kumar_2010_supplement#

A. Kumar and A. J. Thakkar, J. Chem. Phys. 132, 074301 (2010), supplementary material

Source record · Catalogue · Review register

Source kind: compilation

Recorded technique: Supplementary material (EPAPS, Ref. 84 of the paper) of Kumar and Thakkar’s constrained dipole oscillator strength distributions (the paper is kumar_2010): the integrated DOS of the adopted DOSDs per energy interval (Table I, p. 2) and the ten-term pseudospectra {f_i, E_i} reproducing the dipole sums (p. 3).

Materials in structured entries: Ar, Kr, Ne, Xe

Dataset quantities: interval_oscillator_strength, oscillator_strength

Contents: 8 datasets; 4 formulas.

Curation notes#

The library record is UNVERIFIED and untitled; the first page names it: ‘Supplementary material for the paper “Dipole oscillator strength distributions with improved high-energy behavior. Dipole sum rules and dispersion coefficients for Ne, Ar, Kr, and Xe revisited” by Ashok Kumar and Ajit J. Thakkar’ (kumar_2010; file name KumarMeathSupplementary.pdf). ‘The reference numbers are the same as in the paper.’

Table I (IDOS): E_j in eV; the IDOS entries are for [E_j, E_j+1], the last interval ending at infinity; the ‘Discrete’ row sums 17, 20, 25 and 28 discrete transitions for Ne, Ar, Kr, Xe (note e; initial data from Refs. 50, 51, 74, 78, 83 and Natali et al., unpublished). Datasets ‘idos_<gas>’ (rows j, abscissa E_j the LOWER edge of the interval; FORMAT NEED: an integrated oscillator strength over an interval has no quantity of its own, so oscillator_strength at the lower edge is used) and ‘discrete_<gas>’ (index abscissa). Check (2026-09-25): discrete + IDOS sums to 9.99956 (Ne), 18.0006 (Ar), 35.9994 (Kr), 53.9990 (Xe), the electron numbers (S(0) = N).

Constraints and initial data (Table I notes a-d; Refs. of kumar_2010): Ne: initial DOSD from Refs. 50 (Chan et al. 1992, neon = chan_1992_neon), 58 (Samson and Stolte 2002), 73 (Marr and West 1976), 60 (Suzuki and Saito 2003), 71 (Veigele 1973), 56 (Chantler 1995), above E_48 Eq. (9) with b = 3.373(6); scaling spread 100 a-bar = 0.451, 100 s = 0.601; refractivity constraints at 302.2 and 546.2 nm from Ref. 79 (Cuthbertson and Cuthbertson 1932 = cuthbertson_1932). Ar: Refs. 51 (Chan et al. 1992 = chan_1992), 73, 58, 61 (Suzuki and Saito 2005), 69 (Watson 1972), 71; Eq. (9) above E_47 with b = -1.710(7), 100 a-bar = 0.337, 100 s = 0.512; refractivity at 325.1 and 633.0 nm from Ref. 62 (Hohm 1994, not in the library). Kr: Refs. 51, 72 (Lang and Watson 1975), 59 (Suzuki and Saito 2002), 52 (Henke et al. 1993 = henke_1993), 56; Eq. (9) above E_54 with b = -2.594(9), 100 a-bar = 0.147, 100 s = 0.262; refractivity at 177.1 and 263.2 nm from Ref. 81 (Smith et al. 1976 = smith_1976). Xe: Refs. 51, 58, 60, 71; Eq. (9) above E_60 with b = -2.702(10), 100 a-bar = 0.255, 100 s = 0.342; refractivity at 170.2 and 253.7 nm from Ref. 82 (Bideau-Mehu et al. 1981 = bideau_mehu_1981). The constraint values themselves are not printed. So the DOSDs (and the pseudospectra and kumar_2010’s S_k) are tied to those refractivities at two wavelengths each: use as checks, not beside those data in a fit (as kumar_2010, TC-72).

Pseudospectra (p. 3, ‘in a form suitable for cut-and-paste’): recorded as oscillator formulas. The columns are headed ‘f’ and ‘E’ (‘The symbols f and E stand for f and epsilon respectively’, p. 1), but the ‘f’ column holds the energies and the ‘E’ column the strengths (see the formulas’ notes and TC-119). The Kr list is not a library table (the extraction turned it into a line of text on page 3); its numbers were checked against the pdf page image. Energies are in hartree: S(k) with the energies in hartree reproduces kumar_2010’s moments.

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

Datasets#

kumar_2010_supplement/idos_Ne#

{
  "id": "idos_Ne",
  "material": "Ne",
  "file": "Ne/kumar_2010_supplement__idos_Ne.csv",
  "table": "tbl_8fedf8f12d10",
  "quantity": "interval_oscillator_strength",
  "abscissa_unit": "eV",
  "columns": {
    "x_upper": "eV"
  },
  "use": "check"
}

Table I: integrated oscillator strength of the adopted constrained DOSD over [E_j, E_j+1] (the last to infinity), rows j = 18-48, abscissa E_j (eV, the lower edge; 21.56 eV - 100 keV), 31 intervals. Not a line: an interval integral (format need, source notes). Constrained to refractivity data (source notes): a check.

kumar_2010_supplement/discrete_Ne#

{
  "id": "discrete_Ne",
  "material": "Ne",
  "file": "Ne/kumar_2010_supplement__discrete_Ne.csv",
  "table": "tbl_8fedf8f12d10",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check"
}

Table I row ‘Discrete’: 2.800(-1), the summed strength of the 17 discrete transitions of the adopted DOSD (note e), index abscissa. A check.

kumar_2010_supplement/idos_Ar#

{
  "id": "idos_Ar",
  "material": "Ar",
  "file": "Ar/kumar_2010_supplement__idos_Ar.csv",
  "table": "tbl_8fedf8f12d10",
  "quantity": "interval_oscillator_strength",
  "abscissa_unit": "eV",
  "columns": {
    "x_upper": "eV"
  },
  "use": "check"
}

Table I: integrated oscillator strength of the adopted constrained DOSD over [E_j, E_j+1] (the last to infinity), rows j = 21-47, abscissa E_j (eV, the lower edge; 15.76 eV - 100 keV), 27 intervals. Not a line: an interval integral (format need, source notes). Constrained to refractivity data (source notes): a check.

kumar_2010_supplement/discrete_Ar#

{
  "id": "discrete_Ar",
  "material": "Ar",
  "file": "Ar/kumar_2010_supplement__discrete_Ar.csv",
  "table": "tbl_8fedf8f12d10",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check"
}

Table I row ‘Discrete’: 7.623(-1), the summed strength of the 20 discrete transitions of the adopted DOSD (note e), index abscissa. A check.

kumar_2010_supplement/idos_Kr#

{
  "id": "idos_Kr",
  "material": "Kr",
  "file": "Kr/kumar_2010_supplement__idos_Kr.csv",
  "table": "tbl_8fedf8f12d10",
  "quantity": "interval_oscillator_strength",
  "abscissa_unit": "eV",
  "columns": {
    "x_upper": "eV"
  },
  "use": "check"
}

Table I: integrated oscillator strength of the adopted constrained DOSD over [E_j, E_j+1] (the last to infinity), rows j = 26-54, abscissa E_j (eV, the lower edge; 14.03 eV - 100 keV), 29 intervals. Not a line: an interval integral (format need, source notes). Constrained to refractivity data (source notes): a check.

kumar_2010_supplement/discrete_Kr#

{
  "id": "discrete_Kr",
  "material": "Kr",
  "file": "Kr/kumar_2010_supplement__discrete_Kr.csv",
  "table": "tbl_8fedf8f12d10",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check"
}

Table I row ‘Discrete’: 1.092, the summed strength of the 25 discrete transitions of the adopted DOSD (note e), index abscissa. A check.

kumar_2010_supplement/idos_Xe#

{
  "id": "idos_Xe",
  "material": "Xe",
  "file": "Xe/kumar_2010_supplement__idos_Xe.csv",
  "table": "tbl_8fedf8f12d10",
  "quantity": "interval_oscillator_strength",
  "abscissa_unit": "eV",
  "columns": {
    "x_upper": "eV"
  },
  "use": "check"
}

Table I: integrated oscillator strength of the adopted constrained DOSD over [E_j, E_j+1] (the last to infinity), rows j = 29-60, abscissa E_j (eV, the lower edge; 12.17 eV - 100 keV), 32 intervals. Not a line: an interval integral (format need, source notes). Constrained to refractivity data (source notes): a check.

kumar_2010_supplement/discrete_Xe#

{
  "id": "discrete_Xe",
  "material": "Xe",
  "file": "Xe/kumar_2010_supplement__discrete_Xe.csv",
  "table": "tbl_8fedf8f12d10",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check"
}

Table I row ‘Discrete’: 1.597, the summed strength of the 28 discrete transitions of the adopted DOSD (note e), index abscissa. A check.

Formulas#

kumar_2010_supplement/pseudospectrum_Ne#

{
  "id": "pseudospectrum_Ne",
  "form": "oscillator",
  "energy_unit": "hartree",
  "terms": {
    "f": [
      "1.72761e-1",
      "7.05592e-2",
      "2.39565e-1",
      "5.90543e-1",
      "1.10197",
      "1.80237",
      "2.34931",
      "1.71152",
      "1.90122",
      "6.01847e-2"
    ],
    "E": [
      "6.18514e-1",
      "7.25160e-1",
      "8.27158e-1",
      "1.02722",
      "1.39273",
      "2.10855",
      "3.68085",
      "8.11069",
      "4.74204e+1",
      "5.96639e+2"
    ]
  },
  "range_nm": [
    81.0,
    "inf"
  ],
  "material": "Ne",
  "equation": "Ten-term pseudospectrum, page 3, tbl_ef48d8ee5ced",
  "printed": "columns headed f, E: 6.18514e-1 1.72761e-1; 7.25160e-1 7.05592e-2; 8.27158e-1 2.39565e-1; 1.02722 5.90543e-1; 1.39273 1.10197; 2.10855 1.80237; 3.68085 2.34931; 8.11069 1.71152; 4.74204e+1 1.90122; 5.96639e+2 6.01847e-2",
  "variable": "omega: photon energy in hartree; alpha(omega) = sum_i f_i / (E_i^2 - omega^2) in atomic units",
  "state": "none (per atom)",
  "density": "none",
  "range": "The pseudospectrum represents the constrained DOSD below the first resonance; its lowest pole is at 0.618514 hartree (73.67 nm). range_nm lower bound = 1.1 x that wavelength is the extractor's choice (TC-119), not the paper's.",
  "check": "S(k) = sum f_i E_i^k reproduces kumar_2010's Table I for every integer k from 2 to -10 to 3e-4 (the table's rounding), S(0) = 10.0000; S(-2) = 2.66934 against 2.669. Half-integer k are not constrained: S(-0.5) is 3e-4 off (checked 2026-09-25)."
}

COLUMNS SWAPPED IN THE ORIGINAL: the column headed f holds the excitation energies (hartree) and the column headed E the oscillator strengths. Evidence: the E column sums to the electron number (the TRK sum rule S(0) = N), the f column’s smallest entry is at the first resonance, and only this reading reproduces kumar_2010’s S(k) (check). terms.f is therefore the printed E column and terms.E the printed f column (a structural relabelling, like a wrong caption; each coefficient is as printed). Not independent of the refractivity data used as constraints (source notes): a check against those data, not a fit to them.

kumar_2010_supplement/pseudospectrum_Ar#

{
  "id": "pseudospectrum_Ar",
  "form": "oscillator",
  "energy_unit": "hartree",
  "terms": {
    "f": [
      "3.18677e-1",
      "5.02810e-2",
      "5.84382e-1",
      "1.45663",
      "2.30431",
      "1.46024",
      "8.33644e-1",
      "5.68760",
      "4.96822",
      "3.36019e-1"
    ],
    "E": [
      "4.32014e-1",
      "4.61341e-1",
      "5.48086e-1",
      "6.79814e-1",
      "8.90090e-1",
      "1.22282",
      "2.92264",
      "1.04118e+1",
      "4.39529e+1",
      "9.13390e+2"
    ]
  },
  "range_nm": [
    116.0,
    "inf"
  ],
  "material": "Ar",
  "equation": "Ten-term pseudospectrum, page 3, tbl_bdf9d0b1140e",
  "printed": "columns headed f, E: 4.32014e-1 3.18677e-1; 4.61341e-1 5.02810e-2; 5.48086e-1 5.84382e-1; 6.79814e-1 1.45663; 8.90090e-1 2.30431; 1.22282 1.46024; 2.92264 8.33644e-1; 1.04118e+1 5.68760; 4.39529e+1 4.96822; 9.13390e+2 3.36019e-1",
  "variable": "omega: photon energy in hartree; alpha(omega) = sum_i f_i / (E_i^2 - omega^2) in atomic units",
  "state": "none (per atom)",
  "density": "none",
  "range": "The pseudospectrum represents the constrained DOSD below the first resonance; its lowest pole is at 0.432014 hartree (105.47 nm). range_nm lower bound = 1.1 x that wavelength is the extractor's choice (TC-119), not the paper's.",
  "check": "S(k) reproduces kumar_2010's Table I for every integer k from 2 to -10 to 3e-4, S(0) = 18.0000, S(-2) = 11.0787 against 11.08; S(-0.5) is 1.5e-3 off (half-integer k not constrained) (checked 2026-09-25)."
}

kumar_2010_supplement/pseudospectrum_Kr#

{
  "id": "pseudospectrum_Kr",
  "form": "oscillator",
  "energy_unit": "hartree",
  "terms": {
    "f": [
      "2.30481e-1",
      "2.04092e-1",
      "7.97974e-1",
      "1.66947",
      "2.45289",
      "1.93397",
      "1.05176",
      "1.20500e+1",
      "1.48626e+1",
      "7.46743e-1"
    ],
    "E": [
      "3.69130e-1",
      "3.95530e-1",
      "4.80849e-1",
      "5.95979e-1",
      "7.93650e-1",
      "1.15661",
      "2.76628",
      "8.56933",
      "5.46172e+1",
      "2.53759e+3"
    ]
  },
  "range_nm": [
    136.0,
    "inf"
  ],
  "material": "Kr",
  "equation": "Ten-term pseudospectrum, page 3 (text: the Kr list is not a library table; checked against the pdf page image)",
  "printed": "columns headed f, E: 3.69130e-1 2.30481e-1; 3.95530e-1 2.04092e-1; 4.80849e-1 7.97974e-1; 5.95979e-1 1.66947; 7.93650e-1 2.45289; 1.15661 1.93397; 2.76628 1.05176; 8.56933 1.20500e+1; 5.46172e+1 1.48626e+1; 2.53759e+3 7.46743e-1",
  "variable": "omega: photon energy in hartree; alpha(omega) = sum_i f_i / (E_i^2 - omega^2) in atomic units",
  "state": "none (per atom)",
  "density": "none",
  "range": "The pseudospectrum represents the constrained DOSD below the first resonance; its lowest pole is at 0.36913 hartree (123.43 nm). range_nm lower bound = 1.1 x that wavelength is the extractor's choice (TC-119), not the paper's.",
  "check": "S(k) reproduces kumar_2010's Table I for every integer k from 2 to -10 to 2.5e-4, S(0) = 36.0000, S(-2) = 16.7939 against 16.79; S(-0.5) is 4.8e-3 off (half-integer k not constrained) (checked 2026-09-25)."
}

kumar_2010_supplement/pseudospectrum_Xe#

{
  "id": "pseudospectrum_Xe",
  "form": "oscillator",
  "energy_unit": "hartree",
  "terms": {
    "f": [
      "2.76315e-1",
      "3.60490e-1",
      "1.01180",
      "1.97196",
      "2.43455",
      "1.59870",
      "6.57194",
      "8.39325",
      "3.03664e+1",
      "1.01457"
    ],
    "E": [
      "3.10093e-1",
      "3.58976e-1",
      "4.13159e-1",
      "5.08407e-1",
      "6.74362e-1",
      "9.90276e-1",
      "3.02203",
      "6.13092",
      "5.62237e+1",
      "4.90145e+3"
    ]
  },
  "range_nm": [
    162.0,
    "inf"
  ],
  "material": "Xe",
  "equation": "Ten-term pseudospectrum, page 3, tbl_38b4d6bcc5ce",
  "printed": "columns headed f, E: 3.10093e-1 2.76315e-1; 3.58976e-1 3.60490e-1; 4.13159e-1 1.01180; 5.08407e-1 1.97196; 6.74362e-1 2.43455; 9.90276e-1 1.59870; 3.02203 6.57194; 6.13092 8.39325; 5.62237e+1 3.03664e+1; 4.90145e+3 1.01457",
  "variable": "omega: photon energy in hartree; alpha(omega) = sum_i f_i / (E_i^2 - omega^2) in atomic units",
  "state": "none (per atom)",
  "density": "none",
  "range": "The pseudospectrum represents the constrained DOSD below the first resonance; its lowest pole is at 0.310093 hartree (146.93 nm). range_nm lower bound = 1.1 x that wavelength is the extractor's choice (TC-119), not the paper's.",
  "check": "S(k) reproduces kumar_2010's Table I for every integer k from 2 to -10 to 3.8e-4, S(0) = 54.0000, S(-2) = 27.1637 against 27.16; S(-0.5) is 7.3e-3 off (half-integer k not constrained) (checked 2026-09-25)."
}

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.