zheltikov_2007 ============== A\. M\. Zheltikov, "Raman response function of atmospheric air", Opt\. Lett\. 32, 2052 \(2007\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1364/OL\.32\.002052 `__ **Source kind:** theory **Recorded technique:** Model calculation \(no measurement\)\: the Raman response function R\(t\) of air taken as 80 % N2 and 20 % O2, the sum of rotational \(Eq\. 2, a sum of J\-resolved sinusoids weighted by thermal population differences and nuclear\-spin weights\) and vibrational \(Eq\. 3, the Q\-branch lines of each molecule\) parts, at 290 K and 1000 K, and the probe frequency shifts it produces for 50 fs and 10 fs pumps and pulse trains \(pp\. 2052\-2054; results in figures only\)\. **Materials in structured entries:** N2, O2 **Dataset quantities:** raman\_shift, rotational\_constant **Contents:** 6 datasets; 0 formulas. Curation notes -------------- Opt\. Lett\. 32, 2052\-2054 \(2007\) = PDF pages 1\-3 \(p\. = pdf page \+ 2051\)\. Identity checked against the first page\. The library's two UNMAPPED\_GLYPHS warnings \(pdf page 3\) touch the symbols of the text \(tau, lambda, 'Delta t'\), not the numbers; the numbers on p\. 2053 were checked against the PDF's text layer\. MODEL \(with its numbers\)\. Eq\. \(1\)\: R\(t\) = sum\_i R\_ri \+ R\_vi over the mixture's components \(i = 1 N2, i = 2 O2\), normalised as integral R\(t\) dt = 1 \[16\] \(Stolen et al\. 1989, curated as stolen\_1989\) \(p\. 2053\)\. Eq\. \(2\), after Nibbering et al\. \[14\] \(curated as nibbering\_1997\)\: R\_r\(t\) proportional to sum\_J F\_1J sin\(\-omega\_1J t\) \+ F\_2J sin\(\-omega\_2J t\), F\_J = \(rho\_{J\+1} \- rho\_J\) Z\_J \(J \+ 2\)\(J \+ 1\)/\(2J \+ 3\) \(as printed, text layer checked; the cited Nibbering et al\. Eq\. \(16\) has rho\_{J\+2} \- rho\_J, the population difference of the two levels of the J \-\> J \+ 2 line\: rho\_{J\+1} is a misprint or a slip of this paper, noted, not corrected, as no dataset depends on it\), rho\_J = exp\[\-chB J\(J\+1\)/kT\] / {sum\_J Z\_J \(2J \+ 1\) exp\[\-chB J\(J\+1\)/kT\]}, omega\_J = 4 pi B c \(2J \+ 3\), Z\_1J \(N2\) = 1 and 2 for odd and even J, Z\_2J \(O2\) = 1 and 0 for odd and even J, B\_1 ~ 1\.99 and B\_2 ~ 1\.44 cm^\-1 \(p\. 2053\)\. The main revivals are separated by \(4Bc\)^\-1\. Eq\. \(3\)\: R\_v\(t\) proportional to sum\_J V\_1J sin\(\-Omega\_1J t\) \+ V\_2J sin\(\-Omega\_2J t\), Omega\_J ~ Omega\_bar \- alpha J\(J\+1\), Omega\_bar\_1 ~ 2330 and Omega\_bar\_2 ~ 1556 cm^\-1 'the central frequencies of rovibrational Q\-branch transitions', alpha\_1 ~ 0\.0173 and alpha\_2 ~ 0\.0159 cm^\-1 'the constants of rotation\-vibration interaction \[17\]' \(\[17\] = D\. A\. Long, The Raman Effect \(Wiley, 2002\), not in the library\), V\_J = g\_J \(2J \+ 1\) sigma'\_J q\_J^\-1 exp\[\-hcB J\(J\+1\)/kT\], sigma'\_J 'the relative line strengths' \(not given\), g\_J 'the nuclear spin' weight, q\_J the partition sum \(p\. 2053\)\. The relative amplitude of the rotational and vibrational parts 'is chosen in such a way as to fit the results of experiments on three\-color coherent anti\-Stokes Raman scattering' of Lucht et al\. \[18\] \(Opt\. Lett\. 12, 386 \(1987\)\); its value is not printed\. No dephasing is included in Eqs\. \(2\)\-\(3\)\. The probe frequency shift\: Delta n\(t\) proportional to I\_0 integral\_0^inf R\(eta\) psi\(t \- eta\) d eta, Delta omega\(t\) = \(2 pi l/lambda\) d\[Delta n\(t\)\]/dt \(p\. 2054\)\. VALUES\. The constants are model inputs, marked approximate \('~'\) in the text\: recorded as inline points, use = 'check', parameters\.assumed = true\. B\_1 and B\_2 carry no citation; the single citation of the Eq\. \(3\) sentence, \[17\], follows the alpha values and is recorded as their source \(reproduced\_from\); Omega\_bar are recorded without a source\. For comparison\: bendtsen\_1974's 14N2 B\_0 = 1\.989574, nu\_0 = 2329\.9168 and alpha = 0\.017292 cm^\-1; hajigeorgiou\_2013's 16O2 B\_0 = 1\.437675 and G\_1 \- G\_0 = 1556\.3906 cm^\-1\. 'Omega\_bar' is called the central frequency of the Q branch, a band origin to this precision\. Results \(figures only\)\: the rotational response at 290 and 1000 K \(Fig\. 1\), the full response \(Fig\. 2\), probe frequency deviations for 50 and 10 fs pumps \(Fig\. 3\) and for trains of 10 fs pulses spaced by 10 T\_v, T\_v the N2 vibrational period \(Fig\. 4\)\. Not digitised\. Air is not a curated material; N2 and O2 are the datasets' materials\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- zheltikov\_2007/B\_N2 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "B_N2", "material": "N2", "table": "text", "quantity": "rotational_constant", "unit": "cm-1", "abscissa": "label", "use": "check", "parameters": { "constant": "B", "assumed": true } } 1 inline points in the source record. p\. 2053\: 'B\_1 ~ 1\.99 cm^\-1 \.\.\. the rotational constants for N2', a model input of Eq\. \(2\), uncited, approximate\. zheltikov\_2007/B\_O2 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "B_O2", "material": "O2", "table": "text", "quantity": "rotational_constant", "unit": "cm-1", "abscissa": "label", "use": "check", "parameters": { "constant": "B", "assumed": true } } 1 inline points in the source record. p\. 2053\: 'B\_2 ~ 1\.44 cm^\-1 \.\.\. for O2', a model input of Eq\. \(2\), uncited, approximate \(only odd J populated, Z\_2J = 0 for even J\)\. zheltikov\_2007/alpha\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "alpha_N2", "material": "N2", "table": "text", "quantity": "rotational_constant", "unit": "cm-1", "abscissa": "label", "use": "check", "reproduced_from": [ "D. A. Long, The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules (Wiley, 2002)" ], "parameters": { "constant": "alpha_e", "assumed": true } } 1 inline points in the source record. p\. 2053\: 'alpha\_1 ~ 0\.0173 cm^\-1 \.\.\. the constants of rotation\-vibration interaction \[17\]', N2\: the Q\-branch lines Omega\_J ~ Omega\_bar \- alpha J\(J\+1\) of Eq\. \(3\) \(so alpha here is B\_0 \- B\_1, the Q\-branch spacing constant, called the rotation\-vibration interaction constant\)\. A model input, approximate\. zheltikov\_2007/alpha\_O2 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "alpha_O2", "material": "O2", "table": "text", "quantity": "rotational_constant", "unit": "cm-1", "abscissa": "label", "use": "check", "reproduced_from": [ "D. A. Long, The Raman Effect: A Unified Treatment of the Theory of Raman Scattering by Molecules (Wiley, 2002)" ], "parameters": { "constant": "alpha_e", "assumed": true } } 1 inline points in the source record. p\. 2053\: 'alpha\_2 ~ 0\.0159 cm^\-1' for O2, as alpha\_N2 \(the extraction's accent over the 9 is an unmapped glyph; the text layer reads 0\.0159\)\. zheltikov\_2007/Omega\_N2 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "Omega_N2", "material": "N2", "table": "text", "quantity": "raman_shift", "unit": "cm-1", "abscissa": "label", "use": "check", "parameters": { "transition": "v = 0 -> 1 Q branch, central frequency (Omega_bar)", "assumed": true } } 1 inline points in the source record. p\. 2053\: 'Omega\_bar\_1 ~ 2330 cm^\-1 \.\.\. the central frequencies of rovibrational Q\-branch transitions', N2; a model input, approximate, without its own citation\. zheltikov\_2007/Omega\_O2 ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "Omega_O2", "material": "O2", "table": "text", "quantity": "raman_shift", "unit": "cm-1", "abscissa": "label", "use": "check", "parameters": { "transition": "v = 0 -> 1 Q branch, central frequency (Omega_bar)", "assumed": true } } 1 inline points in the source record. p\. 2053\: 'Omega\_bar\_2 ~ 1556 cm^\-1', O2; as Omega\_N2\. 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 :doc:`review register ` for the checks and decisions.