parker_2009
===========

J\. S\. Parker, G\. S\. J\. Armstrong, M\. Boca and K\. T\. Taylor, "From the UV to the static\-field limit\: rates and scaling laws of intense\-field ionization of helium", J\. Phys\. B\: At\. Mol\. Opt\. Phys\. 42, 134011 \(2009\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/parker_2009.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1088/0953\-4075/42/13/134011 <https://doi.org/10.1088/0953-4075/42/13/134011>`__

**Source kind:** theory

**Recorded technique:** Full\-dimensional integration of the two\-electron helium time\-dependent Schrodinger equation \(the HELIUM code\: finite differences in the radial variables, coupled spherical harmonics; Smyth et al\. 1998, smyth\_1998\), infinite nuclear mass\. Laser\-driven single\-ionisation rates at 195 nm up to 32e14 W/cm^2, and static\-field rates for E \< 0\.4 au\: the field is ramped on smoothly, E = E\_max \(1 \- cos\(Omega t\)\)/2 for 0 \< t \< pi/Omega, and the rate is the exponential decay of the population within 18 Bohr of the nucleus \(p\. 8\)\.

**Materials in structured entries:** He

**Dataset quantities:** ionization\_rate

**Contents:** 4 datasets; 2 formulas.

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

Pages are pdf pages\: pdf page 1 is the IOPscience download cover, so the article page is 134011\-\(n\-1\)\. Identity checked against pdf p\. 2\.

WHAT IS TAKEN\. Table 1 \(p\. 8\), 'Static\-field ionization rates from the ground state of helium as a function of peak electric field strength E'\: Gamma \(au\) against E \(au\) for 'Present work', 'Scrinzi et al \[3\]', 'Themelis et al \[4\]' and 'ADK theory \[9\]', one dataset per column \(wavelength\_nm = inf, polarization = static\)\. The library's table is scrambled \(the characters of every row interleaved in one cell per column\)\: the script transcribes it from the image and checks each column's characters against the scrambled cell \(structural fix, no erratum\)\. The rate is that of the atom\: the decay of the two\-electron ground\-state population \(single ionisation\), not per electron\.

CONVERGENCE \(p\. 8, quoted; no overall uncertainty is stated, so none is recorded\)\: 'The integrations were repeated with increasingly large values for the maximum angular momenta L\_max and ramp\-on times T, until no change was observed in the final results' \(L\_max 12 at low field, 24 for E \> 0\.25 au\); 'Reducing delta r to 0\.2 au altered ionization rates by 0\.3% at E = 0\.1 au and by 0\.03% at E = 0\.3 au'\. 'No adiabatic response was observed for E \> 0\.38 au \.\.\. Despite this source of uncertainty, at E = 0\.40 au the measured ionization rate differed from Scrinzi's by only a few per cent' \(p\. 8\); the table has no present\-work value at 0\.40\. A change of functional form at E = 0\.175 au, a component scaling as E^4 \(p\. 3, p\. 8\)\.

REPRODUCED AND CHECK COLUMNS\. \[3\] = A\. Scrinzi, M\. Geissler and T\. Brabec, Phys\. Rev\. Lett\. 83, 706 \(1999\) and \[4\] = S\. I\. Themelis, T\. Mercouris and C\. A\. Nicolaides, Phys\. Rev\. A 61, 024101 \(1999\), full\-dimensional time\-independent methods \(p\. 9\); neither is in the library\. \[9\] ADK\: 'The ADK formula used here is discussed in \[1\]' \(parker\_2007, p\. 9\), whose AC\-ADK is for 'a ground state one\-electron atom with ionization potential 0\.903724 au' and says that of the two\-electron atom is twice it \(parker\_2007 p\. 12\)\. Not reproduced exactly \(computed 2026\-09\-26\)\: the static ADK rate with the Gamma\-function C\_n\*l^2 \(n\* = 0\.7438, l = m = 0\), Ip = 0\.903724 au and two electrons is 0\.783 \+\- 0\.001 of the printed column at every E except 0\.20 au; with Stirling's C\_n\*l^2 = \(2e/n\*\)^\(2n\*\) /\(2 pi n\*\) it is 0\.970 \+\- 0\.001\. At E = 0\.20 au the ratio is 0\.809 \(Gamma form\) and 1\.003 \(Stirling\)\: the printed 1\.07e\-2 departs by \+3\.3 % from the smooth trend of its neighbours, which gives about 1\.11e\-2; probably a misprint of the ADK cell, not corrected \(a formula evaluation, use = check\)\. majety\_2015 Table 1 reprints this ADK column digit for digit, 1\.07e\-2 at 0\.20 included, as it reprints the other three columns \(at the 13 fields 0\.06\-0\.20 au\)\.

FORMULAS\. Eq\. \(8\) \(static fit\) and Eq\. \(7\) \(the laser\-driven fits of Figs\. 3\-5\) are recorded below\. The empirical cycle\-averaged static rate \(p\. 9\)\: 'multiplying equation \(8\) by 0\.146 I^0\.25 works well for I \< 50\.0 x 10^14 W cm^\-2, \(E \< 0\.3773\)', with I = 14\.0484 \(E/0\.2\)^2 \(I in 1e14 W/cm^2, E in au\)\.

195 nm AND THE SCALING LAWS \(figures only, not taken\)\. Fig\. 1 \(p\. 3\)\: rates at 195, 390 and 780 nm and the cycle\-averaged static rates, 0 \< I \< 16e14 W/cm^2; Fig\. 5 \(p\. 5\)\: 195 nm, 1/ln^2\(Gamma\) against I, data up to I = 32\.0e14 W/cm^2\. Text values \(pp\. 3, 6\-7\)\: the 780 nm rates exceed the static rates by factors 100, 8, 3 and 2 at I = 1, 2, 3 and 4e14 W/cm^2; Eq\. \(2\) with A = 548000\.0, d0 = 0\.138, n = 7\.735, xi = 0\.456 \(ponderomotive shift xi0 = 0\.4464 plus Stark xi2 = 0\.0096, 390 nm units\); b0 from the figures 0\.000247 \(780 nm\), 0\.000990 \(390 nm\), 0\.003920 \(195 nm\) against Eq\. \(6\) 0\.000250, 0\.000989, 0\.003856; b1 from the figures 0\.001485, 0\.001630, 0\.001750 against Eq\. \(5\) 0\.001470, 0\.001680, 0\.001930 \('the 10% error at R = 0\.5 stands out'\); a0 = b0 R^2 from Eq\. \(6\) 0\.000993 \(3120 nm\), 0\.001000 \(1560 nm\), 0\.001000 \(780 nm\), 0\.000989 \(390 nm\), 0\.000964 \(195 nm\); for neon's n = 6\.7832, a0 = 0\.00139 at R = 2\. At 195 nm Eq\. \(7\) fails for I \< 1\.0e14 W/cm^2 \(0\.25e14 at 390 nm\)\. The ABI onset\: Scrinzi's 14e14 W/cm^2 \(E = 0\.2 au\) \(p\. 3, p\. 9\)\. None of these is a quantity\: notes only\. At 195 nm \(omega = 2 x 0\.11683 = 0\.23366 au, parker\_2007's omega\_390\) single ionisation of He needs four photons \(Ip/omega = 0\.903724/0\.23366 = 3\.87 at zero intensity; computed 2026\-10\-08\)\: it is not two\-photon ionisation, and no 195 nm rate is held\.

UNMAPPED\_GLYPHS on p\. 4 touch the ponderomotive\-shift text; the Table 1 values do not depend on it\.

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

Datasets
--------

parker\_2009/table1\_present
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_present",
     "material": "He",
     "file": "He/parker_2009__table1_present.csv",
     "table": "tbl_f4122d1f56cb",
     "quantity": "ionization_rate",
     "unit": "au",
     "abscissa": "field",
     "abscissa_unit": "au",
     "use": "primary",
     "parameters": {
       "wavelength_nm": Infinity,
       "polarization": "static",
       "method": "full-dimensional TDSE (HELIUM)"
     }
   }

Table 1 \(p\. 8\), 'Present work'\: full\-dimensional time\-dependent static\-field rates of He, 26 fields 0\.045\-0\.3773 au \(none at 0\.40\)\. Eq\. \(8\) reproduces them within 2\.6 % except at 0\.05 au \(\+7\.3 %\) and 0\.067 au \(\-6\.5 %\) \(computed 2026\-09\-26\)\. Convergence statements in the record's notes; uncertainty not stated\.

parker\_2009/table1\_scrinzi\_1999
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_scrinzi_1999",
     "material": "He",
     "file": "He/parker_2009__table1_scrinzi_1999.csv",
     "table": "tbl_f4122d1f56cb",
     "quantity": "ionization_rate",
     "unit": "au",
     "abscissa": "field",
     "abscissa_unit": "au",
     "use": "reproduced",
     "reproduced_from": [
       "scrinzi_1999"
     ],
     "parameters": {
       "wavelength_nm": Infinity,
       "polarization": "static",
       "method": "full-dimensional complex scaling (Scrinzi et al. 1999)"
     }
   }

Table 1 \(p\. 8\), 'Scrinzi et al \[3\]'\: full\-dimensional time\-independent \(complex\-scaling\) He rates, 15 fields 0\.08\-0\.40 au\. majety\_2015 reprints the 0\.08\-0\.20 au values identically\. The original, scrinzi\_1999/table1\_He \(Table I\), prints all 15 identically \(checked 2026\-09\-27\)\.

parker\_2009/table1\_themelis\_1999
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_themelis_1999",
     "material": "He",
     "file": "He/parker_2009__table1_themelis_1999.csv",
     "table": "tbl_f4122d1f56cb",
     "quantity": "ionization_rate",
     "unit": "au",
     "abscissa": "field",
     "abscissa_unit": "au",
     "use": "reproduced",
     "reproduced_from": [
       "S. I. Themelis, T. Mercouris and C. A. Nicolaides, Phys. Rev. A 61, 024101 (1999)"
     ],
     "parameters": {
       "wavelength_nm": Infinity,
       "polarization": "static",
       "method": "full-dimensional state-specific (Themelis et al. 1999)"
     }
   }

Table 1 \(p\. 8\), 'Themelis et al \[4\]'\: full\-dimensional time\-independent He rates, 19 fields 0\.067\-0\.40 au\. majety\_2015 reprints the 0\.07\-0\.20 au values identically\.

parker\_2009/table1\_adk
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_adk",
     "material": "He",
     "file": "He/parker_2009__table1_adk.csv",
     "table": "tbl_f4122d1f56cb",
     "quantity": "ionization_rate",
     "unit": "au",
     "abscissa": "field",
     "abscissa_unit": "au",
     "use": "check",
     "parameters": {
       "wavelength_nm": Infinity,
       "polarization": "static",
       "method": "ADK formula"
     }
   }

Table 1 \(p\. 8\), 'ADK theory \[9\]'\: a formula evaluation, 27 fields 0\.045\-0\.40 au\. The E = 0\.20 au cell \(1\.07e\-2\) is \+3\.3 % off the smooth trend of the rest \(see the record's notes\); not corrected\.

Formulas
--------

parker\_2009/static\_fit
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "static_fit",
     "material": "He",
     "equation": "Eq. (8), pp. 8-9",
     "printed": "Gamma(E) = (1/E^2) exp(-1/(1.47 x 10^-5 + 0.577 E)) + 6.183 (E - 0.1755)^4 Step(E - 0.1755)",
     "variable": "E: static field in au (E < 0.4 au); Gamma in au; Step(x) = 1 for x > 0, else 0",
     "range": "E < 0.4 au",
     "coefficients": {
       "c0": "1.47e-5",
       "c1": "0.577",
       "A4": "6.183",
       "E0": "0.1755"
     },
     "check": "Reproduces Table 1 'Present work' within 2.6 % at 24 of 26 fields; +7.3 % at 0.05 au and -6.5 % at 0.067 au; +0.2 % at 0.3773 au (computed 2026-09-26)."
   }

'the E^4 model is based on only five data points' \(p\. 9\)\. Times 0\.146 I^0\.25 \(I in 1e14 W/cm^2, I = 14\.0484 \(E/0\.2\)^2\) it gives the cycle\-averaged static rate of Fig\. 1 for I \< 50e14 W/cm^2 \(p\. 9\)\.

parker\_2009/laser\_fit
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "laser_fit",
     "material": "He",
     "equation": "Eq. (7), p. 7",
     "printed": "Gamma(Ibar, R) = exp(-R / sqrt(a0 + a1 Ibar)); 780 nm (R = 2.0): a0 = 0.0009882, a1 = 0.001485; 390 nm (R = 1.0): a0 = 0.0009900, a1 = 0.001630; 195 nm (R = 0.5): a0 = 0.0009800, a1 = 0.001750",
     "variable": "R: wavelength in units of 390 nm; Ibar = I R^2, I the (cycle-averaged) intensity in 1e14 W/cm^2; Gamma in au",
     "range": "Ibar < 16 (390 and 780 nm), Ibar < 8 (195 nm); fails at 195 nm below I = 1.0e14 W/cm^2 (p. 7)",
     "coefficients": {
       "a0_780": "0.0009882",
       "a1_780": "0.001485",
       "a0_390": "0.0009900",
       "a1_390": "0.001630",
       "a0_195": "0.0009800",
       "a1_195": "0.001750"
     },
     "check": "Not checkable: the laser-driven rates are in figures only."
   }

Fits \(the dashed lines of Figs\. 3\-5\) to the non\-resonant trend of the TDSE rates; resonances smoothed away\. 'Over higher intensity ranges, the curves given in equation \(5\) of \[1\] may be used' \(parker\_2007\)\.

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.