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Recommended Values of Standard Frequencies: Iodine (\$ii(lambda) ~~ 532 "unitsml(nm)"\$)

Absorbing molecule 127I2, \$"a"_{10}\$ component, R(56) 32-0 transition [1]

CIPM recommended values

The values

\$f = 563260223513 "unitsml(kHz)"\$
\$ii(lambda) = 532245036.104 "unitsml(fm)"\$

with a relative standard uncertainty of \$8.9 xx 10^(12)\$ apply to the radiation of a frequency-doubled Nd:YAG laser, stabilized with an iodine cell external to the laser, subject to the conditions:

  • cold-finger temperature \$(–15 +- 1) "unitsml(degC)"\$ [2]

  • frequency modulation width, peak-to-peak, \$(1 +- 0.2) "unitsml(MHz)"\$ for \$3f\$ detection cases;

  • saturating beam intensity of \$(17 +- 11) "unitsml(mW*cm^(-2))"\$

Source data

Adopted value

\$f = 563260223513 (5) "unitsml(kHz)"\$
\$u_c//y = 8.9 xx 10^(-12)\$

for which:
\$ii(lambda) = 532245036.104 (5) "unitsml(fm)"\$
\$u_c//y = 8.9 xx 10^(-12)\$

calculated from

\$f // "unitsml(kHz)"\$ \$u_c//y\$ source data

\$563260223515.0\$

\$9.2 xx 10^(-12)\$

\$563260223514.5\$

\$8.9 xx 10^(-12)\$

[1], [2]

\$563260223510.1\$

\$5 xx 10^(-13)\$

[3]

Unweighted mean:

\$f = 563260223513.2 "unitsml(kHz)"\$

The standard uncertainty calculated from the dispersion of the three values is \$2.7 "unitsml(kHz)"\$. Taking into account the frequency dependence on the cell quality and other effects, the CCL preferred to adopt a standard uncertainty of \$5 "unitsml(kHz)"\$, corresponding to a relative standard uncertainty of \$8.9 xx 10^(-12)\$.

Since 2001, it was noted that the global mean has changed from …​..513.2 to …​..511.5 \$"unitsml(kHz)"\$, with a standard deviation of \$2.6 "unitsml(kHz)"\$. Given the possible shifts due to beam alignment, etalon effects and other technical effects, it was decided not to change the 2001 value or uncertainty but rather to define more comprehensively the operating conditions as follows:

  • cold-finger temperature \$(–15 +- 1) "unitsml(degC)"\$ [2]

  • frequency modulation width, peak-to-peak, \$(1 +- 0.2) "unitsml(MHz)"\$ for \$3f\$ detection cases;

  • saturating beam intensity of \$(17 +- 11) "unitsml(mW*cm^(-2))"\$

Other 127I2 absorbing transitions close to this transition may also be used by making reference to the following frequency differences, using the \$"a"_{10}\$ component of the R(56) 32-0 transition as a reference, see also source data :

line no

transition

comp.

\$f_(xy) = [ f(y , x) - f("a"_{10}, R(56) 32-0) ] // "unitsml(kHz)"\$

\$x\$

\$y\$

\$f_(xy)\$

\$u_c // "unitsml(kHz)"\$

1111

P(53) 32-0

\$"a"_1\$

\$2599708.0\$

\$5.0\$

1110

R(56) 32-0

\$"a"_{10}\$

\$0.0\$

 — 

1109

P(83) 33-0

\$"a"_{21}\$

\$–15682075.2\$

\$5.0\$

R(134) 36-0

\$"a"_1\$

\$–17173681.7\$

\$5.0\$

1108

R(106) 34-0

\$"a"_1\$

\$–30434763.4\$

\$5.0\$

1107

R(86) 33-0

\$"a"_1\$

\$–32190406.0\$

\$5.0\$

1106

P(119) 35-0

\$"a"_1\$

\$–36840163.0\$

\$5.0\$

1105

P(54) 32-0

\$"a"_1\$

\$–47588897.1\$

\$5.0\$

1104

R(57) 32-0

\$"a"_1\$

\$–50946884.7\$

\$5.0\$

1103

P(132) 36-0

\$"a"_1\$

\$–73517088.1\$

\$5.0\$

1101

R(145) 37-0

\$"a"_1\$

\$–84992177.6\$

\$5.0\$

R(122) 35-0

\$"a"_1\$

\$–90981724.1\$

\$5.0\$

1100

P(84) 33-0

\$"a"_1\$

\$–95929863.0\$

\$5.0\$

109]

P(104) 34-0

\$"a"_1\$

\$–98069775.0\$

\$5.0\$

P(55) 32-0

\$"a"_1\$

\$–98766591.0\$

\$5.0\$

1098

R(58) 32-0

\$"a"_1\$

\$–102159978.2\$

\$5.0\$

1097

R(87) 33-0

\$"a"_1\$

\$–111935173.1\$

\$5.0\$

where \$f(y,x)\$ represents the frequency of the transition denoted \$y,x\$ and \$f("a"_{10}, " R(56)" "32-0")\$ the frequency of the reference transition. The CCL preferred to assign an uncertainty of \$5 "unitsml(kHz)"\$ to all listed frequency differences, regarding the possible influence of the quality of the iodine cell, background slopes and the small number of data for each frequency difference available.

In 2007 the CIPM [24] at its 96th meeting on a proposition of the CCL [25] recommended (Recommendation 1; CI-2007) that the above list shall be extended to the following lines

transition

comp.

\$f_(xy) = [ f(y , x) - f("a"_{10}, "R(56) 32-0") ] // "unitsml(kHz)"\$

Ref.

\$x\$

\$y\$

\$f_(xy)\$

\$u_c // "unitsml(kHz)"\$

P(142) 37-0

\$"a"_1\$

\$20123511.4\$

\$5.0\$

[26]

R(121) 35-0

\$"a"_1\$

\$27539228.6\$

\$5.0\$

[26]

R(85) 33-0

\$"a"_1\$

\$46496559.1\$

\$5.0\$

[27]

Source data

Holzwarth et al. [4] give

\$f_(a10) = 563260223508.7 "unitsml(kHz)"\$
\$u_c = 5.2 "unitsml(kHz)"\$

at a cold-finger temperature of \$–5 "unitsml(degC)"\$ (iodine pressure = \$2.46 "unitsml(Pa)"\$) [3].

Nevsky et al. [5] give

\$f_(a10) = 563260223507.8 "unitsml(kHz)"\$
\$u_c//y = 2.0 xx 10^(-12)\$

at a cold-finger temperature of \$–5 "unitsml(degC)"\$ (iodine pressure = \$2.46 "unitsml(Pa)"\$).

These two measurements have been carried out with the same iodine cell. Therefore, the CCL decided to consider the arithmetic mean of these two data, i.e.

\$f_(a10) = (563260223508.7 + 563260223507.8)//2 = 563260223508.25 "unitsml(kHz)"\$

For a reference temperature of \$–15 "unitsml(degC)"\$ (iodine pressure = \$0.83 "unitsml(Pa)"\$), using a pressure dependence of \$–4.2 "unitsml(kHz/Pa)"\$ [5], a correction of \$+6.8 "unitsml(kHz)"\$ has to be applied, giving

\$f_(a10) = 563260223515.0 "unitsml(kHz)"\$
\$u_c//y = 9.2 xx 10^(-12)\$.

The following values have been obtained for the frequency differences between several 127I2 absorbing transitions and the R(56) 32-0 transition, at an iodine cold-finger temperature of \$–15 "unitsml(degC)"\$ (iodine pressure = \$0.83 "unitsml(Pa)"\$):

line no

transition

comp.

\$[ f(y , x) - f("a"_{10}," R(56) 32-0)"] // "unitsml(kHz)"\$

\$x\$

\$y\$

[7]

[8]

[4]

[5]

unw. mean

\$u // "unitsml(kHz)"\$

1111

P(53) 32-0

\$"a"_1\$

\$2599708.0\$

\$2599708.0\$

\$2599708.0\$

\$0.0\$

1110

R(56) 32-0

\$"a"_{10}\$

\$0.0\$

\$0.0\$

\$0.0\$

\$0.0\$

\$0.0\$

1109

P(83) 33-0

\$"a"_{21}\$

\$–15682074.1\$

\$–15682076.2\$

\$–15682075.2\$

\$1.5\$

R(134) 36-0

\$"a"_1\$

\$–17173680.4\$

\$–17173682.9\$

\$–17173681.7\$

\$1.8\$

1108

R(106) 34-0

\$"a"_1\$

\$–30434761.5\$

\$–30434765.2\$

\$–30434763.4\$

\$2.6\$

1107

R(86) 33-0

\$"a"_1\$

\$–32190404.0\$

\$–32190408.0\$

\$–32190406.0\$

\$2.8\$

1106

P(119) 35-0

\$"a"_1\$

\$–36840161.5\$

\$–36840164.4\$

\$–36840163.0\$

\$2.1\$

1105

P(54) 32-0

\$"a"_1\$

\$–47588892.5\$

\$–47588898.2\$

\$–47588899.8\$

\$–47588898.0\$

\$–47588897.1\$

\$3.2\$

1104

R(57) 32-0

\$"a"_1\$

\$–50946880.4\$

\$–50946886.4\$

\$–50946887.2\$

\$–50946884.7\$

\$3.7\$

1103

P(132) 36-0

\$"a"_1\$

\$–73517088.1\$

1101

R(145) 37-0

\$"a"_1\$

\$–84992177.6\$

R(122) 35-0

\$"a"_1\$

\$–90981724.1\$

1100

P(84) 33-0

\$"a"_1\$

\$–95929863.0\$

1099

P(104) 34-0

\$"a"_1\$

\$–98069775.0\$

P(55) 32-0

\$"a"_1\$

\$–98766590.0\$

\$–98766591.9\$

\$–98766591.0\$

\$1.4\$

1098

R(58) 32-0

\$"a"_1\$

\$–102159977.4\$

\$–102159979.0\$

\$–102159978.2\$

\$1.2\$

1097

R(87) 33-0

\$"a"_1\$

\$–111935173.1\$

where \$f(y,x)\$ represents the frequency of the transition denoted \$y,x\$ and \$f("a"_{10}, R(56) 32-0)\$ the frequency of the reference transition.

Absolute frequency of the other transitions related to those adopted as recommended and frequency intervals between transitions and hyperfine components

These tables replace those published in BIPM Com. Cons. Long., 2001, 10, 151-167 and Metrologia, 2003, 40, 116-120.

The notation for the transitions and the components is that used in the source references. The values adopted for the frequency intervals are the weighted means of the values given in the references.

For the uncertainties, account has been taken of:

  • the uncertainties given by the authors;

  • the spread in the different determinations of a single component;

  • the effect of any perturbing components;

  • the difference between the calculated and the measured values.

In the tables, \$u_c\$ represents the estimated combined standard uncertainty (\$1 ii(sigma)\$).
All transitions in molecular iodine refer to the B-X system.

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 R(87) 33-0 [no 1097]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_{12}\$

\$582.6721\$

\$0.0020\$

\$"a"_2\$

\$51.5768\$

\$0.0020\$

\$"a"_{13}\$

\$622.8375\$

\$0.0020\$

\$"a"_3\$

\$101.4407\$

\$0.0020\$

\$"a"_{14}\$

\$663.9140\$

\$0.0020\$

\$"a"_4\$

\$282.4331\$

\$0.0020\$

\$"a"_{15}\$

\$730.3226\$

\$0.0020\$

\$"a"_5\$

\$332.2313\$

\$0.0020\$

\$"a"_{16}\$

\$752.4797\$

\$0.0020\$

\$"a"_6\$

\$342.2223\$

\$0.0020\$

\$"a"_{17}\$

\$778.0522\$

\$0.0020\$

\$"a"_7\$

\$390.3168\$

\$0.0020\$

\$"a"_{18}\$

\$799.4548\$

\$0.0020\$

\$"a"_8\$

\$445.6559\$

\$0.0020\$

\$"a"_{19}\$

\$893.1211\$

\$0.0020\$

\$"a"_9\$

\$462.0620\$

\$0.0020\$

\$"a"_{20}\$

\$907.5209\$

\$0.0020\$

\$"a"_{10}\$

\$497.5450\$

\$0.0020\$

\$"a"_{21}\$

\$923.5991\$

\$0.0020\$

\$"a"_{11}\$

\$511.9546\$

\$0.0020\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," R(87) 33-0) "- f ("a"_{10}," R(56) 32-0") = -111935173" (5)" "unitsml(kHz)"\$ [9]

Ref. [10]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 R(87) 33-0 [no 1098]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_{10}\$

\$571.5686\$

\$0.0020\$

\$"a"_2\$

\$259.1938\$

\$0.0020\$

\$"a"_{11}\$

\$697.9347\$

\$0.0020\$

\$"a"_5\$

\$311.8933\$

\$0.0020\$

\$"a"_{12}\$

\$702.8370\$

\$0.0020\$

\$"a"_6\$

\$401.3702\$

\$0.0020\$

\$"a"_{13}\$

\$726.0151\$

\$0.0020\$

\$"a"_7\$

\$416.7177\$

\$0.0020\$

\$"a"_{14}\$

\$732.3220\$

\$0.0020\$

\$"a"_8\$

\$439.9735\$

\$0.0020\$

\$"a"_{15}\$

\$857.9730\$

\$0.0020\$

\$"a"_9\$

\$455.4891\$

\$0.0020\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," R(58) 32-0) "- f ("a"_{10}," R(56) 32-0") = -102159978" (5)" "unitsml(kHz)"\$ [9]

Ref. [11]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 P(55) 32-0

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_{13}\$

\$609.4478\$

\$0.0020\$

\$"a"_2\$

\$37.8987\$

\$0.0020\$

\$"a"_{14}\$

\$648.9064\$

\$0.0020\$

\$"a"_3\$

\$73.8521\$

\$0.0020\$

\$"a"_{15}\$

\$714.0690\$

\$0.0020\$

\$"a"_4\$

\$272.2124\$

\$0.0020\$

\$"a"_{16}\$

\$739.8350\$

\$0.0020\$

\$"a"_7\$

\$373.1260\$

\$0.0020\$

\$"a"_{17}\$

\$763.0081\$

\$0.0020\$

\$"a"_8\$

\$437.4166\$

\$0.0020\$

\$"a"_{18}\$

\$788.2234\$

\$0.0020\$

\$"a"_9\$

\$455.3851\$

\$0.0020\$

\$"a"_{19}\$

\$879.7357\$

\$0.0020\$

\$"a"_{10}\$

\$477.0210\$

\$0.0020\$

\$"a"_{20}\$

\$893.4676\$

\$0.0020\$

\$"a"_{11}\$

\$490.5588\$

\$0.0020\$

\$"a"_{21}\$

\$910.3088\$

\$0.0020\$

\$"a"_{12}\$

\$573.0377\$

\$0.0020\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," P(55) 32-0) "- f ("a"_{10}," R(56) 32-0") = -98766591" (5)" "unitsml(kHz)"\$ [9]

Ref. [11]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 P(104) 34-0 [no 1099]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_9\$

\$466.6137\$

\$0.0020\$

\$"a"_2\$

\$238.8227\$

\$0.0020\$

\$"a"_{10}\$

\$570.8323\$

\$0.0020\$

\$"a"_3\$

\$277.4934\$

\$0.0020\$

\$"a"_{11}\$

\$688.5193\$

\$0.0020\$

\$"a"_4\$

\$293.3463\$

\$0.0020\$

\$"a"_{12}\$

\$699.1488\$

\$0.0020\$

\$"a"_5\$

\$331.4333\$

\$0.0020\$

\$"a"_{13}\$

\$727.8544\$

\$0.0020\$

\$"a"_6\$

\$389.0585\$

\$0.0020\$

\$"a"_{14}\$

\$739.2895\$

\$0.0020\$

\$"a"_7\$

\$405.6376\$

\$0.0020\$

\$"a"_{15}\$

\$856.7001\$

\$0.0020\$

\$"a"_8\$

\$450.2193\$

\$0.0020\$

\$0.0020\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," P(104) 34-0) "- f ("a"_{10}," R(56) 32-0") = -98069775" (5)" "unitsml(kHz)"\$ [9]

Ref. [11]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 P(84) 33-0 [no 1100]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_9\$

\$459.8476\$

\$0.0020\$

\$"a"_2\$

\$249.8445\$

\$0.0020\$

\$"a"_{10}\$

\$571.2806\$

\$0.0020\$

\$"a"_3\$

\$281.2957\$

\$0.0020\$

\$"a"_{11}\$

\$694.0020\$

\$0.0020\$

\$"a"_4\$

\$290.0304\$

\$0.0020\$

\$"a"_{12}\$

\$701.7501\$

\$0.0020\$

\$"a"_5\$

\$320.9041\$

\$0.0020\$

\$"a"_{13}\$

\$726.3808\$

\$0.0020\$

\$"a"_6\$

\$396.5400\$

\$0.0020\$

\$"a"_{14}\$

\$735.0562\$

\$0.0020\$

\$"a"_7\$

\$411.5392\$

\$0.0020\$

\$"a"_{15}\$

\$857.4151\$

\$0.0020\$

\$"a"_8\$

\$444.9362\$

\$0.0020\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," P(84) 33-0) "- f ("a"_{10}," R(56) 32-0") = -95929863" (5)" "unitsml(kHz)"\$ [9]

Ref. [12]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 R(122) 35-0

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_9\$

\$475.9553\$

\$0.0020\$

\$"a"_2\$

\$224.7302\$

\$0.0020\$

\$"a"_{10}\$

\$570.3004\$

\$0.0020\$

\$"a"_3\$

\$273.2394\$

\$0.0020\$

\$"a"_{11}\$

\$681.2572\$

\$0.0020\$

\$"a"_4\$

\$297.0396\$

\$0.0020\$

\$"a"_{12}\$

\$695.4307\$

\$0.0020\$

\$"a"_5\$

\$344.9343\$

\$0.0020\$

\$"a"_{13}\$

\$730.2395\$

\$0.0020\$

\$"a"_6\$

\$378.8637\$

\$0.0020\$

\$"a"_{14}\$

\$745.1865\$

\$0.0020\$

\$"a"_7\$

\$398.2113\$

\$0.0020\$

\$"a"_{15}\$

\$855.9386\$

\$0.0020\$

\$"a"_8\$

\$456.8479\$

\$0.0020\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," R(122) 35-0) "- f ("a"_{10}," R(56) 32-0") = -90981724" (5)" "unitsml(kHz)"\$ [9]

Ref. [12]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 R(145) 37-0 [no 1101]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_{12}\$

\$608.2166\$

\$0.0020\$

\$"a"_2\$

\$111.3681\$

\$0.0020\$

\$"a"_{13}\$

\$680.6255\$

\$0.0020\$

\$"a"_3\$

\$220.5695\$

\$0.0020\$

\$"a"_{14}\$

\$752.7967\$

\$0.0020\$

\$"a"_4\$

\$298.7582\$

\$0.0020\$

\$"a"_{15}\$

\$769.5347\$

\$0.0020\$

\$"a"_5\$

\$376.9445\$

\$0.0020\$

\$"a"_{16}\$

\$799.1414\$

\$0.0020\$

\$"a"_6\$

\$414.9517\$

\$0.0020\$

\$"a"_{17}\$

\$846.4138\$

\$0.0020\$

\$"a"_7\$

\$469.8127\$

\$0.0020\$

\$"a"_{18}\$

\$874.8758\$

\$0.0020\$

\$"a"_8\$

\$491.2288\$

\$0.0020\$

\$"a"_{19}\$

\$940.0615\$

\$0.0020\$

\$"a"_9\$

\$495.5179\$

\$0.0020\$

\$"a"_{20}\$

\$964.5342\$

\$0.0020\$

\$"a"_{10}\$

\$580.7013\$

\$0.0020\$

\$"a"_{21}\$

\$990.2893\$

\$0.0020\$

\$"a"_{11}\$

\$605.3833\$

\$0.0020\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," R(145) 37-0) "- f ("a"_{10}," R(56) 32-0") = -84992178" (5)" "unitsml(kHz)"\$ [9]

Ref. [10]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 P(132) 36-0 [no 1103]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_9\$

\$482.3956\$

\$0.0020\$

\$"a"_2\$

\$215.0115\$

\$0.0020\$

\$"a"_{10}\$

\$569.8339\$

\$0.0020\$

\$"a"_3\$

\$270.3841\$

\$0.0020\$

\$"a"_{11}\$

\$676.1016\$

\$0.0020\$

\$"a"_4\$

\$299.4166\$

\$0.0020\$

\$"a"_{12}\$

\$692.6715\$

\$0.0020\$

\$"a"_5\$

\$354.1318\$

\$0.0020\$

\$"a"_{13}\$

\$731.8283\$

\$0.0020\$

\$"a"_6\$

\$371.6729\$

\$0.0020\$

\$"a"_{14}\$

\$749.1808\$

\$0.0020\$

\$"a"_7\$

\$393.0781\$

\$0.0020\$

\$"a"_{15}\$

\$855.2633\$

\$0.0020\$

\$"a"_8\$

\$461.2856\$

\$0.0020\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," P(132) 36-0) "- f ("a"_{10}," R(56) 32-0") = -73517088" (5)" "unitsml(kHz)"\$ [9]

Ref. [10]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 R(57) 32-0 [no 1104]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_{13}\$

\$610.925\$

\$0.001\$

\$"a"_2\$

\$39.372\$

\$0.001\$

\$"a"_{14}\$

\$650.805\$

\$0.001\$

\$"a"_3\$

\$76.828\$

\$0.001\$

\$"a"_{15}\$

\$715.550\$

\$0.001\$

\$"a"_4\$

\$273.042\$

\$0.001\$

\$"a"_{16}\$

\$741.175\$

\$0.001\$

\$"a"_7\$

\$375.284\$

\$0.001\$

\$"a"_{17}\$

\$764.716\$

\$0.001\$

\$"a"_8\$

\$438.243\$

\$0.001\$

\$"a"_{18}\$

\$789.777\$

\$0.001\$

\$"a"_9\$

\$456.183\$

\$0.001\$

\$"a"_{19}\$

\$881.116\$

\$0.001\$

\$"a"_{10}\$

\$479.201\$

\$0.001\$

\$"a"_{20}\$

\$895.016\$

\$0.001\$

\$"a"_{11}\$

\$492.915\$

\$0.001\$

\$"a"_{21}\$

\$911.901\$

\$0.001\$

\$"a"_{12}\$

\$573.917\$

\$0.001\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," R(57) 32-0) "- f ("a"_{10}," R(56) 32-0") = -50946885" (5)" "unitsml(kHz)"\$ [9]

Ref. [7], [13]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 P(54) 32-0 [no 1105]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_9\$

\$454.563\$

\$0.001\$

\$"a"_2\$

\$260.992\$

\$0.001\$

\$"a"_{10}\$

\$571.536\$

\$0.001\$

\$"a"_3\$

\$285.008\$

\$0.001\$

\$"a"_{11}\$

\$698.614\$

\$0.001\$

\$"a"_4\$

\$286.726\$

\$0.001\$

\$"a"_{12}\$

\$702.935\$

\$0.001\$

\$"a"_5\$

\$310.066\$

\$0.001\$

\$"a"_{13}\$

\$725.834\$

\$0.001\$

\$"a"_6\$

\$402.249\$

\$0.001\$

\$"a"_{14}\$

\$731.688\$

\$0.001\$

\$"a"_8\$

\$417.668\$

\$0.001\$

\$"a"_{15}\$

\$857.961\$

\$0.001\$

\$"a"_8\$

\$438.919\$

\$0.001\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," P(54) 32-0) "- f ("a"_{10}," R(56) 32-0") = -47588897" (5)" "unitsml(kHz)"\$ [9]

Ref. [7], [13]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 P(119) 35-0 [no 1106]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_{13}\$

\$645.617\$

\$0.002\$

\$"a"_2\$

\$75.277\$

\$0.002\$

\$"a"_{14}\$

\$697.723\$

\$0.002\$

\$"a"_3\$

\$148.701\$

\$0.002\$

\$"a"_{15}\$

\$747.389\$

\$0.003\$

\$"a"_4\$

\$290.376\$

\$0.003\$

\$"a"_{16}\$

\$771.197\$

\$0.003\$

\$"a"_5\$

\$349.310\$

\$0.002\$

\$"a"_{17}\$

\$804.769\$

\$0.003\$

\$"a"_6\$

\$371.567\$

\$0.002\$

\$"a"_{18}\$

\$827.641\$

\$0.003\$

\$"a"_9\$

\$474.953\$

\$0.004\$

\$"a"_{19}\$

\$912.125\$

\$0.002\$

\$"a"_{10}\$

\$530.727\$

\$0.002\$

\$"a"_{20}\$

\$930.053\$

\$0.002\$

\$"a"_{11}\$

\$548.787\$

\$0.002\$

\$"a"_{21}\$

\$949.288\$

\$0.003\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," P(119) 35-0) "- f ("a"_{10}," R(56) 32-0") = -36840163" (5)" "unitsml(kHz)"\$ [9]

Ref. [14], [15]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 R(86) 33-0 [no 1107]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_9\$

\$460.973\$

\$0.002\$

\$"a"_2\$

\$248.206\$

\$0.002\$

\$"a"_{10}\$

\$571.262\$

\$0.002\$

\$"a"_3\$

\$280.802\$

\$0.002\$

\$"a"_{11}\$

\$693.205\$

\$0.002\$

\$"a"_4\$

\$290.502\$

\$0.002\$

\$"a"_{12}\$

\$701.377\$

\$0.002\$

\$"a"_5\$

\$322.524\$

\$0.002\$

\$"a"_{13}\$

\$726.710\$

\$0.002\$

\$"a"_6\$

\$395.386\$

\$0.002\$

\$"a"_{14}\$

\$735.795\$

\$0.002\$

\$"a"_7\$

\$410.696\$

\$0.002\$

\$"a"_{15}\$

\$857.383\$

\$0.002\$

\$"a"_8\$

\$445.759\$

\$0.002\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," R(86) 33-0) "- f ("a"_{10}," R(56) 32-0") = -32190406" (5)" "unitsml(kHz)"\$ [9]

Ref. [15], [16]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 R(106) 34-0 [no 1108]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_9\$

\$467.984\$

\$0.002\$

\$"a"_2\$

\$236.870\$

\$0.002\$

\$"a"_{10}\$

\$570.799\$

\$0.002\$

\$"a"_3\$

\$276.941\$

\$0.002\$

\$"a"_{11}\$

\$687.539\$

\$0.002\$

\$"a"_4\$

\$293.861\$

\$0.002\$

\$"a"_{12}\$

\$698.663\$

\$0.002\$

\$"a"_5\$

\$333.350\$

\$0.002\$

\$"a"_{13}\$

\$728.261\$

\$0.002\$

\$"a"_6\$

\$387.636\$

\$0.002\$

\$"a"_{14}\$

\$740.185\$

\$0.002\$

\$"a"_7\$

\$404.635\$

\$0.002\$

\$"a"_{15}\$

\$856.675\$

\$0.002\$

\$"a"_8\$

\$451.175\$

\$0.002\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," R(106) 34-0) "- f ("a"_{10}," R(56) 32-0") = -30434763" (5)" "unitsml(kHz)"\$ [9]

Ref. [15], [16], [17]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 R(134) 36-0

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_9\$

\$462.603\$

\$0.009\$

\$"a"_2\$

\$212.287\$

\$0.007\$

\$"a"_{10}\$

\$484.342\$

\$0.007\$

\$"a"_3\$

\$269.634\$

\$0.022\$

\$"a"_{11}\$

\$674.703\$

\$0.009\$

\$"a"_4\$

\$300.097\$

\$0.011\$

\$"a"_{12}\$

\$691.951\$

\$0.008\$

\$"a"_5\$

\$356.801\$

\$0.008\$

\$"a"_{13}\$

\$732.405\$

\$0.008\$

\$"a"_6\$

\$369.644\$

\$0.008\$

\$"a"_{14}\$

\$750.434\$

\$0.009\$

\$"a"_7\$

\$391.684\$

\$0.009\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," R(106) 36-0) "- f ("a"_{10}," R(56) 32-0") = -17173682" (5)" "unitsml(kHz)"\$ [9]

Ref. [15], [16]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 P(83) 33-0 [no 1109]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_{11}\$

\$507.533\$

\$0.004\$

\$"a"_2\$

\$48.789\$

\$0.004\$

\$"a"_{13}\$

\$620.065\$

\$0.004\$

\$"a"_3\$

\$95.839\$

\$0.008\$

\$"a"_{14}\$

\$659.930\$

\$0.004\$

\$"a"_4\$

\$281.343\$

\$0.010\$

\$"a"_{15}\$

\$728.070\$

\$0.004\$

\$"a"_5\$

\$330.230\$

\$0.004\$

\$"a"_{16}\$

\$750.131\$

\$0.004\$

\$"a"_6\$

\$338.673\$

\$0.004\$

\$"a"_{17}\$

\$774.805\$

\$0.004\$

\$"a"_7\$

\$385.830\$

\$0.004\$

\$"a"_{18}\$

\$796.125\$

\$0.004\$

\$"a"_8\$

\$444.365\$

\$0.006\$

\$"a"_{19}\$

\$890.709\$

\$0.005\$

\$"a"_9\$

\$460.503\$

\$0.004\$

\$"a"_{20}\$

\$904.712\$

\$0.005\$

\$"a"_{10}\$

\$493.533\$

\$0.006\$

\$"a"_{21}\$

\$920.475\$

\$0.004\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," P(83) 33-0) "- f ("a"_{10}," R(56) 32-0") = -15682075" (5)" "unitsml(kHz)"\$ [9]

Ref. [15], [16]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 R(56) 32-0 [no 1110]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$–571.542\$

\$0.0015\$

\$"a"_{10}\$

\$0\$

 — 

\$"a"_2\$

\$–311.844\$

\$0.0015\$

\$"a"_{11}\$

\$126.513\$

\$0.0015\$

\$"a"_5\$

\$–260.176\$

\$0.0015\$

\$"a"_{12}\$

\$131.212\$

\$0.0015\$

\$"a"_6\$

\$–170.064\$

\$0.0015\$

\$"a"_{13}\$

\$154.488\$

\$0.0015\$

\$"a"_7\$

\$–154.548\$

\$0.0015\$

\$"a"_{14}\$

\$160.665\$

\$0.0015\$

\$"a"_8\$

\$–131.916\$

\$0.0015\$

\$"a"_{15}\$

\$286.412\$

\$0.0015\$

\$"a"_9\$

\$–116.199\$

\$0.0015\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 P(53) 32-0 [no 1111]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_{17}\$

\$762.623\$

\$0.006\$

\$"a"_2\$

\$37.530\$

\$0.006\$

\$"a"_{18}\$

\$788.431\$

\$0.008\$

\$"a"_3\$

\$73.060\$

\$0.007\$

\$"a"_{19}\$

\$879.110\$

\$0.006\$

\$"a"_4\$

\$271.326\$

\$0.016\$

\$"a"_{20}\$

\$892.953\$

\$0.009\$

\$"a"_{15}\$

\$712.935\$

\$0.012\$

\$"a"_{21}\$

\$910.093\$

\$0.006\$

\$"a"_{16}\$

\$739.274\$

\$0.008\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," P(53) 32-0) "- f ("a"_{10}," R(56) 32-0") = 2599708" (5)" "unitsml(kHz)"\$ [9]

Ref. [15], [16]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 P(142) 37-0 [no 1112]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_8\$

\$467369.1\$

\$2\$

\$"a"_2\$

\$201862.3\$

\$2\$

\$"a"_9\$

\$491394.9\$

\$2\$

\$"a"_3\$

\$266700.6\$

\$2\$

\$"a"_{10}\$

\$569318.6\$

\$2\$

\$"a"_4\$

\$302571.3\$

\$2\$

\$"a"_{11}\$

\$669162.1\$

\$2\$

\$"a"_5\$

\$361836.0\$

\$2\$

\$"a"_{12}\$

\$688963.6\$

\$2\$

\$"a"_6\$

\$366696.9\$

\$2\$

\$"a"_{13}\$

\$734239.7\$

\$2\$

\$"a"_7\$

\$386204.6\$

\$2\$

\$"a"_{14}\$

\$754848.4\$

\$2\$

\$"a"_{15}\$

\$854522.3\$

\$2\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_{21}," P(142) 37-0) "- f ("a"_{10}," R(56) 32-0") = 20123511.4" (5.0)" "unitsml(kHz)"\$ [25], [26]

Ref. [25], [26]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 P(121) 35-0 [no 1113]

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_{11}\$

\$553248.7\$

\$2\$

\$"a"_2\$

\$78094.0\$

\$2\$

\$"a"_{12}\$

\$594812.8\$

\$2\$

\$"a"_3\$

\$154328.5\$

\$2\$

\$"a"_{13}\$

\$594812.8\$

\$2\$

\$"a"_4\$

\$291034.5\$

\$2\$

\$"a"_{14}\$

\$702090.3\$

\$2\$

\$"a"_5\$

\$351499.2\$

\$2\$

\$"a"_{15}\$

\$749153.7\$

\$2\$

\$"a"_6\$

\$374970.5\$

\$2\$

\$"a"_{16}\$

\$773429.2\$

\$2\$

\$"a"_7\$

\$433704.3\$

\$2\$

\$"a"_{17}\$

\$808079.0\$

\$2\$

\$"a"_8\$

\$456783.2\$

\$2\$

\$"a"_{18}\$

\$831410.9\$

\$2\$

\$"a"_9\$

\$476593.6\$

\$2\$

\$"a"_{19}\$

\$914362.6\$

\$2\$

\$"a"_{10}\$

\$534662.3\$

\$2\$

\$"a"_{20}\$

\$932813.8\$

\$2\$

\$"a"_{21}\$

\$952564.0\$

\$2\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_{21}," P(121) 35-0) "- f ("a"_{10}," R(56) 32-0") = 27539228.6" (5.0)" "unitsml(kHz)"\$ [25], [26]

Ref. [25], [26]

\$ii(lambda) ~~ 532 "unitsml(nm)"\$ 127I2 R(85) 33-0

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_n\$

[\$f ("a"_n) - f ("a"_1)\$]/\$"unitsml(MHz)"\$

\$u_c//"unitsml(MHz)"\$

\$"a"_1\$

\$0\$

 — 

\$"a"_{11}\$

\$510619.4\$

\$2\$

\$"a"_2\$

\$50732.5\$

\$2\$

\$"a"_{12}\$

\$582132.0\$

\$2\$

\$"a"_3\$

\$99742.3\$

\$2\$

\$"a"_{13}\$

\$621988.5\$

\$2\$

\$"a"_4\$

\$281946.2\$

\$2\$

\$"a"_{14}\$

\$662825.5\$

\$2\$

\$"a"_5\$

\$331678.7\$

\$2\$

\$"a"_{15}\$

\$729463.3\$

\$2\$

\$"a"_6\$

\$341087.6\$

\$2\$

\$"a"_{16}\$

\$751718.8\$

\$2\$

\$"a"_7\$

\$389099.9\$

\$2\$

\$"a"_{17}\$

\$777078.3\$

\$2\$

\$"a"_8\$

\$445205.3\$

\$2\$

\$"a"_{18}\$

\$798584.8\$

\$2\$

\$"a"_9\$

\$461608.4\$

\$2\$

\$"a"_{19}\$

\$892318.3\$

\$2\$

\$"a"_{10}\$

\$496293.9\$

\$2\$

\$"a"_{20}\$

\$906642.5\$

\$2\$

\$"a"_{21}\$

\$922692.5\$

\$2\$
Frequency referenced to

\$"a"_{10}\$, R(56) 32-0, 127I2: \$f = 563260223513 "unitsml(kHz)"\$ [9]
\$f ("a"_1," R(85) 33-0) "- f ("a"_{10}," R(56) 32-0") = 46496559.1" (5.0)" "unitsml(kHz)"\$ [25], [27]

Ref. [25], [27]

References

  • [1], Diddams S. A., Jones D. J., Ye J., Cundiff S. T., Hall J. L., Ranka J. K., Windeler R. S., Holzwarth R., Udem T., Hänsch T. W., Direct Link between Microwave and Optical Frequencies with a \$300 "unitsml(THz)"\$ Femtosecond Laser Comb, Phys. Rev. Lett., 2000, 84, 5102-5105.

  • [2], Ye J., Ma Long Sheng, Hall J. L., Molecular Iodine Clock, Phys. Rev. Lett., 2001, 87, 270801/1-4.

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1. All transitions in I2 refer to the \$"B"^3Pi" "0_u^+ - X^1 Sigma_g^+\$ system.
2. For the specification of operating conditions, such as temperature, modulation width and laser power, the symbols \$pm\$ refer to a tolerance, not an uncertainty.
3. For the iodine cold-finger temperature to iodine pressure conversion the formula derived by Gillespie and Fraser [6] has been used.