chen_2007 ========= Y\.\-H\. Chen, S\. Varma, A\. York and H\. M\. Milchberg, "Single\-shot, space\- and time\-resolved measurement of rotational wavepacket revivals in H2, D2, N2, O2, and N2O", Opt\. Express 15, 11341 \(2007\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1364/OE\.15\.011341 `__ **Source kind:** measurement **Recorded technique:** Single\-shot supercontinuum spectral interferometry in a room\-temperature gas cell \(2\.4\-7\.8 atm\)\: 110\-fs, 800\-nm pump; xenon supercontinuum probe and reference; the alignment \ \- 1/3 from the probe phase \(Eq\. \(2\)\), with 1D space resolution; revivals of H2, D2, N2, O2, N2O, their collisional dephasing, and density\-matrix simulations with literature Delta alpha \(pp\. 11343\-11356\)\. **Materials in structured entries:** D2, H2, N2, N2O, O2 **Dataset quantities:** dephasing\_time, polarizability\_anisotropy, rotational\_constant **Contents:** 9 datasets; 0 formulas. Curation notes -------------- Journal pages 11341\-11357 = PDF pages 1\-17\. Identity checked against the first page\. NO ABSOLUTE n2 OR Delta alpha IS MEASURED\: the measured quantity is the alignment \(scaled by the literature Delta alpha\); the Delta alpha values are inputs of the simulations, all cited to \[26\] = lin\_1976 \(the pdf text layer prints '\[26\]' after each, the markdown lost two of them\)\. They are recorded as reproduced \(or excluded, D2\)\. DEFINITIONS \(Gaussian, pp\. 11343\-11344\)\: Eq\. \(1\) n^2\(t\) = 1 \+ 4 pi N \(Delta alpha \\_t \+ alpha\_perp\); Eq\. \(2\) Delta n\(t\) = 2 pi N n0^\-1 Delta alpha \(\\_t \- 1/3\); Eq\. \(3\) adds the electronic hyperpolarizability terms \|E\(t\)\|^2 \(\ alpha\(3\)\_xxxx \+ \(1/2\)\ alpha\(3\)\_xxzz \+ \ alpha\(3\)\_zzzz\); the isotropic prompt part '\(1/2\)\[\.\.\.\]\|E\(t\)\|^2 = n2 I\(t\)' with \ = \ = 8/15, \ = 1/5 \(p\. 11344\)\. N2 and N2O\: 'the orientational effects \.\.\. dominate the isotropic prompt response n2 I in the vicinity of the 110 fs pump pulse' \(p\. 11349\); for H2 and D2 the prompt n2 I dominates \(pp\. 11355\-11356\)\. VALUES \(text\)\. Delta alpha \(cm3\)\: N2 0\.93e\-24, N2O 2\.79e\-24 \(p\. 11349, '\[26\]'\), O2 1\.14e\-24 \(p\. 11353\), D2 1\.14e\-24 \(p\. 11355, '\[26\]'\), H2 0\.30e\-24 \(p\. 11356, '\[26\]'\)\. Lin et al\.'s values are N2 9\.3, N2O 27\.9, O2 11\.4, H2 3\.02, D2 2\.92 \(x 1e\-25\)\: N2, N2O, O2 and H2 agree \(H2 rounded\); D2's 1\.14e\-24 is Lin's O2 value, 3\.9 times Lin's D2 and wahlstrand\_2015's 3\.0e\-25 \(TC\-292\)\: excluded\. Fitted rotational constants\: H2 B = 61\.8 cm^\-1, D2 B = 30\.4 cm^\-1 \(from the omega\_2,0 = 3\.44e13 s^\-1 peak\)\: the B\_fit\_\* datasets \(2026\-09\-26\); used B, cited to \[26\]\: N2 2\.0 \(p\. 11349 and p\. 11350\), O2 1\.44 \(p\. 11353; T = \(2cB\)^\-1 = 11\.6 ps\), N2O 0\.41 \(p\. 11349\) and 0\.412 \(p\. 11354\) cm^\-1 \(inputs, not stored\)\. Dephasing\: O2 1/gamma = 23\.2 ps at 5\.1 atm \(Fig\. 5\), N2O 23\.8 ps at 2\.4 atm \(Fig\. 6\)\: the T2\_\* datasets \(2026\-09\-26\); the N2O rate linear in pressure, 1\.46 x 10^10 s^\-1 atm^\-1 \(p\. 11356, Fig\. 9, from four pressures 2\.4\-6\.4 atm shown only in the figure\), is not stored \(a rate per pressure is not a dephasing time; as a linewidth coefficient it would be gamma/\(2 pi\) = 2\.32 GHz/atm HWHM, an interpretation the paper does not make\)\. FITTED B \(p\. 11355; text layer checked\)\. D2\: 'the peak at omega = 3\.44 x 10^13 s^\-1 is immediately identified as omega\_2,0, and allows us to extract the value of B\_D2 = 30\.4 cm^\-1'; omega\_2,0 = 12 pi c B, so B = 3\.44e13/\(12 pi c\) = 30\.44 cm^\-1 \(checked\)\. H2\: 'the rotational constant that best fits the Fourier\-transformed response is B\_H2 = 61\.8 cm^\-1, in good agreement with previous values \[26\]'\. No uncertainty is stated for either \(the stated errors, ~2 % for D2 and ~15 % for H2, are of the extracted phase shift\)\. These are effective constants of the j = 0 \-\> 2 beat only \(omega\_2,0 = 6B, centrifugal distortion ignored\), from a Fourier transform over a window of ~2\.5 T \(D2\) or ~3 T \(H2\)\: coarse\. For comparison, teal\_1935's S\(0\) lines give 6B\_eff = 354\.5 cm^\-1 \(H2, B\_eff = 59\.1\) and 178\.8 cm^\-1 \(D2, 29\.8\)\: Chen's values are 4\.6 % and 2\.0 % higher\. FINDING \(p\. 11355, text layer checked\)\: 'The spin of the H nucleus is I\_N = 1/2, so that even j states are 3 times more populated than odd j states' reverses the H2 nuclear\-spin weights \(shelton\_1987 Table 2\: g\_ns = 1 for even J and 3 for odd J; solprop's degeneracy\_even 1, degeneracy\_odd 3\); whether the simulations of Fig\. 8\(c\) used the printed or the correct weights cannot be told\. The D2 statement \(even j twice as populated as odd j, p\. 11355\) agrees with shelton\_1987 \(2/1\)\. DEPHASING \(pp\. 11352\-11353\)\. O2\: 'a damping rate of gamma\_j,j\-2 = gamma = 4\.31 x 10^10 s^\-1 \(or dephasing time 1/gamma = 23\.2 ps\) was used\. The damping rate was obtained from a fit to the declining peak amplitudes in the time sequence data of Fig\. 5\(a\)\. Since dephasing is dominated by elastic molecular collisions, there should be little j dependence of the rate; hence we put gamma\_j,j\-2 = gamma' \(p\. 11353; the Fig\. 5 caption, p\. 11352, prints '23\.2 ps', its last digit with an unmapped dot glyph in the extraction; the text layer reads 23\.2\)\. 1/gamma is the decay time of the rotational coherences rho\_j,j\-2 \(the alignment revivals\), a T2 of the pure rotational Raman \(S\-branch\) coherences taken the same for all j\. Room temperature; no uncertainty stated\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- chen\_2007/dalpha\_N2 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "dalpha_N2", "material": "N2", "table": "text", "quantity": "polarizability_anisotropy", "unit": "cm3", "scale": 1e-24, "abscissa_unit": "nm", "use": "reproduced", "reproduced_from": [ "lin_1976" ] } 1 inline points in the source record. p\. 11349\: 'Delta alpha\_N2 = 0\.93 x 10^\-24 cm3 \.\.\. \[26\]' \(lin\_1976\: 9\.3 x 1e\-25\)\. Wavelength not stated\. chen\_2007/dalpha\_N2O ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "dalpha_N2O", "material": "N2O", "table": "text", "quantity": "polarizability_anisotropy", "unit": "cm3", "scale": 1e-24, "abscissa_unit": "nm", "use": "reproduced", "reproduced_from": [ "lin_1976" ] } 1 inline points in the source record. p\. 11349\: 'Delta alpha\_N2O = 2\.79 x 10^\-24 cm3 \[26\]' \(lin\_1976\: 27\.9 x 1e\-25\)\. chen\_2007/dalpha\_O2 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "dalpha_O2", "material": "O2", "table": "text", "quantity": "polarizability_anisotropy", "unit": "cm3", "scale": 1e-24, "abscissa_unit": "nm", "use": "reproduced", "reproduced_from": [ "lin_1976" ] } 1 inline points in the source record. p\. 11353\: 'Delta alpha\_O2 = 1\.14 x 10^\-24 cm3 \[26\]' \(lin\_1976\: 11\.4 x 1e\-25\)\. chen\_2007/dalpha\_H2 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "dalpha_H2", "material": "H2", "table": "text", "quantity": "polarizability_anisotropy", "unit": "cm3", "scale": 1e-24, "abscissa_unit": "nm", "use": "reproduced", "reproduced_from": [ "lin_1976" ] } 1 inline points in the source record. p\. 11356\: 'Delta alpha\_H2 = 0\.30 x 10^\-24 cm3 \[26\]' \(lin\_1976\: 3\.02 x 1e\-25, rounded\)\. chen\_2007/dalpha\_D2 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "dalpha_D2", "material": "D2", "table": "text", "quantity": "polarizability_anisotropy", "unit": "cm3", "scale": 1e-24, "abscissa_unit": "nm", "use": "excluded", "reproduced_from": [ "lin_1976" ] } 1 inline points in the source record. p\. 11355\: 'Delta alpha\_D2 = 1\.14 x 10^\-24 cm3 \[26\]'\. The cited source \(lin\_1976\) gives 2\.92 x 1e\-25 for D2 and 11\.4 x 1e\-25 for O2\: the printed D2 value is O2's, a misquotation \(it is also 3\.9 times wahlstrand\_2015's measured 3\.0 x 1e\-25\)\. Excluded; which value the simulation of Fig\. 7\(c\) used cannot be told from the paper\. chen\_2007/B\_fit\_H2 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "B_fit_H2", "material": "H2", "table": "text", "quantity": "rotational_constant", "unit": "cm-1", "abscissa": "label", "use": "check", "parameters": { "constant": "B", "vibrational_state_v": 0 } } 1 inline points in the source record. p\. 11355\: 'the rotational constant that best fits the Fourier\-transformed response is B\_H2 = 61\.8 cm^\-1'\. An effective constant of the j = 0 \-\> 2 beat \(omega\_2,0 = 12 pi c B, no centrifugal distortion\), from alignment revivals in 7\.8 atm H2 at room temperature over ~3 T; no uncertainty stated\. 4\.6 % above the B\_eff = 59\.1 cm^\-1 that teal\_1935's S\(0\) line implies\. chen\_2007/B\_fit\_D2 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "B_fit_D2", "material": "D2", "table": "text", "quantity": "rotational_constant", "unit": "cm-1", "abscissa": "label", "use": "check", "parameters": { "constant": "B", "vibrational_state_v": 0 } } 1 inline points in the source record. p\. 11355\: the Fourier peak 'at omega = 3\.44 x 10^13 s^\-1 is immediately identified as omega\_2,0, and allows us to extract the value of B\_D2 = 30\.4 cm^\-1' \(omega\_2,0 = 12 pi c B gives 30\.44\)\. An effective constant of the j = 0 \-\> 2 beat, 7\.8 atm D2, room temperature; no uncertainty stated\. 2\.0 % above the B\_eff = 29\.8 cm^\-1 of teal\_1935's S\(0\)\. chen\_2007/T2\_O2 ~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "T2_O2", "material": "O2", "table": "text", "quantity": "dephasing_time", "unit": "ps", "abscissa": "pressure", "abscissa_unit": "atm", "use": "check", "parameters": { "transition": "pure rotational S branch (the rho_j,j-2 coherences, one gamma for all j)", "perturber": "self" } } 1 inline points in the source record. p\. 11353 and the Fig\. 5 caption \(p\. 11352\)\: 'damping rate of gamma\_j,j\-2 = gamma = 4\.31 x 10^10 s^\-1 \(or dephasing time 1/gamma = 23\.2 ps\)', from an exponential fit to the declining revival peaks of 5\.1 atm O2 at room temperature \(up to t = 1\.25 T\); taken j\-independent\. The decay time of the rotational coherences, i\.e\. T2 of the pure rotational S\-branch lines as a group\. No uncertainty stated\. chen\_2007/T2\_N2O ~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "T2_N2O", "material": "N2O", "table": "text", "quantity": "dephasing_time", "unit": "ps", "abscissa": "pressure", "abscissa_unit": "atm", "use": "check", "parameters": { "transition": "pure rotational S branch (the rho_j,j-2 coherences, one gamma for all j)", "perturber": "self" } } 1 inline points in the source record. Fig\. 6 caption \(p\. 11353\)\: 'The dephasing time constant 1/gamma = 23\.8 ps was obtained by fitting the peak amplitudes of \(a\) to an exponential', 2\.4 atm N2O at room temperature \(up to t = T\)\. As T2\_O2\. The rate at 2\.4\-6\.4 atm is linear in pressure, 1\.46 x 10^10 s^\-1 atm^\-1 \(p\. 11356; Fig\. 9\); at 2\.4 atm that line gives 1/gamma = 28\.5 ps if it passes through zero \(it need not\)\. No uncertainty stated\. 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.