kligler_1980
============

D\. J\. Kligler, J\. Bokor and C\. K\. Rhodes, "Collisional and radiative properties of the H2 E,F 1Sigma\_g\+ state", Phys\. Rev\. A 21, 607 \(1980\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/kligler_1980.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1103/PhysRevA\.21\.607 <https://doi.org/10.1103/PhysRevA.21.607>`__

**Source kind:** measurement

**Recorded technique:** Two\-photon excitation of H2 \(and HD\) to the v = 2 level of the inner well of the E,F 1Sigma\_g\+ state by a transverse\-discharge ArF\* laser \(Lambda Physik EMG\-500; 100 mJ, about 10 ns FWHM, untuned band about 7 Angstrom, 170 cm^\-1, centred at 193\.4 nm\), line narrowed and tuned by two intracavity fused\-silica prisms to about 1 Angstrom \(25 cm^\-1\) over 192\.6\-194\.2 nm, the wavelength calibrated on O2 Schumann\-Runge absorption dips \(0\.5 Angstrom\); the focused beam in a cell at 10 mtorr to several atm\. The near\-infrared E,F \-\> B fluorescence \(\(2,0\) near 750 nm, \(2,1\) near 830 nm\) collected at right angles, time resolved \(RCA C31034A photomultiplier, 10 nm interference filters, Tektronix R7912 digitiser\) or spectrally resolved \(an optical multichannel analyser, about 2 Angstrom\)\. The excited\-state photoionisation cross section from the saturation of the fluorescence with laser energy \(Eqs\. 16\-19, Fig\. 5\); rotational relaxation from rotationally selective excitation \(Figs\. 6, 8\); a first\-Born calculation of the E,F \-\> C quenching cross section \(Eqs\. 5\-14\) \(pp\. 609\-615\)\.

**Materials in structured entries:** H2

**Dataset quantities:** collisional\_quenching\_rate\_coefficient, excited\_state\_photoionization\_cross\_section, radiative\_lifetime

**Contents:** 10 datasets; 0 formulas.

Curation notes
--------------

Phys\. Rev\. A 21\(2\), 607\-617 \(February 1980\) = PDF pages 1\-11 \(journal page = PDF page \+ 606\); a scan with a text layer\. Identity checked against the first page \(PHYSICAL REVIEW A VOLUME 21, NUMBER 2, FEBRUARY 1980; received 31 July 1979; Kligler and Bokor, Stanford, and Rhodes, Chicago Circle\) on 2026\-10\-09\. Every number below was read on the rendered pages \(pp\. 607, 610, 612\-614\) and Table II's image\.

MATERIAL AND WORDING\. H2 is an optmat material \(hydrogen, normal\)\. The vocabulary's radiative\_lifetime, collisional\_quenching\_rate\_coefficient and excited\_state\_photoionization\_cross\_section speak of 'the atom'; here the level is a rovibronic level of the molecule \(E,F 1Sigma\_g\+, v = 2\), and the meaning is otherwise the same \(the inverse total radiative decay rate; k2 in 1/tau = 1/tau\_rad \+ k2\[M\]; the one\-photon photoionisation cross section of the excited level\)\. Taken under that reading; the definitions may be widened to say 'atom or molecule'\.

WHAT IS TAKEN \(inline text values; no table holds them\)\. Radiative lifetimes \(radiative\_lifetime, ns\)\: the E,F \(v = 2\) lifetime '100 \+\- 20 nsec' measured in the earlier Letter \(Ref\. 1, D\. J\. Kligler and C\. K\. Rhodes, Phys\. Rev\. Lett\. 40, 309 \(1978\), held as kligler\_1978b, TC\-1043\), reproduced \(tau\_EF\_v2\); 'the calculated value \[17, 19\] of 90 nsec' \(Wolniewicz 1969; Spindler 1969\), reproduced \(tau\_EF\_v2\_calc\); the C 1Pi\_u \(v = 2\) lifetime 'tau\_C\(v = 2\) = 0\.88 nsec' that the authors obtain from Allison and Dalgarno's C \-\> X transition probabilities \(p\. 612\), check \(tau\_C\_v2\)\. Collisional removal of E,F \(v = 2\) \(collisional\_quenching\_rate\_coefficient, cm3/s\)\: by H2, \(2\.1 \+\- 0\.4\) x 10^\-9 \(kq\_self\_EF\), and by He, \(0\.8 \+\- 0\.4\) x 10^\-9 \(kq\_He\_EF\), both from Ref\. 1 and reproduced \(p\. 610\); this paper's first\-Born rate for the channel E,F \(v = 2\) \+ H2 \-\> C 1Pi\_u \(v = 2\) \+ H2, '2\.3 x 10^\-9 cm3/sec at 300 K' \(p\. 612; kq\_self\_EF\_C\_born, primary, the paper's own calculation\), which it compares with the measured 2\.1; the rotational relaxation of E,F \(v = 2\) in H2, upper limits 'k\_R^{2,0} \<= 3 x 10^\-12 cm3/sec and k\_R^{3,1} \<= 6 x 10^\-12 cm3/sec' \(p\. 614, from S\[P\(2\)\]/S\[P\(4\)\] and S\[P\(1\)\]/S\[P\(3\)\] \<= 0\.1 in Fig\. 6 with R\_L = 3 nsec^\-1, Eqs\. 20\-21\), as the state\-to\-state channels J = 2 \-\> 0 and 3 \-\> 1 \(kr\_self\_J2\_J0, kr\_self\_J3\_J1; check, upper limits\)\. The excited\-state photoionisation cross section at 193 nm \(excited\_state\_photoionization\_cross\_section, cm2\)\: '8 x 10^\-19 cm2 \<= sigma\_pi \<= 4 x 10^\-18 cm2' \(p\. 613, Fig\. 5, Eq\. 19 with tau\_C\), held as the interval \(2\.4 \+\- 1\.6\) x 10^\-18, a bound \(as bruce\_1990 holds a printed limit\), check\: 'this experiment does not actually measure the E,F\-state photoionization cross section, but rather the cross section for photoionization of the collisionally mixed, E,F and C states' \(sigma\_pi\_EF\); and Cohn's calculation for E,F \(v = 2\) \-\> H2\+ \(X, v = 2\) at 6\.4 eV, '2\.6 x 10^\-18 cm2' \(A\. Cohn, J\. Chem\. Phys\. 57, 2456 \(1972\), not in the library\), reproduced \(sigma\_pi\_cohn\)\.

CHECKED\. Fig\. 3's level energies \(E,F v = 2\: J = 0 103 552, J = 1 103 598, J = 2 103 682, J = 3 103 987; C v = 2\: J = 1 103 620, J = 2 103 729, J = 3 103 892 cm^\-1; from Dieke's tables, Ref\. 34\) against Table II's two\-photon transitions \(p\. 613\)\: Q\(0\) = 103 552 and S\(0\) = 103 682 are the J = 0 and J = 2 levels; Q\(1\) 103 479 and S\(1\) 103 869 plus F''\(1\) = 118\.49 \(balakrishnan\_1994's value\) give 103 597\.5 and 103 987\.5; the 22 cm^\-1 between the J = 1 levels of E,F and C \(Fig\. 3\) is 103 620 \- 103 598\. Arithmetic by hand, no script \(no table is taken\)\. FINDING\: Table I's ranges \(p\. 608\) and Table II's lines differ by 1 cm^\-1 at three ends \(O branch '102 893\-103 198' against O\(3\) = 102 892 and O\(2\) = 103 197; S branch '103 674\-' against S\(3\) = 103 673\)\: rounding; nothing taken depends on them\. The effective lifetime at high pressure, tau\_eff = 2 tau\_C = 1\.8 nsec \(Eq\. 15, p\. 613\), follows from tau\_C = 0\.88 \(1\.76\)\.

COMPARISONS\. bischel\_1979 \(TC\-917\) infers from Ref\. 1's rates total quenching cross sections of 8\.0 \+\- 1\.6 x 10^\-15 cm2 \(H2\) and 3\.0 \+\- 1\.5 x 10^\-15 \(He\); this paper's abstract gives '~100 Angstrom^2' for H2 and its Table III the rotational cross sections \<= 0\.12 and \<= 0\.24 Angstrom^2 \(H2\) and 14 Angstrom^2 \(HD, J = 1 \-\> 0\)\. marinero\_1982 quotes the 100 \+\- 20 ns lifetime from this paper and Ref\. 1\. For OEP 8\: the E,F level is not one of OEP 8's resonances; H2 is the gas whose two\-photon resonance near 193 nm \(and 202 nm\) these numbers describe\: a radiative lifetime of 100 ns, collisional removal 2\.1e\-9 cm3/s \(about 19 ns at 1 bar and 300 K, a derived number\), and photoionisation of order 1e\-18 cm2 at 193 nm\.

NOT TAKEN \(no quantity\)\: the level energies of Fig\. 3 and the two\-photon transition energies of Tables I and II \(p\. 608, 613; reproduced from Dieke's tables, Ref\. 34, rounded to 1 cm^\-1; level\_energy is for atoms and ions, electronic\_state\_energy for an electronic state's Te, T0 or onset, not a rovibronic level\)\: NOT TAKEN \(no quantity; molecular\_level\_energy declined, TC\-1040, a primary source wanted; the same tables put marinero\_1982's E,F \- X \(0,0\) Q lines about 8 cm^\-1 below the modern values, see that record's finding\)\. The \(2,1\)/\(2,0\) emission intensity ratio 1\.4 \+\- 0\.2 against Wolniewicz's A ratio 1\.51 \(p\. 609; a branching ratio of bands\); Table I's emission wavelengths \(830, 750 nm and HD, D2\); the H2 quadrupole moment Q = 0\.484 au \(Kolos and Wolniewicz 1964\) and the Franck\-Condon factor q\_{2,2} = 0\.794 \(Lin 1974\), inputs to the calculation \(p\. 611\-612\); Table III's rotational relaxation cross sections \(derived from the rate coefficients by the mean thermal speed at 300 K\) and Jonkman et al\.'s and Akins et al\.'s values; the HD results, k\_R^{1,0} = \(3 \+\- 1\) x 10^\-10 cm3/sec and k\_R^{0,1} / k\_R^{1,0} = 2\.1 \+\- 0\.5 against detailed balance 2\.46 \(p\. 615; HD is not an optmat material\), and the HD Q\(0\), Q\(1\) lines at 103 221 and 103 173 cm^\-1; R\_L = sigma\_pi I / h omega \+ 1 / \(2 tau\_C\) ~ 3 nsec^\-1 and Fig\. 5's intercept\-to\-slope ratio 0\.05 mJ^\-1 \(apparatus quantities\); the figures \(spectra\)\. No two\-photon absorption coefficient or cross section is printed \(Eq\. 16 defines alpha = sigma / I in cm4/W, p\. 613; the conclusions say it was measured, in Ref\. 1 or 13\); no three\-photon ionisation cross section is printed \(Sec\. V gives only the one\-photon sigma\_pi of the excited state, although the introduction announces 'the cross section for three\-photon ionization of H2'\)\.

FURTHER DATA CITED\: D\. J\. Kligler and C\. K\. Rhodes, Phys\. Rev\. Lett\. 40, 309 \(1978\) \(the E,F lifetime, quenching and two\-photon excitation\) is held as kligler\_1978b \(TC\-1043\); kligler\_1978 is the XeO paper, Ref\. 12\. NOT IN THE LIBRARY\: A\. Cohn, J\. Chem\. Phys\. 57, 2456 \(1972\); B\. R\. Marx, J\. Simons and L\. Allen, J\. Phys\. B 11, 1273 \(1978\) \(two\-photon line\-shape factor\); L\. Wolniewicz, J\. Chem\. Phys\. 51, 5002 \(1969\); A\. C\. Allison and A\. Dalgarno, At\. Data 1, 289 \(1970\)\. W\. K\. Bischel, J\. Bokor, D\. J\. Kligler and C\. K\. Rhodes, IEEE J\. Quantum Electron\. 15, 380 \(1979\) \(Ref\. 13\) is bischel\_1979\.

**Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets
--------

kligler\_1980/tau\_EF\_v2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "tau_EF_v2",
     "material": "H2",
     "table": "text",
     "quantity": "radiative_lifetime",
     "unit": "ns",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "kligler_1978b"
     ],
     "parameters": {
       "method": "measured: decay rate of the E,F -> B fluorescence after two-photon ArF* excitation against H2 pressure, zero-pressure intercept (Ref. 1)"
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

1 inline points in the source record.

p\. 610\: 'In earlier work \[Ref\. 1\] the decay rate of the H2 E,F \-\> B fluorescence was measured as a function of pressure, and the radiative and collisional electronic relaxation rates of the E,F state were determined from these data\. The E,F\-state radiative lifetime was found to be 100 \+\- 20 nsec in excellent agreement with the calculated value \[17, 19\] of 90 nsec' \(tau\_EF\_v2\_calc\)\. The same group's Letter, not in the library, so the best copy available\. Level of the uncertainty not stated\.

kligler\_1980/tau\_EF\_v2\_calc
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "tau_EF_v2_calc",
     "material": "H2",
     "table": "text",
     "quantity": "radiative_lifetime",
     "unit": "ns",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "L. Wolniewicz, J. Chem. Phys. 51, 5002 (1969)",
       "R. J. Spindler, J. Quant. Spectrosc. Radiat. Transf. 9, 1041 (1969)"
     ],
     "parameters": {
       "method": "calculated (E,F -> B transition probabilities of Wolniewicz 1969 with Spindler's Franck-Condon factors, as cited)"
     }
   }

1 inline points in the source record.

p\. 610\: 'the calculated value \[17, 19\] of 90 nsec' \(Wolniewicz's E,F \-\> B transition probabilities, Spindler's Franck\-Condon factors\)\. No uncertainty\.

kligler\_1980/tau\_C\_v2
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "tau_C_v2",
     "material": "H2",
     "table": "text",
     "quantity": "radiative_lifetime",
     "unit": "ns",
     "abscissa": "label",
     "use": "check",
     "parameters": {
       "method": "calculated: the inverse of the sum of Allison and Dalgarno's C -> X transition probabilities from v = 2 (At. Data 1, 289 (1970))"
     }
   }

1 inline points in the source record.

p\. 612\: 'From the theoretical calculations of Allison and Dalgarno for the C 1Pi\_u \-\> X 1Sigma\_g\+ transition probabilities \[31\], we obtain tau\_C\(v = 2\) = 0\.88 nsec'; used for tau\_eff = 2 tau\_C = 1\.8 nsec \(Eq\. 15\)\. The authors' sum of another source's calculated rates, so check\. No uncertainty\.

kligler\_1980/kq\_self\_EF
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kq_self_EF",
     "material": "H2",
     "table": "text",
     "quantity": "collisional_quenching_rate_coefficient",
     "unit": "cm3/s",
     "scale": 1e-09,
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "kligler_1978b"
     ],
     "parameters": {
       "perturber": "self",
       "order": 2,
       "channel": "total",
       "method": "time-resolved E,F -> B fluorescence against H2 pressure (Ref. 1)"
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

1 inline points in the source record.

p\. 610\: 'The total deactivation rate due to collisions with ground\-state H2 molecules was found to be \(2\.1 \+\- 0\.4\) x 10^\-9 cm3/sec' \(Ref\. 1, the slope of the decay rate against pressure\)\. The dominant channel is E,F \+ H2 \-\> C 1Pi\_u \+ H2 \(reaction 3\), by this paper's Born calculation \(kq\_self\_EF\_C\_born\)\. Temperature not stated \(room temperature\)\. Level not stated\.

kligler\_1980/kq\_He\_EF
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kq_He_EF",
     "material": "H2",
     "table": "text",
     "quantity": "collisional_quenching_rate_coefficient",
     "unit": "cm3/s",
     "scale": 1e-09,
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "kligler_1978b"
     ],
     "parameters": {
       "perturber": "He",
       "order": 2,
       "channel": "total",
       "method": "time-resolved E,F -> B fluorescence against He pressure (Ref. 1)"
     },
     "uncertainty": {
       "column": true,
       "level": "not stated"
     }
   }

1 inline points in the source record.

p\. 610\: 'with helium as the collision partner, the rate was \(0\.8 \+\- 0\.4\) x 10^\-9 cm3/sec' \(Ref\. 1\); its size for a nonreactive partner led to the hypothesis of collisional transfer to C 1Pi\_u\. Temperature not stated\. Level not stated\.

kligler\_1980/kq\_self\_EF\_C\_born
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kq_self_EF_C_born",
     "material": "H2",
     "table": "text",
     "quantity": "collisional_quenching_rate_coefficient",
     "unit": "cm3/s",
     "scale": 1e-09,
     "abscissa": "label",
     "use": "primary",
     "parameters": {
       "perturber": "self",
       "order": 2,
       "channel": "C 1Pi_u (v = 2)",
       "temperature_k": 300,
       "method": "first Born approximation for the dipole-quadrupole interaction (the 2s sigma -> 2p pi transition dipole 3 e a0 with the H2 quadrupole moment 0.484 au), P(b) = 1 inside b_h, Franck-Condon factor q_22 = 0.794, the E,F - C detunings of Fig. 3 (22 cm^-1 for J = 1), Boltzmann averaged (Eqs. 5-14)"
     }
   }

1 inline points in the source record.

p\. 612\: 'Averaging the product of velocity and cross section over a Boltzmann distribution of kinetic energies gives a rate constant for process \(3\) of 2\.3 x 10^\-9 cm3/sec at 300 K\. This result agrees remarkably well with the experimental determination of \(2\.1 \+\- 0\.4\) x 10^\-9' \(kq\_self\_EF\)\. Process \(3\)\: H2\(E,F\) \+ H2\(X\) \-\> H2\(C 1Pi\_u\) \+ H2\(X\)\. The paper's own calculation; no uncertainty\.

kligler\_1980/kr\_self\_J2\_J0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kr_self_J2_J0",
     "material": "H2",
     "table": "text",
     "quantity": "collisional_quenching_rate_coefficient",
     "unit": "cm3/s",
     "scale": 1e-12,
     "abscissa": "label",
     "use": "check",
     "parameters": {
       "perturber": "self",
       "order": 2,
       "channel": "E,F 1Sigma_g+ (v = 2, J = 0)",
       "limit": "upper",
       "method": "absence of P(2) emission after rotationally selective two-photon excitation of J = 2 (Fig. 6), steady-state analysis (Eqs. 20-21)"
     }
   }

1 inline points in the source record.

p\. 614\: 'k\_R^{2,0} \<= 3 x 10^\-12 cm3/sec', the rotational relaxation J = 2 \-\> 0 within E,F \(v = 2\) by H2, from S\[P\(2\)\]/S\[P\(4\)\] \<= 0\.1 \(the ~10 % noise of Fig\. 6, Q\(2\) excited, 20 psi gauge\) with Eqs\. 20\-21 and the electronic loss rate R\_L ~ 3 nsec^\-1\. An upper limit \(parameters\.limit\); Table III gives it as sigma\_R \<= 0\.24 Angstrom^2\.

kligler\_1980/kr\_self\_J3\_J1
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "kr_self_J3_J1",
     "material": "H2",
     "table": "text",
     "quantity": "collisional_quenching_rate_coefficient",
     "unit": "cm3/s",
     "scale": 1e-12,
     "abscissa": "label",
     "use": "check",
     "parameters": {
       "perturber": "self",
       "order": 2,
       "channel": "E,F 1Sigma_g+ (v = 2, J = 1)",
       "limit": "upper",
       "method": "absence of P(1) emission after rotationally selective two-photon excitation of J = 3 (Fig. 6), steady-state analysis (Eqs. 20-21)"
     }
   }

1 inline points in the source record.

p\. 614\: 'k\_R^{3,1} \<= 6 x 10^\-12 cm3/sec', the rotational relaxation J = 3 \-\> 1 within E,F \(v = 2\) by H2, from S\[P\(1\)\]/S\[P\(3\)\] \<= 0\.1 \(Fig\. 6, Q\(3\) excited\) with Eqs\. 20\-21\. An upper limit; Table III gives sigma\_R \<= 0\.12 Angstrom^2\.

kligler\_1980/sigma\_pi\_EF
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "sigma_pi_EF",
     "material": "H2",
     "table": "text",
     "quantity": "excited_state_photoionization_cross_section",
     "unit": "cm2",
     "scale": 1e-18,
     "abscissa_unit": "nm",
     "use": "check",
     "parameters": {
       "initial_level": "E,F 1Sigma_g+ (v = 2, inner well), collisionally mixed with C 1Pi_u (v = 2)",
       "method": "saturation of the two-photon-excited fluorescence against ArF* laser energy, steady-state rate equations (Eqs. 16-19), tau_eff = 2 tau_C = 1.8 ns"
     },
     "uncertainty": {
       "column": true,
       "level": "bound"
     }
   }

1 inline points in the source record.

p\. 613\: 'On the basis of these data, we estimate that 8 x 10^\-19 cm2 \<= sigma\_pi \<= 4 x 10^\-18 cm2\. This large uncertainty arises primarily from the uncertainty in converting the measured laser energy to the actual laser intensity at the focus\.' Held as the interval 0\.8\-4\.0 x 10^\-18 cm2\: value 2\.4, bound half\-width 1\.6 \(the printed bounds are the information; 2\.4 is their midpoint, not a printed value\)\. From the saturation of the E,F \-\> B fluorescence \(830 nm\) with laser energy at high pressure, sigma\_pi = \(hbar omega / 2 tau\_C\)\(B / m\) \(Eq\. 19; Fig\. 5, B/m = 0\.05 mJ^\-1\)\. Check\: the paper says it measures the photoionisation of the collisionally mixed E,F and C \(v = 2\) states, not of E,F alone\. Agrees with Cohn's 2\.6 x 10^\-18 \(sigma\_pi\_cohn\)\.

kligler\_1980/sigma\_pi\_cohn
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "sigma_pi_cohn",
     "material": "H2",
     "table": "text",
     "quantity": "excited_state_photoionization_cross_section",
     "unit": "cm2",
     "scale": 1e-18,
     "abscissa_unit": "nm",
     "use": "reproduced",
     "reproduced_from": [
       "A. Cohn, J. Chem. Phys. 57, 2456 (1972)"
     ],
     "parameters": {
       "initial_level": "E,F 1Sigma_g+ (v = 2)",
       "final_state": "H2+ X 2Sigma_g+ (v+ = 2)",
       "method": "calculated (Cohn 1972)"
     }
   }

1 inline points in the source record.

p\. 613\: 'For photoionization from H2 \(E,F 1Sigma\_g\+; v = 2\) to H2\+ \(X 2Sigma\_g\+; v = 2\) at 6\.4 eV \(3\.3 eV above threshold\), Cohn calculates sigma\_pi = 2\.6 x 10^\-18 cm2\.' The x is the ArF\* photon \(6\.4 eV, 193 nm\)\. A partial cross section into one vibrational level of the ion\. No uncertainty\.

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 </register>` for the checks and decisions.