koszykowski_1987

M. L. Koszykowski, L. A. Rahn, R. E. Palmer and M. E. Coltrin, “Theoretical and experimental studies of high-resolution inverse Raman spectra of N2 at 1-10 atm”, J. Phys. Chem. 91, 41 (1987)

Source record · Catalogue · Review register

DOI: 10.1021/j100285a012

Source kind: measurement

Recorded technique: Quasi-cw inverse Raman spectroscopy (p. 2): a single-mode argon-ion probe near 514 nm and a pulse-amplified single-mode dye pump (8 ns, 0.003 cm-1 = 90 MHz FWHM), crossed beams; Raman shifts to +- 0.001 cm-1 (wavemeter and etalon). N2 Q branch at 295 K and 1, 5 and 10 atm. Quasi-classical trajectory calculations of the N2-N2 state-to-state rates on a multipole and an atom-atom Lennard-Jones surface, and exponential-gap (EG) and modified exponential-gap (MEG) scaling laws fitted to the 1-atm spectrum through the S-matrix (relaxation-matrix) line shape, Eq. (3.1).

Materials in structured entries: N2

Dataset quantities: None recorded.

Contents: 0 datasets; 2 formulas.

Curation notes

Identity checked against the first page (pp. 41-46, received 1 May 1986). The library holds two downloads of this article: Koszykowski_1987_TheoreticalExperimentalStudies (downloaded 2019, used here) and Koszykowski_1987_TheoreticalExperimentalStudies_9b762d (the same DOI, ‘version_of_record’, downloaded 2026): their texts are identical apart from the download banners and the order of the footnotes (compared 2026-09-26); the first pdf page of each also carries the end of the preceding article. Page numbers here are pdf pages (1-6). Material: 14N2 (no isotopologue).

NOTHING IS TABULATED. The experimental 1, 5 and 10 atm spectra (Figs. 1, 5), the J-dependent Q-branch collisional broadening coefficients (FWHM) at 295 K from Ref. 20 (Rosasco, Lempert and Hurst, Chem. Phys. Lett. 97, 435 (1983)) and from the calculations (Fig. 2), and the state-to-state rates (Figs. 4, 6, 7) are in figures only (not digitised). The scaling laws are recorded as formulas.

WIDTH CONVENTION. FULL widths: Eq. (4.3), p. 4, ‘the diagonal relaxation elements, or equivalently the collisional line widths Gamma_j (fwhm), are given by Gamma_j/2 = sum_{i != j} gamma_ij’; Fig. 2’s broadening coefficients are ‘(fwhm)’. The rates are per atm (‘p is the pressure’; alpha in cm-1 atm-1) at 295 K.

TEXT VALUES. ‘fits to the IRS data required a pressure-induced frequency shift of between -0.003 and -0.004 cm-1 atm-1’ for the Q branch (p. 5; not extracted: a range inferred from the fits). Trajectory convergence: 500-1000 trajectories give the total relaxation rates to better than 10 % (p. 3). Potentials: multipole d = 2.9 A, n = 7.6 (widths about 25 % too low); Lennard-Jones eps = 30.54 cm-1, sigma = 3.341 A (agreement within errors) (p. 3). The EG law with alpha = 0.02, beta = 1.6 gives widths ‘too small for J < 6, and ... too large for J >= 6’ (p. 4).

solprop cites this paper (as ‘J. Phys. Chem. 91, 41 (1987)’) for the statement that its N2 6 ps Q-branch dephasing time is ‘an inherited effective band approximation’: the paper indeed shows the Q branch collapsing into one collisionally narrowed line above 1 atm (Figs. 1, 5); it gives no single dephasing time.

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

Datasets

No datasets are recorded.

Formulas

koszykowski_1987/eq41_exponential_gap

{
  "id": "eq41_exponential_gap",
  "material": "N2",
  "equation": "Eqs. (4.1)-(4.3), p. 4",
  "printed": "gamma_ji = alpha p exp(-beta Delta E_ij/kT) (J-increasing, i < j); gamma_ij = [(2J_i + 1)/(2J_j + 1)] gamma_ji exp(Delta E_ij/kT); Gamma_j/2 = sum_{i != j} gamma_ij",
  "variable": "p: pressure in atm; Delta E_ij the rotational energy gap; T = 295 K; alpha in cm-1 atm-1; Gamma_j the FWHM of Q(J) in cm-1",
  "state": "pure N2, 295 K",
  "density": "unknown",
  "range": "295 K, Q branch, 1 atm (the rates also used at 5 and 10 atm)",
  "coefficients": {
    "alpha": "0.02",
    "alpha_error": "0.003",
    "beta": "1.6",
    "beta_error": "0.05"
  },
  "check": "No printed width to compare with (Fig. 2 only). Evaluated with the N2 levels of B = 1.990 cm-1 (shelton_1987 Table 2), same-parity J only (scratch, 2026-09-26): FWHM 91.6, 88.7, 89.7, 91.8, 87.7, 72.0 x 1e-3 cm-1/atm for J = 2, 4, 6, 10, 14, 20: nearly flat below J = 14, as the paper says ('too small for J < 6, and ... too large for J >= 6')."
}

These alpha and beta are from ‘fitting all of the calculated points’ of the trajectory calculations (p. 4); the fit to the 1-atm spectrum gave ‘similar best-fit values’ that are not printed.

koszykowski_1987/eq44_modified_exponential_gap

{
  "id": "eq44_modified_exponential_gap",
  "material": "N2",
  "equation": "Eqs. (4.2)-(4.4), p. 4; temperature factor p. 5",
  "printed": "gamma_ji = alpha p [(1 + 1.5 E_i/kT delta)/(1 + 1.5 E_i/kT)]^2 exp(-beta Delta E_ij/kT); gamma_ij by Eq. (4.2); Gamma_j/2 = sum_{i != j} gamma_ij; at other temperatures alpha multiplied by (T0/T)^n",
  "variable": "p: pressure in atm; E_i the rotational energy of the initial (lower) level i; Delta E_ij the gap; alpha in cm-1 atm-1; Gamma_j the FWHM of Q(J) in cm-1",
  "state": "pure N2",
  "density": "unknown",
  "range": "295 K fit (1 atm spectrum; 5 and 10 atm predicted); the temperature factor from trajectories at 1000 and 1700 K and 'initial experimental results' to 1500 K",
  "coefficients": {
    "alpha": "0.023",
    "alpha_error": "0.003",
    "beta": "1.67",
    "beta_error": "0.15",
    "delta": "1.26",
    "delta_error": "0.06",
    "a": "1.5",
    "n_scattering": "1.2-1.3",
    "T0_scattering": "300",
    "n_experiment": "1.346",
    "n_experiment_error": "0.006",
    "T0_experiment": "295"
  },
  "check": "No printed width to compare with (Fig. 2 only). Evaluated as for eq41 (scratch, 2026-09-26): FWHM 126.3, 99.0, 91.6, 88.4, 85.9, 82.5, 71.9, 52.6 x 1e-3 cm-1/atm for J = 0, 2, 4, 6, 8, 10, 14, 20 at 295 K."
}

The modified exponential-gap (MEG) law, fitted to the 1-atm spectrum; ‘no spin degeneracy factor was included’ (p. 5). n = 1.2-1.3 (T0 = 300 K) from the scattering calculations; n = 1.346 +- 0.006 (T0 = 295 K) from ‘Initial experimental results’ of Ref. 28 (printed ‘Rahn, L. A.; Palmer, R. E. J. Opt. Soc. Am. B 1983, 3, 1164’), p. 5. Millot et al. (millot_1992) use this law for O2 with a = 1.5. Rahn & Palmer’s paper (rahn_1986, the 1986 volume) prints n = 1.346 +- 0.06, ten times the +- 0.006 quoted here (TC-526).

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.