geohegan_1986
=============

D\. B\. Geohegan, A\. W\. McCown and J\. G\. Eden, "Resonantly enhanced three\-photon ionization of krypton", Phys\. Rev\. A 33, 269\-275 \(1986\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/geohegan_1986.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1103/PhysRevA\.33\.269 <https://doi.org/10.1103/PhysRevA.33.269>`__

**Source kind:** measurement

**Recorded technique:** \(2\+1\) resonance\-enhanced three\-photon ionisation of Kr by a free\-running ArF laser \(Lambda Physik EMG 150 EST\), the photoelectrons detected by the attenuation of a 9\.08 GHz microwave field \(pp\. 269\-271; the apparatus of McCown et al\. 1982, mccown\_1982\)\. The laser's spectrum \('Delta lambda ~ 0\.5 nm or ~140 cm^\-1 full width at half maximum', peak at 193\.3 nm, Fig\. 1, p\. 269\) covers the two\-photon 4p6 1S0 \-\> 6p\[1/2\]0, 6p\[3/2\]2 and 6p\[5/2\]2 resonances; only 6p\[3/2\]2 \(two\-photon wavelength 193\.44 nm, where the photon fluence is 0\.7 of its peak\) is taken to contribute, as no fluorescence from the other 6p levels was seen \(pp\. 269, 271\)\. Focused to a line along a 22 mm o\.d\. Suprasil cell, 10 to 300 Torr of 99\.995 % Kr; the energy monitored on a calibrated meter \(10 % pick\-off\), the focal area from burn patterns \(beam width W\(x\), Eq\. 11; length 3\.0 cm; filling factor 1/F = 258, p\. 272\)\. Absolute peak electron density from Eq\. \(1\) with beta\_g = 0\.935 cm^\-1 measured and nu\_m/\[Kr\] = 7\.0 x 10^\-8 cm3 s^\-1 scaled from xenon \(Eq\. 9\), assuming 5\.3 eV electrons \(a 2P3/2 core; 4\.6 eV would change n\_e by ~20 %, p\. 271\)\. Minimum detectable n\_e ~ 5 x 10^10 cm^\-3 \(p\. 270\)\. Data confined to Kr below 50 Torr, above which associative ionisation of 5s metastables adds electrons \(p\. 272\)\. Peak intensities up to ~250 MW/cm2 \(Figs\. 4, 5\); the pulse a triangle of full width tau ~ 30 ns at the 10 % points \(Eqs\. 12\-13\); the polarisation is not stated\.

**Materials in structured entries:** Kr

**Dataset quantities:** excited\_state\_photoionization\_cross\_section, multiphoton\_ionization\_cross\_section

**Contents:** 2 datasets; 0 formulas.

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

Journal pp\. 269\-275 = PDF pages 1\-7 \(a scan with a text layer; PDF page 8 repeats Fig\. 3\)\. Identity checked against the first page \(Physical Review A, volume 33, number 1, January 1986; received 19 August 1985\) on 2026\-10\-08\. The printed title is 'Resonantly enhanced three\-photon ionization of krypton' \(no wavelength\)\.

THE PROCESS\. Kr's ionisation potential is 112 915 cm^\-1 for the 2P3/2 ion \(p\. 269, quoted\), more than two ArF photons\: ionisation at 193 nm needs three, and the measured rate is resonantly enhanced by the two\-photon 4p5 6p\[3/2\]2 level\. For Kr below 50 Torr and above 50\-100 MW/cm2 the photoionisation of 6p\[3/2\]2 is saturated and n\_e rises as I^2\: the rate\-limiting step is the two\-photon excitation \(pp\. 272, 273\); at 50 Torr and below ~100 MW/cm2 n\_e rises as I^3 \(Fig\. 5\)\.

THE DEFINITION \(p\. 271, Eq\. 3\)\: n\_e = \[Kr\] sigma int I^N dt / hbar omega, 'sigma is the generalized N\-photon ionization cross section' \(unit cm^2N W^\-\(N\-1\), the form of mccown\_1982's alpha\)\. With N = 2 and the triangular pulse, sigma = 3 hbar omega n\_p / \(\[Kr\] I\_max^2 tau\) \(Eq\. 15\)\.

NOT TAKEN\: THE EFFECTIVE TWO\-PHOTON CROSS SECTION\. 'From Fig\. 3 and Eq\. \(15\), the effective two\-photon ionization cross section was determined to be 2 x 10^\-32 cm^4 W^\-1' \(p\. 273; Fig\. 4 holds the data, Fig\. 3 the waveforms\: likely a slip\), 'for an ArF laser with a bandwidth \(FWHM\) of 140 cm^\-1' \(p\. 275\)\. It is the rate of the two\-photon excitation of 6p\[3/2\]2 averaged over the laser's two\-photon spectrum, 2\.1 THz off the line centre, with the ionisation step saturated\: not a two\-photon ionisation cross section \(the atom cannot be ionised by two 193 nm photons\), so multiphoton\_ionization\_cross\_section would not mean it; and not the frequency\-integrated generalised cross section of two\_photon\_excitation\_cross\_section \(cm4, W = sigma g Phi^2 with g normalised to one\), into which it converts only through the line shape\. Nor is the line\-centre value 'the absorption cross section given in Sec\. IV becomes 5 x 10^\-28 cm^4 W^\-1' \(p\. 275; Eq\. 28 with a Gaussian line, an estimated atomic width delta ~ 300 MHz \(Ref\. 17\), Delta = 4 THz, 2 omega\_L \- omega\_0 = 2\.1 THz\)\: sigma = sigma\_0 g\(omega\) with g peak\-normalised \(Eq\. 23\), not frequency\-integrated, and the 300 MHz is an estimate\. The conclusions print it '5 x 20^\-28' \(p\. 275, image checked\)\: a misprint for 5 x 10^\-28 \(Sec\. V B\), not data\. Checked\: the factor \(sqrt\(2\) Delta / delta\) exp\[\(\(2 omega\_L \- omega\_0\)/Delta\)^2\] = 24 840 takes 2 x 10^\-32 to 4\.97 x 10^\-28, the printed 5 x 10^\-28\.

CHECKED \(Eq\. 15\)\. The quadratic least\-squares lines of Fig\. 4 \(read on the library's figure image at native resolution, the frame calibrated to its end ticks\)\: n\_p = 0\.0714, 0\.130 and 0\.325 x 10^13 cm^\-3 at 100 MW/cm2 \(times \(I/100\)^2\) for 10, 20 and 50 Torr; with tau = 30 ns, hbar omega = 6\.414 eV and the gas at 296 K \(not stated\), Eq\. \(15\) gives 2\.25, 2\.05 and 2\.05 x 10^\-32 cm4 W\-1\: the printed 2 x 10^\-32\.

WHAT IS TAKEN\. \(1\) The upper\-limit estimate of the 6p\[3/2\]2 photoionisation cross section at 193 nm, ~6 x 10^\-19 cm2 \(Eq\. 16, p\. 273\)\: sigma\_PI I\_min Delta t / hbar omega ~ 1 with I\_min ~ 60 MW/cm2 and Delta t ~ 25 ns, 'by assuming that the ionization process is saturated even at the lowest intensities studied'\. Checked\: hbar omega / \(I\_min Delta t\) = 6\.85 x 10^\-19 cm2 \(hbar omega = 6\.414 eV\), printed as '~6'\. \(2\) Footnote 2 \(p\. 275\)\: the upper limit of the nonresonant three\-photon ionisation cross section of Kr at 248 nm, 3 x 10^\-45 cm6 W\-2, from no detectable electrons with 300 Torr of Kr and 800 mJ, 15 ns FWHM KrF pulses \(n\_e \<~ 10^9 cm^\-3\)\. In the photon\-flux convention, sigma\_3 = sigma \(hbar omega\)^2 = 1\.9 x 10^\-81 cm6 s2 at 5\.0 eV\: uiterwaal\_1998's 1\.2 x 10^\-82 at 248\.6 nm lies 16 times below it\.

NOT TAKEN, quoted values \(no wavelength or conditions stated with them, and the originals not in the library\)\: the two\-photon absorption cross section of 4p6 1S0 \-\> 4p5 6p\[3/2\]2 estimated by Bokor and co\-workers \(J\. Bokor, J\. Zavelovich and C\. K\. Rhodes, Phys\. Rev\. A 21, 1453 \(1980\)\) and Bischel et al\. \(W\. K\. Bischel, J\. Bokor, D\. J\. Kligler and C\. K\. Rhodes, IEEE J\. Quantum Electron\. QE\-15, 380 \(1979\)\) for a 100 cm^\-1 ArF laser, '\(1\-2\.3\) x 10^\-31 cm^4 W^\-1' \(p\. 273\), a range and a bandwidth average that fits no quantity; the 6p\[3/2\]2 photoionisation cross sections of Chang and Kim \(T\. N\. Chang and Y\. S\. Kim, Phys\. Rev\. A 26, 2278 \(1982\)\) and Bokor et al\., '8\.0 x 10^\-19 and 3\.2 x 10^\-19 cm^2, respectively' \(p\. 273\), whose photon energies are not stated here; McGuire's \(Phys\. Rev\. A 24, 835 \(1981\)\) nonresonant three\-photon sigma near 200 nm, 'no larger than 10^\-45 cm^6 W^\-2' \(p\. 269, a bound read from a calculation\); Gornik et al\.'s Xe 6p\[3/2\]2 two\-photon alpha ~ 1\.2 x 10^\-27 cm4 W\-1 \(J\. Chem\. Phys\. 75, 68 \(1981\), p\. 275\); the quenching and radiative rates \(pp\. 272\-274\); Kr's ionisation potential \(quoted\)\.

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

Datasets
--------

geohegan\_1986/sigma\_pi\_6p\_Kr
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "sigma_pi_6p_Kr",
     "material": "Kr",
     "table": "text",
     "scale": 1e-19,
     "quantity": "excited_state_photoionization_cross_section",
     "unit": "cm2",
     "abscissa_unit": "nm",
     "use": "check",
     "parameters": {
       "initial_level": "4p5 6p[3/2]2",
       "limit": "upper",
       "method": "saturation estimate, Eq. (16): sigma_PI = hbar omega / (I_min Delta t), I_min ~ 60 MW/cm2, Delta t ~ 25 ns",
       "wavelength_nm": 193
     }
   }

1 inline points in the source record.

Eq\. \(16\), p\. 273\: 'An upper\-limit estimate for the photoionization cross section for the 6p\[3/2\]2 state at 193 nm', sigma\_PI ~ 6 x 10^\-19 cm2, from sigma\_PI I\_min Delta t / hbar omega ~ 1 with I\_min ~ 60 MW/cm2 \(Fig\. 5\) and Delta t ~ 25 ns, assuming the ionisation step saturated at the lowest intensity studied\. An estimate and an upper limit, not a measured value \(the record's notes\)\.

geohegan\_1986/sigma3\_limit\_Kr
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "sigma3_limit_Kr",
     "material": "Kr",
     "table": "text",
     "scale": 1e-45,
     "quantity": "multiphoton_ionization_cross_section",
     "unit": "cm6 W-2",
     "abscissa_unit": "nm",
     "use": "check",
     "parameters": {
       "photons": 3,
       "polarization": "not stated",
       "limit": "upper",
       "method": "microwave-absorption electron detection, KrF laser, 800 mJ, 15 ns FWHM, 300 Torr Kr: no electrons detected",
       "definition": "n_e = [Kr] sigma int I^N dt / hbar omega (Eq. 3), N = 3: sigma in cm6 W-2",
       "wavelength_nm": 248,
       "pulse_ns": 15,
       "pulse_definition": "FWHM (footnote 2)"
     }
   }

1 inline points in the source record.

Footnote 2, p\. 275\: 'the upper limit for the nonresonant three\-photon ionization cross section for Kr at 248 nm is estimated to be 3 x 10^\-45 cm6 W\-2', from no detectable electrons \(n\_e \<~ 10^9 cm\-3\) with 300 Torr of Kr and 800 mJ, 15 ns FWHM KrF pulses\. The source's definition \(Eq\. 3, N = 3\); sigma\_3 = sigma \(hbar omega\)^2 = 1\.9 x 10^\-81 cm6 s2 on the photon flux \(the record's notes\)\. An upper limit\.

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.