mikhailov_1959 ============== G\. V\. Mikhailov, "The influence of temperature and pressure on the Raman spectrum of nitrogen", Sov\. Phys\. JETP 9, 974 \(1959\) \[Zh\. Eksp\. Teor\. Fiz\. 36, 1368 \(1959\)\] `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` No DOI is recorded. **Source kind:** measurement **Recorded technique:** Spontaneous Raman spectra of N2 gas at 27 C and 7\-114 atm \(and at 200 C, and of the liquid at \-190 C\), excited by the Hg 4047 and 4358 A lines in a high\-pressure illuminator with a multiple\-reflection mirror system, photographed with a HUET V\-III spectrograph \(22\.7 cm\-1/mm at 4047 A, 36\.2 cm\-1/mm at 4358 A\) on Agfa plates, 3\-40 h exposures; microphotometer traces, three or four plates per pressure\. 'the total width of the excitation line, of the slit, and of the apparatus function \.\.\. \(~1\.5 cm\-1 for the gas \.\.\.\) was excluded from the results' \(p\. 2\)\. **Materials in structured entries:** N2 **Dataset quantities:** raman\_linewidth **Contents:** 8 datasets; 1 formula. Curation notes -------------- IDENTITY\. The library copy is the English translation, Sov\. Phys\. JETP 9, 974\-978 \(1959\), whose first page reads 'J\. Exptl\. Theoret\. Phys\. \(U\.S\.S\.R\.\) 36, 1368\-1373 \(May, 1959\)', 'Submitted to JETP editor December 7, 1958'; the library identity is ASSERTED \(no DOI\)\. jammu\_1966 and herring\_1986 \(Ref\. 4, 'G\. V\. Milahailov, Zh\. Eksp\. Teor\. Fiz\. 36, 1368 \(1959\) \[Sov\. Phys\.\-JETP 9, 974 \(1959\)\]'\) cite this paper\. Page numbers are pdf pages 1\-5\. solprop's unverified 'Sov\. Phys\. JETP 36, 9 \(1959\)' for N2's 6 ps is this paper\: 36 is the Russian volume and 9 the translation's volume of the same 1959 paper, the one the library's papers \(jammu\_1966, herring\_1986\) cite as Mikhailov 1959\. What it supports\: 6 ps is 1/\(pi Delta nu\) for Delta nu = 1\.77 cm\-1 \(solprop's 53\.05e9 Hz\), and this paper's width of the unresolved N2 Q branch at 27 C is 1\.7\-2\.4 cm\-1 at 15\-114 atm \(Table I\) and 1\.75 cm\-1 calculated \(1\.8 \+\- 0\.2 measured\) at 50 atm \(Table II\), which give 6\.1 ps and 5\.9 ps\. But that width is NOT a collisional dephasing width\: 'the rotational splitting introduces a basic length into the observed width of the Q branch' \(p\. 4\)\: delta nu\_rot = 1\.54 cm\-1 of the 1\.75 comes from the unresolved rotational structure \(Q\(J\) spread by alpha J\(J\+1\)\), the collisional part being 0\.2 cm\-1 at 50 atm \(Table II\), about 0\.005 cm\-1/atm \(formula collision\_width with rho\_nu = 0\.43 A\)\. The pressure\-independent part extrapolated to zero pressure is 1\.6 cm\-1 \(p\. 4\)\. So the 6 ps is the dephasing of the whole Q\-branch envelope at room temperature, independent of pressure, and it is not a collision time\. WIDTH CONVENTION\: not stated\. The paper speaks only of 'line width' \(delta omega, delta nu\) measured on microphotometer traces after removing the apparatus width; whether it is the full width at half maximum or the half width is never said\. Recorded as width = "not stated"\. jammu\_1966 \(Table II\) lists this author's N2 coefficients as HWHM per atm, 47\.5 and 26\.5 x 10^\-3 cm\-1/atm below and above 25 atm, values that this paper's Table I does not give directly \(the slopes of Table I's delta omega are about 0\.16 cm\-1/atm between 7 and 25 atm and 0\.044 cm\-1/atm between 25 and 80 atm\)\: perhaps from the 1960 paper\. TABLE I \(p\. 2\)\: 'the average width for the transitions with J = 0 \- 15 is given for the rotational lines'; 'The average error in the measurements of the line widths comprised about 10 %' \(p\. 2\)\. The rotational lines overlap from 20 atm and blend above 80 atm; the slope changes at 25 atm \(Fig\. 3\)\. The 3 atm width is '~0\.5' 'Measured by V\. A\. Iozenas, Moscow State University' \(excluded\: approximate, another observer\)\. 'The frequency shift of the Raman scattering lines lies within the limits of the errors of measurement \(~1 cm\-1\)' \(p\. 3\)\. TEXT \(p\. 3\)\: at 200 C \(the gas at 'p = 90 atmos, reduced to 27 C', i\.e\. the density of 90 atm at 27 C\), delta omega = 8\.5 \+\- 2 cm\-1 and delta nu = 5\.4 \+\- 1\.5 cm\-1 \(inline datasets\)\. Table II prints the 200 C row at '50 atmos' at 27 C\: the text and the table disagree on the density of the 200 C measurement \(unresolved\)\. Liquid N2 \(\-190 C\)\: delta nu = 0\.4 \+\- 0\.2 cm\-1, calculated 0\.5 \(0\.45 \+ 0\.05\) at 0\.5 g/cm3 \(not extracted\: not the gas\)\. CONSTANTS AND ERRORS\. The Q\-branch structure calculation \(p\. 4\) uses 'B = 1\.998 cm\-1, alpha = 0\.171 cm\-1 and T = 300 K'\. alpha is printed ten times too large\: bendtsen\_1974 \(Table VIII\) gives alpha = 0\.017292 cm\-1 for 14N2, and the paper's own delta nu\_rot = 1\.54 cm\-1 needs the intensity scale kT alpha/B of about 1\.8 cm\-1, i\.e\. alpha about 0\.017 \(with 0\.171 it would be 18 cm\-1\)\. Not recorded as data \(an input of the calculation, uncited\)\. The effective collision radius for the rotational lines is 3\.9 A in the abstract but 3\.3 A in the text \(p\. 3\); neither reproduces Table I through the formula \(see collision\_width\)\. **Recorded bibliographic identity status:** ASSERTED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- mikhailov\_1959/table1\_rotational ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_rotational", "material": "N2", "file": "N2/mikhailov_1959__table1_rotational.csv", "table": "tbl_e9551d96728b", "quantity": "raman_linewidth", "unit": "cm-1", "abscissa": "pressure", "abscissa_unit": "atm", "use": "primary", "excluded_rows": { "3atm": "printed '~0.5*': approximate, 'Measured by V. A. Iozenas, Moscow State University' (table note)" }, "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "rotational S and O lines, average over J = 0-15", "width": "not stated", "perturber": "self", "temperature_k": 300.15 } } Table I \(p\. 2\), delta omega\: the width of the N2 pure rotational Raman lines, 'the average width for the transitions with J = 0 \- 15', at 27 C, apparatus width removed; pure N2\. Width convention not stated \(see the source notes\)\. Lines overlap from 20 atm; the slope changes at 25 atm\. mikhailov\_1959/table1\_vibrational ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_vibrational", "material": "N2", "file": "N2/mikhailov_1959__table1_vibrational.csv", "table": "tbl_e9551d96728b", "quantity": "raman_linewidth", "unit": "cm-1", "abscissa": "pressure", "abscissa_unit": "atm", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "Q branch, unresolved (v = 0 -> 1)", "width": "not stated", "perturber": "self", "temperature_k": 300.15 } } Table I \(p\. 2\), delta nu\: the width of the unresolved N2 vibrational Q branch \(v = 0 \-\> 1\) at 27 C, apparatus width removed\. Mostly the rotational structure of the branch \(1\.54 cm\-1 calculated, 1\.6 cm\-1 extrapolated to zero pressure, p\. 4\), not a collisional width\. Width convention not stated\. mikhailov\_1959/text\_rotational\_200C ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "text_rotational_200C", "material": "N2", "table": "text", "quantity": "raman_linewidth", "unit": "cm-1", "abscissa": "none", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "rotational S and O lines, average over J", "width": "not stated", "perturber": "self", "temperature_k": 473.15 } } 1 inline points in the source record. p\. 3\: 'the nitrogen lines are wider at 200 C than at room temperature\: delta omega = 8\.5 \+\- 2 cm\-1', at 'p = 90 atmos, reduced to 27 C' \(the density of 90 atm at 27 C; Table II says 50 atm for its 200 C row\)\. Rotational lines, J\-averaged as in Table I\. Width convention not stated\. mikhailov\_1959/text\_vibrational\_200C ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "text_vibrational_200C", "material": "N2", "table": "text", "quantity": "raman_linewidth", "unit": "cm-1", "abscissa": "none", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "Q branch, unresolved (v = 0 -> 1)", "width": "not stated", "perturber": "self", "temperature_k": 473.15 } } 1 inline points in the source record. p\. 3\: 'delta nu = 5\.4 \+\- 1\.5 cm\-1' for the unresolved Q branch at 200 C, 'p = 90 atmos, reduced to 27 C'; repeated in Table II \(experimental, 200 C, where the density is given as 50 atm at 27 C\)\. Width convention not stated\. mikhailov\_1959/table2\_rotational\_structure ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_rotational_structure", "material": "N2", "file": "N2/mikhailov_1959__table2_rotational_structure.csv", "table": "tbl_57a9c368f39b", "quantity": "raman_linewidth", "unit": "cm-1", "abscissa": "label", "columns": { "temperature": "C" }, "use": "check", "parameters": { "transition": "Q branch, unresolved (v = 0 -> 1)", "width": "not stated" } } Table II \(p\. 4\), 'Calculated for the gas', delta nu\_rot\: the width of the unresolved rotational structure of the N2 Q branch \(the averaged intensity distribution of p\. 4 with B = 1\.998 cm\-1 and alpha printed 0\.171 cm\-1; see the source notes\), at the density of 50 atm at 27 C\. Not a collisional width\. mikhailov\_1959/table2\_collisional ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_collisional", "material": "N2", "file": "N2/mikhailov_1959__table2_collisional.csv", "table": "tbl_57a9c368f39b", "quantity": "raman_linewidth", "unit": "cm-1", "abscissa": "label", "columns": { "temperature": "C" }, "use": "check", "parameters": { "transition": "Q branch (v = 0 -> 1)", "width": "not stated", "perturber": "self" } } Table II \(p\. 4\), 'Calculated for the gas', delta nu\_col\: the collisional width of the Q branch from delta = 2 pi N v rho^2 with rho\_nu = 0\.43 A, at the density of 50 atm at 27 C \(formula collision\_width\: 0\.027 x 0\.43^2 x 50 = 0\.25 cm\-1 at 27 C, printed 0\.2\)\. mikhailov\_1959/table2\_total ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_total", "material": "N2", "file": "N2/mikhailov_1959__table2_total.csv", "table": "tbl_57a9c368f39b", "quantity": "raman_linewidth", "unit": "cm-1", "abscissa": "label", "columns": { "temperature": "C" }, "use": "check", "parameters": { "transition": "Q branch, unresolved (v = 0 -> 1)", "width": "not stated", "perturber": "self" } } Table II \(p\. 4\), 'Calculated for the gas', delta nu = delta nu\_rot \+ delta nu\_col, at the density of 50 atm at 27 C\. The 27 C value, 1\.75 cm\-1, is 1/\(pi c x 6\.06 ps\)\: the width solprop's 6 ps N2 dephasing time corresponds to\. mikhailov\_1959/table2\_experimental ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table2_experimental", "material": "N2", "file": "N2/mikhailov_1959__table2_experimental.csv", "table": "tbl_57a9c368f39b", "quantity": "raman_linewidth", "unit": "cm-1", "abscissa": "label", "columns": { "temperature": "C" }, "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "transition": "Q branch, unresolved (v = 0 -> 1)", "width": "not stated", "perturber": "self" } } Table II \(p\. 4\), 'Experimental' delta nu of the Q branch\: the 200 C value repeats the text's 5\.4 \+\- 1\.5 \(text\_vibrational\_200C, whose density the text gives as 90 atm at 27 C, the table as 50 atm\); the 27 C value, 1\.8 \+\- 0\.2, lies between Table I's 40 and 60 atm values\. Formulas -------- mikhailov\_1959/collision\_width ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "collision_width", "material": "N2", "equation": "text, p. 3", "printed": "delta = 0.027 rho^2 p (from delta = 2 pi N v rho^2)", "variable": "rho: the effective optical collision radius in A; p: pressure in atm; delta: the line width in cm-1; N2 at 27 C", "state": "pure N2 at 27 C", "density": "ideal", "range": "0-25 atm (the collision-broadening region for the rotational lines, p. 3)", "coefficients": { "k": "0.027", "rho_rotational_text": "3.3", "rho_rotational_abstract": "3.9", "rho_vibrational": "0.43" }, "check": "Scratch, 2026-09-26: with rho_nu = 0.43 A, 0.0050 cm-1/atm, 0.25 cm-1 at 50 atm (Table II delta nu_col 0.2 at 27 C). With rho_omega = 3.3 A (text) 0.294 cm-1/atm and with 3.9 A (abstract) 0.41 cm-1/atm, whereas Table I's rotational widths rise by 0.164 cm-1/atm between 7 and 25 atm (4.7 cm-1 at 25 atm against 7.4 from the formula with 3.3 A): the rotational radius does not reproduce Table I. The 0.027 prefactor equals 2 pi N v rho^2 / c at 1 atm and 300.15 K (N = 2.445e19 cm-3) with v = 527 m/s, about the rms speed of N2 (517 m/s)." } Collision \(impact\) theory, p\. 3, citing Sobel'man \(Ref\. 7\); the width convention is not stated\. 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.