sato_2011
=========

T\. Sato, A\. Iwasaki, K\. Ishibashi, T\. Okino, K\. Yamanouchi, J\. Adachi, A\. Yagishita, H\. Yazawa, F\. Kannari, M\. Aoyma, K\. Yamakawa, K\. Midorikawa, H\. Nakano, M\. Yabashi, M\. Nagasono, A\. Higashiya and T\. Ishikawa, "Determination of the absolute two\-photon ionization cross section of He by an XUV free electron laser", J\. Phys\. B\: At\. Mol\. Opt\. Phys\. 44, 161001 \(2011\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/sato_2011.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1088/0953\-4075/44/16/161001 <https://doi.org/10.1088/0953-4075/44/16/161001>`__

**Source kind:** measurement

**Recorded technique:** He\+ ion yields from two\-photon ionisation of He by the SPring\-8 Compact SASE Source \(SCSS\) test accelerator, an XUV free\-electron laser \(self\-amplified spontaneous emission\), at 61\.4, 58\.4, 56\.0 and 53\.4 nm \(20\.2, 21\.2, 22\.1 and 23\.2 eV; bandwidth '~0\.2 nm', an 'averaged shot\-to\-shot spectral fluctuation of around 0\.5 nm', p\. 4\), 20 Hz pulsed He/H2 beam \(97 % He, 3 % H2; 0\.8 atm stagnation, 0\.5 mm orifice and skimmer; beam 1\.6 mm wide at the focus\), Wiley\-McLaren time\-of\-flight mass spectrometer along the polarisation direction of the light, every shot's ion signals and pulse energy \(an upstream intensity monitor, Richter et al\. 2003\) recorded; 5000 shots at 61\.4 nm and 30 000 at the others \(p\. 2\)\. The light was focused by a SiC concave mirror \(f = 100 mm\) to '10 um' diameter; the pulse energies at the focus, from the upstream ones \(13, 18, 24, 30 uJ\) and three SiC reflectivities, 1\.3, 2\.7, 4\.8 and 6\.7 uJ at 53\.4, 56\.0, 58\.4 and 61\.4 nm \(p\. 2\)\. The pulse length is not measured\: the cross sections 'were evaluated by assuming that the temporal pulse width of XUV light was 300 fs, which is considered to be a typical value' \(p\. 3\)\. Absolute calibration\: the simultaneous one\-photon H2\+ yield of the H2 in the beam, with H2's literature cross section \(Table 2's last row, Chung et al\. 1993, Ref\. 14; the text before Eq\. 5 cites Ref\. 12, Nikolopoulos and Lambropoulos, a slip\)\: Eq\. 5, sigma\_He^\(2\) = N2 Y1 sigma\_H2 / \(N1 Y2\) x hc / \(lambda I\), from Eqs\. 3\-4\. Second and third harmonics \(below 1 % and 0\.5 %\) are taken as negligible after the mirrors; three\-photon ionisation is below 10^\-3 of the two\-photon yield \(Ref\. 11, theory\)\.

**Materials in structured entries:** He

**Dataset quantities:** multiphoton\_ionization\_cross\_section

**Contents:** 4 datasets; 0 formulas.

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

Journal pp\. 161001\-1 to 161001\-5 = PDF pages 2 to 6 \(PDF page 1 is the IOPscience download banner, its only image\); the journal page is the PDF page less one\. Born digital\: every page has a text layer and the tables are text; Figs\. 1\-3 are embedded images \(565 px wide\)\. Identity checked on the first page \(PDF p\. 2\: 'J\. Phys\. B\: At\. Mol\. Opt\. Phys\. 44 \(2011\) 161001 \(5pp\)', Fast Track Communication, Takahiro Sato et al\., The University of Tokyo and RIKEN SPring\-8; received 19 April 2011, published 13 July 2011\) on 2026\-10\-08\. The library's identity is VALIDATED\_WITH\_WARNINGS \(its acquisition could not corroborate the authors automatically\); the first page prints the title, the authors, the DOI and the locator\. The library copy is the version of record\. The author list prints 'Makoto Aoyma'\.

THE CROSS SECTION \(Eqs\. 1\-5, pp\. 3\-4\)\. The yields are fitted as Y1 = a1 I^n1 \(He\+\) and Y2 = a2 I^n2 \(H2\+\), I 'a non\-dimensional XUV light intensity at the focal spot proportional to the photon number per unit area', over each wavelength's shot\-to\-shot fluctuation of the pulse energy \(central intensities '~4 x 10^13' \(61\.4 nm\), '~3' \(58\.4\), '~2' \(56\.0\) and '~1\.3 x 10^13 W cm^\-2' \(53\.4\), p\. 4\); then Y1 = eta N1 sigma\_He^\(2\)\(lambda, I\) \(lambda I / hc\)^2 tau \(Eq\. 3\) and Y2 = eta N2 sigma\_H2 \(lambda I / hc\) tau \(Eq\. 4\), eta the detection efficiency, N the numbers of atoms and molecules in the focal volume, tau 'the averaged temporal width' of the pulses\: so sigma\_He^\(2\) is the rate's coefficient, Gamma = sigma Phi^2 with Phi = lambda I / hc the photon flux \(photons cm^\-2 s^\-1\), and it is reported as a function of the intensity, sigma ~ Y1 / \(Y2 I\) ~ I^\(n1 \- n2 \- 1\)\. Table 1's exponents n1 \(He\+\)\: 1\.8 \(2\), 1\.1 \(1\), 1\.7, 0\.9 \(2\); n2 \(H2\+\)\: 0\.90 \(2\), 0\.78 \(2\), 0\.82 \(2\), 0\.89 \(1\) at 61\.4, 58\.4, 56\.0, 53\.4 nm \(not taken\: no quantity holds the exponent of a yield; read by the script\)\. 'n1 \.\.\. at 58\.4 and 53\.4 nm \.\.\. much smaller than 2, showing clearly the existence of the intermediate resonance levels' \(pp\. 3\-4\)\. Equal detection efficiency for He\+ and H2\+ is assumed \(eta in both Eqs\. 3\-4\); the focal volume, the spatial and temporal profiles and the photon statistics enter only through the intensity I, whose absolute value rests on the pulse energy, the 10 um spot and the assumed 300 fs\: the paper gives no formula for it\. A flat\-top estimate, E / \(300 fs pi \(5 um\)^2\), gives 2\.8, 2\.0, 1\.15 and 0\.55 x 10^13 W cm^\-2 at 61\.4, 58\.4, 56\.0 and 53\.4 nm, 0\.71, 0\.68, 0\.57 and 0\.42 of the central intensities the text gives \(the script\)\. PHOTON STATISTICS\: the SASE pulses' statistics \(and a G^\(2\) factor for a two\-photon rate\) are not mentioned and no correction is stated; the calibration against H2's one\-photon yield does not remove such a factor \(the two yields scale as I^2 and I\)\. The decrease of sigma with I that the paper reports at all four wavelengths is interpreted by the authors, with van der Hart and Bingham \(2005\), as light\-dressed\- state formation \(pp\. 4\-5\)\.

RESONANCES\. 58\.4 nm is on the 2 1P \(1s2p\) \<\- 1 1S transition '\(21\.22 eV, 58\.43 nm\)', one\-photon resonant two\-photon ionisation; 53\.4 nm on the tail of 3 1P \(1s3p\) '\(23\.09 eV, 53\.70 nm\)' \(p\. 2\); 61\.4 and 56\.0 nm off resonance\. With a 0\.2 nm bandwidth and 0\.5 nm shot\-to\-shot fluctuation the 58\.4 nm value is an average over the resonance's profile; 'the extent of the decrease in the experimental cross section when the XUV light\-field intensity increases is found to be smaller than that in the theoretical cross section \.\.\., which may be ascribed to an averaged shot\-to\-shot spectral fluctuation of around 0\.5 nm' \(p\. 4\)\. The wavelengths are the nominal FEL settings, in vacuum \(the paper gives photon energies with them\)\.

UNCERTAINTY\. Table 2 prints the measured values with an error in parentheses on the last digit, '2\.6 \(6\)', '23 \(7\)', '7 \(5\)', and none for '0\.9' \(56\.0 nm\); the paper does not say what the errors include or their level \('The hatched areas \.\.\. represent the ranges of uncertainties', Fig\. 2 caption; none is drawn for 56\.0 nm\)\. Recorded per point \(sigma column\), level not stated\. The assumed 300 fs enters as 1/tau\: a pulse of 150 or 600 fs would double or halve every value, which the stated errors do not include as far as the paper says\.

EXTRACTED \(tools/extract/sato\_2011\.py\)\. Table 2 \(p\. 3, tbl\_bc8ebb788440, cells checked against the table image\)\: the measured row \(this work\) and the two theory rows \(other papers' values\: reproduced, not this source's\)\. The text's extrapolated values at 1e10 W/cm2 \(p\. 5\) inline \(dataset text\_1e10\)\. Use\: check, the house convention for the gases' multiphoton cross sections \(as uiterwaal\_1998's measurements\)\: no model of optmat fits them\.

THE CHECKS \(the script fails if one is missed\)\: the inline values are the text's sentence \(the PDF's text layer\); the text's LOPT values '8\.0 x 10^\-52, 360 x 10^\-52 and 2\.7 x 10^\-52' are Table 2's Theory^c column; the extrapolation to 1e10 W/cm2 by Eq\. 5 with Table 1's exponents, sigma\(1e13\) x 10^\(\-3 \(n1 \- n2 \- 1\)\), gives 5\.19 \(61\.4 nm, text 5\.1\) and 2\.06 \(56\.0 nm, text 2\.2\), within 10 % \(Table 2's 0\.9 has one figure\)\. DOUBT\: at 58\.4 nm it gives 2520 x 10^\-52 against the text's 550\: Table 1's n1 \- n2 \- 1 = \-0\.68 there, the text's value implies \-0\.46 \(n1 = 1\.32 with n2 = 0\.78, or n2 = 0\.56 with n1 = 1\.1\); Table 1's errors \(0\.1 and 0\.02, added\) allow 1100 to 5800\. Fig\. 2's lines \(an image\) are not read; which of Table 1's exponent and the text's value is wrong is not established\. Fig\. 3's squares \(1e13 W/cm2\) lie at Table 2's values on the rendered page \(inspected, not read\)\.

REPRODUCED COLUMNS\. Theory^b, 'R\-matrix Floquet method' at 1e13 W/cm2\: H\. W\. van der Hart and P\. Bingham, J\. Phys\. B 38, 207 \(2005\), Ref\. 11, not in the library \('The authors also thank Professor H W van der Hart for having provided them with his theoretical data'; Fig\. 3's lines are 'converted from the ionization rates reported by van der Hart and Bingham'\)\. Theory^c, LOPT\: Nikolopoulos and Lambropoulos \(2001\), Ref\. 12 \(nikolopoulos\_2001\), perturbative and so independent of the intensity in the caption; none at 53\.4 nm\. Against nikolopoulos\_2001's committed figure files \(log\-interpolated at 20\.193, 21\.230, 22\.140 eV\)\: its Fig\. 3 \(the D wave\) gives 8\.35, 349 and 2\.73 x 10^\-52, within 4 % of Theory^c's 8\.0, 360, 2\.7; its Fig\. 4 S \+ D total gives 7\.7, 9\.8 and 2\.1 \(its 1s2p peak lies at 20\.95 eV\)\: the column follows Fig\. 3's D\-wave curve\.

NOT TAKEN\. Table 2's last row, the one\-photon ionisation cross sections of H2, 7\.4, 6\.4, 5\.9 and 5\.2 x 10^\-18 cm2 at 61\.4, 58\.4, 56\.0 and 53\.4 nm\: Chung, Lee, Masuoka and Samson, J\. Chem\. Phys\. 99, 885 \(1993\), Ref\. 14 \('Experiment'\), the reference of the calibration, not this paper's measurement and not in the library\. Table 1 \(the exponents; above\)\. Fig\. 1 \(TOF spectra\)\. Fig\. 2 \(image\)\: the cross sections against intensity, 2e12 to 5e13 W/cm2, drawn as straight lines \(Eq\. 5 with the fitted exponents over each wavelength's fluctuation range, extrapolated dotted\) with uncertainty bands\. Fig\. 3 \(image\)\: the cross sections against wavelength at 1, 2 and 5 x 10^13 W/cm2, the 1e13 values printed in Table 2, the 2e13 and 5e13 only drawn \(read from the lines of Fig\. 2\), with van der Hart and Bingham's curves\. A raster reading of Figs\. 2\-3 would give the 2e13 and 5e13 values and test the 58\.4 nm slope\.

FURTHER TWO\-PHOTON DATA CITED, not in the library\: Hasegawa et al\., Phys\. Rev\. A 71, 023407 \(2005\), Ref\. 5 \(He, high\-harmonic XUV\); Hoshina et al\., J\. Phys\. B 39, 813 \(2006\), Ref\. 6 \(D2\); van der Hart and Bingham \(2005\), Ref\. 11\.

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

Datasets
--------

sato\_2011/tbl2\_obs
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "tbl2_obs",
     "material": "He",
     "file": "He/sato_2011__tbl2_obs_He.csv",
     "table": "tbl_bc8ebb788440",
     "quantity": "multiphoton_ionization_cross_section",
     "unit": "cm4 s",
     "scale": 1e-52,
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "photons": 2,
       "polarization": "linear",
       "intensity_w_cm2": 10000000000000.0,
       "pulse_fs": 300,
       "pulse_fs_definition": "assumed, 'a typical value of the temporal pulse width of the XUV light source' (p. 3); not measured",
       "method": "He+ yield relative to the one-photon H2+ yield of 3 % H2 in the beam (Eq. 5), with H2's literature cross section (Chung et al. 1993); SCSS free-electron laser, 10 um focus; yields' intensity dependence fitted as power laws over the shot-to-shot fluctuation",
       "definition": "Y1 = eta N1 sigma (lambda I / hc)^2 tau (Eq. 3): Gamma = sigma Phi^2 with Phi = lambda I / hc the photon flux in cm^-2 s^-1; sigma a function of the intensity, ~ I^(n1 - n2 - 1)",
       "photon_statistics": "not discussed (SASE); no correction stated",
       "polarization_note": "the time-of-flight axis was 'parallel to the polarization direction of the XUV light' (p. 2); the paper does not name the polarisation"
     }
   }

Table 2 \(p\. 3\), 'Obs\.' \('This work'\)\: the two\-photon ionisation cross section of He at 1e13 W/cm2, in 10^\-52 cm4 s, at 61\.4, 58\.4 \(1s2p resonance\), 56\.0 and 53\.4 nm \(tail of 1s3p\)\: 2\.6 \(6\), 23 \(7\), 0\.9, 7 \(5\)\. The error in parentheses on the last digit, recorded per point \(none printed for 56\.0 nm\); level not stated\. Evaluated with an assumed 300 fs pulse \(scales as 1/tau\)\. At 1e13 W/cm2, below the central intensity of each wavelength's data except 53\.4 nm \(1\.3e13\)\: taken from the fitted power law I^\(n1 \- n2 \- 1\) \(Table 1\)\.

sato\_2011/tbl2\_rmf
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "tbl2_rmf",
     "material": "He",
     "file": "He/sato_2011__tbl2_rmf_He.csv",
     "table": "tbl_bc8ebb788440",
     "quantity": "multiphoton_ionization_cross_section",
     "unit": "cm4 s",
     "scale": 1e-52,
     "abscissa_unit": "nm",
     "use": "check",
     "reproduced_from": [
       "H. W. van der Hart and P. Bingham, J. Phys. B: At. Mol. Opt. Phys. 38, 207 (2005)"
     ],
     "uncertainty": {
       "level": "not stated"
     },
     "parameters": {
       "photons": 2,
       "polarization": "linear",
       "intensity_w_cm2": 10000000000000.0,
       "method": "R-matrix Floquet theory (van der Hart and Bingham 2005), non-perturbative, at 1e13 W/cm2",
       "definition": "the ionisation rate converted to a cross section by the authors (Fig. 3 caption), Gamma = sigma Phi^2 as for the measurement"
     }
   }

Table 2 \(p\. 3\), 'Theory \(R\-matrix Floquet method\) \[11\]' at 1e13 W/cm2, in 10^\-52 cm4 s\: 8\.5, 63, 3\.5, 6\.9 at 61\.4, 58\.4, 56\.0, 53\.4 nm\. Van der Hart and Bingham's values, converted from their ionisation rates and supplied to the authors \('provided them with his theoretical data', p\. 5\); the original is not in the library\. No uncertainty\.

sato\_2011/tbl2\_lopt
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "tbl2_lopt",
     "material": "He",
     "file": "He/sato_2011__tbl2_lopt_He.csv",
     "table": "tbl_bc8ebb788440",
     "quantity": "multiphoton_ionization_cross_section",
     "unit": "cm4 s",
     "scale": 1e-52,
     "abscissa_unit": "nm",
     "use": "check",
     "reproduced_from": [
       "nikolopoulos_2001"
     ],
     "uncertainty": {
       "level": "not stated"
     },
     "parameters": {
       "photons": 2,
       "polarization": "linear",
       "method": "lowest-order perturbation theory, two-electron B-spline basis (Nikolopoulos and Lambropoulos 2001)",
       "definition": "Gamma = sigma Phi^2 (LOPT), Phi the photon flux in cm^-2 s^-1"
     }
   }

Table 2 \(p\. 3\), 'Theory \(LOPT\) \[12\]', in 10^\-52 cm4 s\: 8\.0, 360, 2\.7 at 61\.4, 58\.4, 56\.0 nm \('\-' at 53\.4 nm\: no value\); quoted again in the text \(p\. 5\)\. Nikolopoulos and Lambropoulos's lowest\-order perturbation theory, independent of intensity\. Within 4 % of nikolopoulos\_2001's Fig\. 3 \(D wave\) at these photon energies, not its Fig\. 4 S \+ D total \(the record's notes\)\. No uncertainty\.

sato\_2011/text\_1e10
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "text_1e10",
     "material": "He",
     "table": "text",
     "quantity": "multiphoton_ionization_cross_section",
     "unit": "cm4 s",
     "scale": 1e-52,
     "abscissa_unit": "nm",
     "use": "check",
     "uncertainty": {
       "level": "not stated"
     },
     "parameters": {
       "photons": 2,
       "polarization": "linear",
       "intensity_w_cm2": 10000000000.0,
       "pulse_fs": 300,
       "pulse_fs_definition": "assumed (p. 3)",
       "method": "Table 2's measurement extrapolated along Fig. 2's lines (Eq. 5 with the fitted exponents) to 1e10 W/cm2",
       "definition": "Y1 = eta N1 sigma (lambda I / hc)^2 tau (Eq. 3): Gamma = sigma Phi^2 with Phi the photon flux in cm^-2 s^-1",
       "photon_statistics": "not discussed (SASE); no correction stated"
     }
   }

3 inline points in the source record.

p\. 5 \(journal; PDF p\. 6\)\: 'the cross sections at 1 x 10^10 W cm^\-2 are estimated to be 5\.1 x 10^\-52, 550 x 10^\-52 and 2\.2 x 10^\-52 cm4s at 61\.4, 58\.4, and 56\.0 nm', the straight lines of Fig\. 2 extrapolated three decades below the data \('consistent with' the LOPT values 8\.0, 360, 2\.7\)\. Not measured at 1e10 W/cm2\: an extrapolation of the power law\. At 58\.4 nm Table 1's exponents give 2520 instead \(the record's notes, a doubt\)\. No uncertainty given\.

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.