scrinzi_1999#

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

Source record · Catalogue · Review register

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#

{
  "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 review register for the checks and decisions.