lin_1976#
C. H. Lin, J. P. Heritage, T. K. Gustafson, R. Y. Chiao and J. P. McTague, “Birefringence arising from the reorientation of the polarizability anisotropy of molecules in collisionless gases”, Phys. Rev. A 13, 813 (1976)
Source record · Catalogue · Review register
Source kind: theory
Recorded technique: Theory of the orientational (rotational) nonlinear refractive index of collisionless linear and symmetric-top molecular gases: stationary response from the quadratic and quartic Stark shifts of the rotational levels (perturbation series in K = Delta alpha <E.E> / 2hBc, sum rules over M), and the transient response (refractive-index bursts, revivals) from a first-order density-matrix calculation; numerical tables for several gases using literature Delta alpha and B (secs. III-VII).
Materials in structured entries: CO2, D2, H2, N2, N2O, O2
Dataset quantities: polarizability_anisotropy
Contents: 6 datasets; 0 formulas.
Curation notes#
Journal pages 813-829 = PDF pages 1-17 (the library pdf has no usable text layer: values read from the table image, which matches the cells file). Identity checked against the first page. Second copy: Unverified_5a357c1fd082 is the NASA technical memorandum NASA-TM-X-70344 (63 pp., 1974; same authors, same title ‘Birefringing arising ...’ in the NASA header): its Table I cells are identical to the PRA’s (compared cell by cell 2026-09-26), Tables II-IV too; its reference numbering differs (the CS2 observation is note 24 there, 18 here). The PRA is used.
WHAT IS TAKEN: Table I’s Delta alpha of the curated linear molecules, all quoted from other works: CO2 20.3, N2O 27.9, N2 9.3, O2 11.4 (footnote b = Ref. 16, ‘J. O. Hershfelder, C. F. Curties, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, 1954)’, i.e. Hirschfelder, Curtiss and Bird) and H2 3.02, D2 2.92 (footnote c, K. B. MacAdam and N. F. Ramsey, Phys. Rev. A 6, 898 (1972)), in ‘10^-25 esu’ (= 1e-25 cm3, a polarizability volume). No wavelength is stated for any of them: the abscissa is ‘not stated’. These are the Delta alpha that wahlstrand_2012, nibbering_1997 and chen_2007 quote as ‘Lin et al.’.
DEFINITIONS (Gaussian; p. 815): n = n0 + n2 <E.E> + n4 <E.E>^2 + n6 <E.E>^3, <E.E> the time-averaged squared field (per mean square field, as hellwarth_1990’s n2); susceptibility -8 pi N dDeltaW/d<E.E>, Eq. (5). Thermal-equilibrium (collision-dominated, long-pulse) value (p. 815, the ‘usual classical expression’): n2 = (4 pi N/45)(Delta alpha)^2 / (kT n0). Collisionless (Eq. (9a), p. 816): n2 = -(2 pi N / kT n0) N2(eta) Delta alpha^2 / Z eta, eta = hBc/kT; high-temperature limit (Eq. (16), p. 818): n2 = (2 pi N/30) Delta alpha^2 / (kT n0), ‘a factor of 3/4 smaller than the usual thermal equilibrium value’; low-temperature limit (Eqs. (15a)-(15c)): n2 = (4 pi N/135) (Delta alpha)^2 / (hBc n0), n4 = (6 pi N/8505) (Delta alpha)^3 / ((hBc)^2 n0), n6 = -(26 pi N/1913625) (Delta alpha)^4 / ((hBc)^3 n0). HIGHER ORDERS (notes only): these n4, n6 are the rotational (orientational) saturation of a collisionless gas at low temperature (saturated value ~4.9 against 4.2 for full alignment, Fig. 4), not electronic higher-order Kerr terms; for the high-temperature limit n4 and n6 are not evaluated.
TABLE I (p. 819) n2 (rotational, collisionless, 10^-12 esu/mole; not extracted: the unit is n2 per unit molar density, mol cm^-3, and the values are model results from the reproduced Delta alpha): CO2 12.6, N2O 23.7, N2 2.56, O2 3.94 (300 K), H2 0.434 (35 K), D2 0.803 (39 K). Check (2026-09-26): Eq. (16) with N = N_A gives 2.63 for N2 at 300 K (2.56 printed, which includes nuclear statistics, p. 819). Table IV (p. 826): N2O at 296 K, 1 atm: n2(T, P) = 1.07 x 10^-15 ‘esu/cm3’, optimum pulse 0.41 ps; 23.7e-12 x the molar density (4.12e-5 mol cm^-3) is 0.98e-15 (9 % lower; not resolved). Table III (p. 824): revival spacing tau_d = 1/4Bc and optimum pulse width at 296 K: CO2 21.37, 0.42 ps; N2O 20.26, 0.41 ps. Rotational constants B (Table I, Herzberg): CO2 0.3902, N2O 0.4116, N2 2.001, O2 1.438, H2 59.30, D2 29.90 cm^-1.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
lin_1976/dalpha_hirschfelder_CO2#
{
"id": "dalpha_hirschfelder_CO2",
"material": "CO2",
"file": "CO2/lin_1976__dalpha_hirschfelder_CO2.csv",
"table": "tbl_7ac00c24db21",
"quantity": "polarizability_anisotropy",
"unit": "cm3",
"scale": 1e-25,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"J. O. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954)"
]
}
Table I, Delta alpha (1e-25 esu = cm3), footnote b (Hirschfelder, Curtiss and Bird). Wavelength not stated. The table’s temperature column (300 K) is that of the n2 calculation, not of the anisotropy.
lin_1976/dalpha_hirschfelder_N2O#
{
"id": "dalpha_hirschfelder_N2O",
"material": "N2O",
"file": "N2O/lin_1976__dalpha_hirschfelder_N2O.csv",
"table": "tbl_7ac00c24db21",
"quantity": "polarizability_anisotropy",
"unit": "cm3",
"scale": 1e-25,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"J. O. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954)"
]
}
Table I, Delta alpha (1e-25 esu = cm3), footnote b (Hirschfelder, Curtiss and Bird). Wavelength not stated. The table’s temperature column (300 K) is that of the n2 calculation, not of the anisotropy.
lin_1976/dalpha_hirschfelder_N2#
{
"id": "dalpha_hirschfelder_N2",
"material": "N2",
"file": "N2/lin_1976__dalpha_hirschfelder_N2.csv",
"table": "tbl_7ac00c24db21",
"quantity": "polarizability_anisotropy",
"unit": "cm3",
"scale": 1e-25,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"J. O. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954)"
]
}
Table I, Delta alpha (1e-25 esu = cm3), footnote b (Hirschfelder, Curtiss and Bird). Wavelength not stated. The table’s temperature column (300 K) is that of the n2 calculation, not of the anisotropy.
lin_1976/dalpha_hirschfelder_O2#
{
"id": "dalpha_hirschfelder_O2",
"material": "O2",
"file": "O2/lin_1976__dalpha_hirschfelder_O2.csv",
"table": "tbl_7ac00c24db21",
"quantity": "polarizability_anisotropy",
"unit": "cm3",
"scale": 1e-25,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"J. O. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954)"
]
}
Table I, Delta alpha (1e-25 esu = cm3), footnote b (Hirschfelder, Curtiss and Bird). Wavelength not stated. The table’s temperature column (300 K) is that of the n2 calculation, not of the anisotropy.
lin_1976/dalpha_macadam_ramsey_H2#
{
"id": "dalpha_macadam_ramsey_H2",
"material": "H2",
"file": "H2/lin_1976__dalpha_macadam_ramsey_H2.csv",
"table": "tbl_7ac00c24db21",
"quantity": "polarizability_anisotropy",
"unit": "cm3",
"scale": 1e-25,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"K. B. MacAdam and N. F. Ramsey, Phys. Rev. A 6, 898 (1972)"
]
}
Table I, Delta alpha (1e-25 esu = cm3), footnote c (MacAdam and Ramsey). Wavelength not stated. The table’s temperature column (35 K) is that of the n2 calculation, not of the anisotropy.
lin_1976/dalpha_macadam_ramsey_D2#
{
"id": "dalpha_macadam_ramsey_D2",
"material": "D2",
"file": "D2/lin_1976__dalpha_macadam_ramsey_D2.csv",
"table": "tbl_7ac00c24db21",
"quantity": "polarizability_anisotropy",
"unit": "cm3",
"scale": 1e-25,
"abscissa_unit": "nm",
"use": "reproduced",
"reproduced_from": [
"K. B. MacAdam and N. F. Ramsey, Phys. Rev. A 6, 898 (1972)"
]
}
Table I, Delta alpha (1e-25 esu = cm3), footnote c (MacAdam and Ramsey). Wavelength not stated. The table’s temperature column (39 K) is that of the n2 calculation, not of the anisotropy.
Formulas#
No formulas are recorded.
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.