scrinzi_1999
============

A\. Scrinzi, M\. Geissler and T\. Brabec, "Ionization Above the Coulomb Barrier", Phys\. Rev\. Lett\. 83, 706 \(1999\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/scrinzi_1999.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1103/PhysRevLett\.83\.706 <https://doi.org/10.1103/PhysRevLett.83.706>`__

**Source kind:** theory

**Recorded technique:** Static\-field ionisation rates from the complex\-scaling method\: the coordinates of the full two\-electron Hamiltonian \(Eq\. \(1\), dipole approximation, Z = 2 for He; one electron, Z = 1, for H\) are multiplied by e^\(i theta\), and 'the resulting non\-Hermitian Hamiltonian has complex eigenvalues, whose imaginary parts give one\-half of the ionization rate'; eigenvalues found variationally, in an explicitly correlated basis for He \(Scrinzi & Piraux, Phys\. Rev\. A 58, 1310 \(1998\)\) and finite elements for H\. The time\-dependent Schrodinger equation of H \(velocity gauge, Laguerre expansion, complex\-scaling boundary\) for the quasistatic test \(pp\. 706\-707\)\.

**Materials in structured entries:** He

**Dataset quantities:** ionization\_rate

**Contents:** 1 dataset; 0 formulas.

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

Journal pp\. 706\-709 = PDF pages 1\-4\. Identity checked on the first page\.

EXTRACTED\: Table I \(p\. 708, tbl\_695d85562032, image checked\), 'Static field ionization rates from the ground state of He in atomic units', w against E, 60 fields from 0\.08 to 1\.70 au\: one dataset\. The rate is the full two\-electron atom's total rate, Gamma = \-2 Im\(E\) of the complex\-scaled resonance \(p\. 707\), per atom \(not per electron\)\. 'The numerical data is accurate to at least two digits' \(caption\)\: recorded here, not as a dataset uncertainty \(the statement is a lower bound on the precision, without a level\)\. The caption's conversions\: 1 au of time = 2\.419 x 10^\-17 s, 1 au of field = 5\.142 x 10^11 V/m\.

STRUCTURAL FIX \(script\)\: the extracted cells read '0\.463 3 1027' for '0\.463 x 10^\-7' \(the multiplication sign and the minus sign lost\); the image confirms each factor, and the script rewrites the cells as 0\.463e\-7\.

REPRINTS \(re\-pointed, identical\)\: parker\_2009/table1\_scrinzi\_1999 \(15 fields, 0\.08\-0\.40 au\) and majety\_2015/table1\_scrinzi\_1999\_He \(11 fields, 0\.08\-0\.20 au\) reprint this table's values to the printed three digits \(checked 2026\-09\-27\: every reprinted value equals Table I's, e\.g\. 0\.463e\-7 = 4\.63e\-8 at 0\.08 au, 0\.977e\-1 = 9\.77e\-2 at 0\.40 au\)\.

TEXT \(pp\. 707\-708\)\: for H, the ADK rate is within 20 % of the exact one below the barrier\-suppression field E\_bs = I\_p^2/4 \(1/16 au for H\) and 'strongly overestimates' above it; for He, 'in the tunneling regime we find reasonable agreement between the numerical and analytical results within about 30%', and 'In the barrier suppression regime ionization is less than predicted by the ADK theory' \(Fig\. 1, figure only\)\. The quasistatic approximation holds for H \(5 fs sech pulses at 800 nm and wavelengths 1\-0\.25 um at fixed tau omega\_0; the text's 'mm' is um\) above E\_qs ~ 0\.1 au, where the TDSE and the quasistatic yields differ by less than 5 % \(Fig\. 2\)\: 0\.5 \< gamma\_qs \< 2\. gamma\_bs = 16 omega\_0/\(2 I\_p\)^\(3/2\) \(p\. 707\); about 0\.05 at 10 um, 0\.5\-2 in the UV to near infrared\. Fig\. 3\: the He harmonic cutoff against pulse duration \(800 nm\) from Table I and from ADK; ADK underestimates it by 40 % for a single\-cycle pulse \(p\. 708\)\.

FIGURES \(not digitised\)\: Fig\. 1, static rates of H and He against field \(numerical and ADK\); Fig\. 2, H ionisation yield against peak field \(TDSE and quasistatic\); Fig\. 3, the He cutoff harmonic against pulse duration\.

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

Datasets
--------

scrinzi\_1999/table1\_He
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "table1_He",
     "material": "He",
     "file": "He/scrinzi_1999__table1_He.csv",
     "table": "tbl_695d85562032",
     "quantity": "ionization_rate",
     "unit": "au",
     "abscissa": "field",
     "abscissa_unit": "au",
     "use": "primary",
     "parameters": {
       "wavelength_nm": Infinity,
       "polarization": "static",
       "method": "full-dimensional complex scaling (explicitly correlated two-electron basis)"
     }
   }

Table I, p\. 708\: the static\-field ionisation rate of the He ground state \(the whole atom, both electrons; Gamma = \-2 Im E of the complex\-scaled resonance\), fields 0\.08\-1\.70 au\. 'Accurate to at least two digits' \(caption; record notes\)\. Converged correlated two\-electron calculation\: the first accurate He rates, per the authors \(p\. 706\)\.

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.