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 <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/koszykowski_1987.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1021/j100285a012 <https://doi.org/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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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 :doc:`review register </register>` for the checks and decisions.