dalgarno_1960#

A. Dalgarno and A. E. Kingston, Proc. R. Soc. London A 259, 424 (1960)

Source record · Catalogue · Review register

DOI: 10.1098/rspa.1960.0237

Source kind: fit

Recorded technique: Semi-empirical: n^2 - 1 expanded in the Cauchy sums S(-2), S(-4), S(-6), ... (Eq. 2); S(-2) and S(-4) estimated from long-wavelength refractive indices of Cuthbertson and Cuthbertson (1911, 1932) and Korff and Breit (1932), the higher sums from the interpolation formula S(k) = {a + b/(2.5 - k) + c/(2.5 - k)^2}^k S(0) (Eq. 18) with a the first excitation energy (pp. 424-429).

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

Dataset quantities: cauchy_moment, polarizability

Contents: 15 datasets; 5 formulas.

Curation notes#

Not independent data: the polarizabilities and dispersion formulas are derived from Cuthbertson and Cuthbertson’s refractivities (cuthbertson_1910, cuthbertson_1932) and Korff and Breit’s (1932) compilation. Energies are in rydbergs, so S(k) is in Ry^k: the datasets convert with scale 2^-k. Eq. (1) gives n^2 - 1 ‘at atmospheric pressure’ with the prefactor 2.00e-4 (4 pi N a0^3 with Loschmidt’s number, i.e. 0 degrees C, 1 atm, ideal gas); the Cuthbertsons’ data are for 0 degrees C, 760 mm.

Table 1’s helium ‘exact’ S(k) are sums over Dalgarno and Stewart’s (1960) oscillator strengths (S(-1) from Pekeris), the other column Eq. (18); atomic hydrogen’s are not extracted (H is not a curated species). Table 3 (expectation values of (sum r_i)^2) and the Verdet-constant formulas (in microminutes, from Eq. 5) are not extracted: they are not dispersion data (the Verdet formulas are consequences of the n^2 - 1 series). The Kr n^2 - 1 formula has no element label in the library’s Markdown; it is the fourth of the five (He, Ne, Ar, Kr, Xe order).

Consistency (checked 2026-09-24): the static limits of the n^2 - 1 formulas, converted with Lorentz-Lorenz at Loschmidt’s number and the paper’s a0^3 = 1.482e-25 cm^3, give He 1.384, Ar 11.084, Kr 16.737, Xe 27.29 (Table 2: 1.384, 11.080, 16.734, 27.292) but Ne 2.668 against Table 2’s 2.663 (0.2 %); not resolved. The He formula gives n - 1 = 3.4897e-5 at 5462 A, Cuthbertson and Cuthbertson’s 3.489e-5.

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

Datasets#

dalgarno_1960/s_exact_0#

{
  "id": "s_exact_0",
  "material": "He",
  "file": "He/dalgarno_1960__s_exact_0.csv",
  "table": "tbl_61824749ae46",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 1,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "check"
}

Table 1, helium S(0) ‘exact’ (from Dalgarno and Stewart’s oscillator strengths; S(-1) from Pekeris), in Ry^0; scale 2^(0) gives atomic units.

dalgarno_1960/s_eq18_0#

{
  "id": "s_eq18_0",
  "material": "He",
  "file": "He/dalgarno_1960__s_eq18_0.csv",
  "table": "tbl_61824749ae46",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 1,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "check"
}

Table 1, helium S(0) from the interpolation formula Eq. (18), in Ry^0; scale 2^(0) gives atomic units.

dalgarno_1960/s_exact_m1#

{
  "id": "s_exact_m1",
  "material": "He",
  "file": "He/dalgarno_1960__s_exact_m1.csv",
  "table": "tbl_61824749ae46",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 2,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "check"
}

Table 1, helium S(-1) ‘exact’ (from Dalgarno and Stewart’s oscillator strengths; S(-1) from Pekeris), in Ry^-1; scale 2^(1) gives atomic units.

dalgarno_1960/s_eq18_m1#

{
  "id": "s_eq18_m1",
  "material": "He",
  "file": "He/dalgarno_1960__s_eq18_m1.csv",
  "table": "tbl_61824749ae46",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 2,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "check"
}

Table 1, helium S(-1) from the interpolation formula Eq. (18), in Ry^-1; scale 2^(1) gives atomic units.

dalgarno_1960/s_exact_m2#

{
  "id": "s_exact_m2",
  "material": "He",
  "file": "He/dalgarno_1960__s_exact_m2.csv",
  "table": "tbl_61824749ae46",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 4,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "check"
}

Table 1, helium S(-2) ‘exact’ (from Dalgarno and Stewart’s oscillator strengths; S(-1) from Pekeris), in Ry^-2; scale 2^(2) gives atomic units.

dalgarno_1960/s_eq18_m2#

{
  "id": "s_eq18_m2",
  "material": "He",
  "file": "He/dalgarno_1960__s_eq18_m2.csv",
  "table": "tbl_61824749ae46",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 4,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "check"
}

Table 1, helium S(-2) from the interpolation formula Eq. (18), in Ry^-2; scale 2^(2) gives atomic units.

dalgarno_1960/s_exact_m4#

{
  "id": "s_exact_m4",
  "material": "He",
  "file": "He/dalgarno_1960__s_exact_m4.csv",
  "table": "tbl_61824749ae46",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 16,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "check"
}

Table 1, helium S(-4) ‘exact’ (from Dalgarno and Stewart’s oscillator strengths; S(-1) from Pekeris), in Ry^-4; scale 2^(4) gives atomic units.

dalgarno_1960/s_eq18_m4#

{
  "id": "s_eq18_m4",
  "material": "He",
  "file": "He/dalgarno_1960__s_eq18_m4.csv",
  "table": "tbl_61824749ae46",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 16,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "check"
}

Table 1, helium S(-4) from the interpolation formula Eq. (18), in Ry^-4; scale 2^(4) gives atomic units.

dalgarno_1960/s_exact_m6#

{
  "id": "s_exact_m6",
  "material": "He",
  "file": "He/dalgarno_1960__s_exact_m6.csv",
  "table": "tbl_61824749ae46",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 64,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "check"
}

Table 1, helium S(-6) ‘exact’ (from Dalgarno and Stewart’s oscillator strengths; S(-1) from Pekeris), in Ry^-6; scale 2^(6) gives atomic units.

dalgarno_1960/s_eq18_m6#

{
  "id": "s_eq18_m6",
  "material": "He",
  "file": "He/dalgarno_1960__s_eq18_m6.csv",
  "table": "tbl_61824749ae46",
  "quantity": "cauchy_moment",
  "unit": "au",
  "scale": 64,
  "abscissa": "order",
  "abscissa_unit": "1",
  "use": "check"
}

Table 1, helium S(-6) from the interpolation formula Eq. (18), in Ry^-6; scale 2^(6) gives atomic units.

dalgarno_1960/alpha_He#

{
  "id": "alpha_He",
  "material": "He",
  "file": "He/dalgarno_1960__alpha_He.csv",
  "table": "tbl_07f29f0464dd",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "use": "check"
}

Table 2, static polarizability in a0^3 (the paper’s a0^3 = 1.482e-25 cm^3), derived from the Cuthbertsons’ refractivities through the formulas below; not independent of those data.

dalgarno_1960/alpha_Ne#

{
  "id": "alpha_Ne",
  "material": "Ne",
  "file": "Ne/dalgarno_1960__alpha_Ne.csv",
  "table": "tbl_07f29f0464dd",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "use": "check"
}

Table 2, static polarizability in a0^3 (the paper’s a0^3 = 1.482e-25 cm^3), derived from the Cuthbertsons’ refractivities through the formulas below; not independent of those data.

dalgarno_1960/alpha_Ar#

{
  "id": "alpha_Ar",
  "material": "Ar",
  "file": "Ar/dalgarno_1960__alpha_Ar.csv",
  "table": "tbl_07f29f0464dd",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "use": "check"
}

Table 2, static polarizability in a0^3 (the paper’s a0^3 = 1.482e-25 cm^3), derived from the Cuthbertsons’ refractivities through the formulas below; not independent of those data.

dalgarno_1960/alpha_Kr#

{
  "id": "alpha_Kr",
  "material": "Kr",
  "file": "Kr/dalgarno_1960__alpha_Kr.csv",
  "table": "tbl_07f29f0464dd",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "use": "check"
}

Table 2, static polarizability in a0^3 (the paper’s a0^3 = 1.482e-25 cm^3), derived from the Cuthbertsons’ refractivities through the formulas below; not independent of those data.

dalgarno_1960/alpha_Xe#

{
  "id": "alpha_Xe",
  "material": "Xe",
  "file": "Xe/dalgarno_1960__alpha_Xe.csv",
  "table": "tbl_07f29f0464dd",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "angstrom",
  "use": "check"
}

Table 2, static polarizability in a0^3 (the paper’s a0^3 = 1.482e-25 cm^3), derived from the Cuthbertsons’ refractivities through the formulas below; not independent of those data.