E) = n - 1 (x 10^4) at the hydrogen Lyman alpha line (the paper names the line, 0.75 Ry; wavelength 1215.67 A as printed by Mahon et al. 1979). The paper does not state the density N of its Eq. (1); taken as NTP, as the measurements compared are. Marmo’s Rayleigh-scattering value (unpublished; see lyman_marmo_Ne). Marmo’s Ne/Ar ratio, 0.152, is reproduced by Leonard 1974 (Table III(b), Ref. 40).

liggett_1968/lyman_dalgarno_Ne#

{
  "id": "lyman_dalgarno_Ne",
  "material": "Ne",
  "file": "Ne/liggett_1968__lyman_dalgarno_Ne.csv",
  "table": "tbl_7b2a63bc8b39",
  "quantity": "refractivity",
  "scale": 0.0001,
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "state": "1atm_0C",
  "density": "unknown",
  "use": "reproduced",
  "reproduced_from": [
    "A. Dalgarno (as quoted by F. Marmo in a private communication)"
  ]
}

Table III, delta(E) = n - 1 (x 10^4) at the hydrogen Lyman alpha line (the paper names the line, 0.75 Ry; wavelength 1215.67 A as printed by Mahon et al. 1979). The paper does not state the density N of its Eq. (1); taken as NTP, as the measurements compared are. ‘Calculation, Ref. 21’ (Dalgarno, private communication via Marmo).

liggett_1968/lyman_theory_Ne#

{
  "id": "lyman_theory_Ne",
  "material": "Ne",
  "file": "Ne/liggett_1968__lyman_theory_Ne.csv",
  "table": "tbl_7b2a63bc8b39",
  "quantity": "refractivity",
  "scale": 0.0001,
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "state": "1atm_0C",
  "density": "unknown",
  "use": "check"
}

Table III, delta(E) = n - 1 (x 10^4) at the hydrogen Lyman alpha line (the paper names the line, 0.75 Ry; wavelength 1215.67 A as printed by Mahon et al. 1979). The paper does not state the density N of its Eq. (1); taken as NTP, as the measurements compared are. ‘This paper’: the Kramers-Kronig calculation with cross sections and oscillator strengths scaled to the accepted polarizability and the TRK sum rule; results ‘generally agree ... to within 10 %’ (abstract).

liggett_1968/lyman_dalgarno_Ar#

{
  "id": "lyman_dalgarno_Ar",
  "material": "Ar",
  "file": "Ar/liggett_1968__lyman_dalgarno_Ar.csv",
  "table": "tbl_7b2a63bc8b39",
  "quantity": "refractivity",
  "scale": 0.0001,
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "state": "1atm_0C",
  "density": "unknown",
  "use": "reproduced",
  "reproduced_from": [
    "A. Dalgarno (as quoted by F. Marmo in a private communication)"
  ]
}

Table III, delta(E) = n - 1 (x 10^4) at the hydrogen Lyman alpha line (the paper names the line, 0.75 Ry; wavelength 1215.67 A as printed by Mahon et al. 1979). The paper does not state the density N of its Eq. (1); taken as NTP, as the measurements compared are. ‘Calculation, Ref. 21’ (Dalgarno, private communication via Marmo).

liggett_1968/lyman_theory_Ar#

{
  "id": "lyman_theory_Ar",
  "material": "Ar",
  "file": "Ar/liggett_1968__lyman_theory_Ar.csv",
  "table": "tbl_7b2a63bc8b39",
  "quantity": "refractivity",
  "scale": 0.0001,
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "state": "1atm_0C",
  "density": "unknown",
  "use": "check"
}

Table III, delta(E) = n - 1 (x 10^4) at the hydrogen Lyman alpha line (the paper names the line, 0.75 Ry; wavelength 1215.67 A as printed by Mahon et al. 1979). The paper does not state the density N of its Eq. (1); taken as NTP, as the measurements compared are. ‘This paper’: the Kramers-Kronig calculation with cross sections and oscillator strengths scaled to the accepted polarizability and the TRK sum rule; results ‘generally agree ... to within 10 %’ (abstract).

liggett_1968/lyman_heddle_1963_Ar#

{
  "id": "lyman_heddle_1963_Ar",
  "material": "Ar",
  "file": "Ar/liggett_1968__lyman_heddle_1963_Ar.csv",
  "table": "tbl_7b2a63bc8b39",
  "quantity": "refractivity",
  "scale": 0.0001,
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "state": "1atm_0C",
  "density": "unknown",
  "use": "reproduced",
  "reproduced_from": [
    "heddle_1963"
  ]
}

Table III, delta(E) = n - 1 (x 10^4) at the hydrogen Lyman alpha line (the paper names the line, 0.75 Ry; wavelength 1215.67 A as printed by Mahon et al. 1979). The paper does not state the density N of its Eq. (1); taken as NTP, as the measurements compared are. ‘Measurement using Cherenkov radiation, Ref. 8’: Heddle et al.’s value at 1210 +- 30 A, listed here under Lyman alpha; identical to heddle_1963/experiment_Ar at 1210 A.

liggett_1968/lyman_kingston_1964_Ar#

{
  "id": "lyman_kingston_1964_Ar",
  "material": "Ar",
  "file": "Ar/liggett_1968__lyman_kingston_1964_Ar.csv",
  "table": "tbl_7b2a63bc8b39",
  "quantity": "refractivity",
  "scale": 0.0001,
  "abscissa_unit": "angstrom",
  "wavelength_medium": "vacuum",
  "state": "1atm_0C",
  "density": "unknown",
  "use": "reproduced",
  "reproduced_from": [
    "kingston_1964"
  ]
}

Table III, delta(E) = n - 1 (x 10^4) at the hydrogen Lyman alpha line (the paper names the line, 0.75 Ry; wavelength 1215.67 A as printed by Mahon et al. 1979). The paper does not state the density N of its Eq. (1); taken as NTP, as the measurements compared are. ‘Calculation, Ref. 2’ (Kingston 1964). Kingston’s own value at 1216 A is 5.30 (his Table III; 5.542 at 1200 A in Table I); 5.20 is not in his paper as printed (unexplained).

liggett_1968/accepted_polarizability_Ne#

{
  "id": "accepted_polarizability_Ne",
  "material": "Ne",
  "table": "text",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "use": "reproduced",
  "reproduced_from": [
    "cuthbertson_1932"
  ]
}

1 inline points in the source record.

p. 2: ‘the accepted value, alpha = 2.70 atomic units’ (Ref. 4, C. and M. Cuthbertson 1932), to which the neon oscillator strengths and cross sections were scaled.

liggett_1968/accepted_polarizability_Ar#

{
  "id": "accepted_polarizability_Ar",
  "material": "Ar",
  "table": "text",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "use": "reproduced",
  "reproduced_from": [
    "cuthbertson_1932"
  ]
}

1 inline points in the source record.

p. 3: ‘the accepted values ... alpha = 11.1 atomic units’ (Ref. 4), to which the argon cross sections were scaled.

Formulas#

liggett_1968/cross_section_Ne_13p0#

{
  "id": "cross_section_Ne_13p0",
  "material": "Ne",
  "equation": "Table I, p. 2",
  "printed": "1.12 \\times 10^{3}E^{-2.59} (MB)",
  "variable": "E: photon energy in rydbergs; sigma in megabarns",
  "state": "per atom",
  "density": "unknown",
  "range": "13.0-63.7 Ry",
  "coefficients": {
    "A": "1.12e3",
    "p": "2.59"
  },
  "check": "Not checkable against printed values (the cross sections enter only the Kramers-Kronig integral)."
}

Photoionisation cross-section power law sigma = A E^-p used above 11 Ry for neon (compiled by Piech and Levinger 1964, Ref. 10; Table I note b); Table I note a: ‘Allen, Ref. 16 and Lukerskii, Ref. 15’. Not a refractivity formula; recorded because the x-ray refractivities of Tables IV-V follow from it through Parratt and Hempstead’s integrals.

liggett_1968/cross_section_Ne_63p7#

{
  "id": "cross_section_Ne_63p7",
  "material": "Ne",
  "equation": "Table I, p. 2",
  "printed": "3.24 \\times 10^{4}E^{-2.72} (MB)",
  "variable": "E: photon energy in rydbergs; sigma in megabarns",
  "state": "per atom",
  "density": "unknown",
  "range": "63.7-227.8 Ry",
  "coefficients": {
    "A": "3.24e4",
    "p": "2.72"
  },
  "check": "Not checkable against printed values (the cross sections enter only the Kramers-Kronig integral)."
}

liggett_1968/cross_section_Ne_227p8#

{
  "id": "cross_section_Ne_227p8",
  "material": "Ne",
  "equation": "Table I, p. 2",
  "printed": "1.10 \\times 10^{5}E^{-2.89} (MB)",
  "variable": "E: photon energy in rydbergs; sigma in megabarns",
  "state": "per atom",
  "density": "unknown",
  "range": "227.8-911.3 Ry",
  "coefficients": {
    "A": "1.10e5",
    "p": "2.89"
  },
  "check": "Not checkable against printed values (the cross sections enter only the Kramers-Kronig integral)."
}

liggett_1968/cross_section_Ar_18p2#

{
  "id": "cross_section_Ar_18p2",
  "material": "Ar",
  "equation": "Table I, p. 2",
  "printed": "1.13 \\times 10^{5}E^{-2.75} (MB)",
  "variable": "E: photon energy in rydbergs; sigma in megabarns",
  "state": "per atom",
  "density": "unknown",
  "range": "18.2-21.6 Ry",
  "coefficients": {
    "A": "1.13e5",
    "p": "2.75"
  },
  "check": "Not checkable against printed values (the cross sections enter only the Kramers-Kronig integral)."
}

Photoionisation cross-section power law sigma = A E^-p used beyond the K edge region for argon, fitted by the authors to Allen’s compilation (Ref. 16) and Lukerskii (Ref. 15); Table I note a: ‘Allen, Ref. 16 and Lukerskii, Ref. 15’. Not a refractivity formula; recorded because the x-ray refractivities of Tables IV-V follow from it through Parratt and Hempstead’s integrals.

liggett_1968/cross_section_Ar_21p6#

{
  "id": "cross_section_Ar_21p6",
  "material": "Ar",
  "equation": "Table I, p. 2",
  "printed": "5.94 \\times 10^{4}E^{-2.40} (MB)",
  "variable": "E: photon energy in rydbergs; sigma in megabarns",
  "state": "per atom",
  "density": "unknown",
  "range": "21.6-60.7 Ry",
  "coefficients": {
    "A": "5.94e4",
    "p": "2.40"
  },
  "check": "Not checkable against printed values (the cross sections enter only the Kramers-Kronig integral)."
}

liggett_1968/cross_section_Ar_60p7#

{
  "id": "cross_section_Ar_60p7",
  "material": "Ar",
  "equation": "Table I, p. 2",
  "printed": "1.48 \\times 10^{5}E^{-2.61} (MB)",
  "variable": "E: photon energy in rydbergs; sigma in megabarns",
  "state": "per atom",
  "density": "unknown",
  "range": "60.7-235.9 Ry",
  "coefficients": {
    "A": "1.48e5",
    "p": "2.61"
  },
  "check": "Not checkable against printed values (the cross sections enter only the Kramers-Kronig integral)."
}

liggett_1968/cross_section_Ar_235p9#

{
  "id": "cross_section_Ar_235p9",
  "material": "Ar",
  "equation": "Table I, p. 2",
  "printed": "3.30 \\times 10^{6}E^{-2.75} (MB)",
  "variable": "E: photon energy in rydbergs; sigma in megabarns",
  "state": "per atom",
  "density": "unknown",
  "range": "235.9-4564.5 Ry",
  "coefficients": {
    "A": "3.30e6",
    "p": "2.75"
  },
  "check": "Not checkable against printed values (the cross sections enter only the Kramers-Kronig integral)."
}

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.