otobe_2004#
T. Otobe, K. Yabana and J.-I. Iwata, “First-principles calculations for the tunnel ionization rate of atoms and molecules”, Phys. Rev. A 69, 053404 (2004)
Source record · Catalogue · Review register
DOI: 10.1103/PhysRevA.69.053404
Source kind: theory
Recorded technique: Static-field tunnel ionisation rates from Gamow states of the Kohn-Sham equation (density functional theory). Step one: the static Kohn-Sham equation with the dipole potential e F z, emission suppressed by a spherical wall (Eq. (27)), self-consistent, so that the atom’s static polarisation screens the field. Step two: with that Hamiltonian fixed, each occupied orbital’s Gamow state from the Kohn-Sham equation with a linear absorbing potential -i W0 (r - R)/Delta R between R = 10 and R + Delta R = 30 Angstrom (Eqs. (19), (21); Table I), whose complex eigenvalue epsilon_i = epsilon_i^R + i Gamma_i (Eq. (5)) gives the orbital’s ionisation rate w_i = -(2/hbar) Gamma_i (Eq. (10)). Exchange and correlation: the self-interaction-corrected optimized effective potential in Krieger, Li and Iafrate’s approximation (KLI-SIC, Eqs. (11)-(17)), so that the highest orbital energy approximates the ionisation potential and the potential falls as -e^2/r. Valence electrons only, with Troullier-Martins norm-conserving pseudopotentials (l up to 2; R_ps = 1.4 Angstrom for the rare gases). Real-space adaptive grid (Eqs. (24)-(26); h = 0.2, a = 5.0, k = 10.0, n = 2, Table I). W0 checked to leave the rates unchanged (Fig. 3, p. 053404-6).
Materials in structured entries: Xe
Dataset quantities: ionization_rate
Contents: 3 datasets; 0 formulas.
Curation notes#
Journal pp. 053404-1 to -11 = PDF pages 1-11. Identity checked against the first page (T. Otobe and K. Yabana; J.-I. Iwata; Phys. Rev. A 69, 053404 (2004)).
WHAT IS TAKEN. Table II (p. -6, tbl_a857b4484f15): ‘Orbital energy of each Gamow state of Xe atom ... under the static electric field parallel to the z axis ... Numbers in brackets denote powers of 10’ (caption): the complex energies of the p_x, p_y and p_z orbitals at six field strengths labelled by a ‘Laser intensity’ of 4, 5, 6, 7, 8 and 9 x 10^13 W/cm^2. One dataset per orbital: the imaginary part Gamma_i (eV, negative, as printed: -12.27-i1.07[-5] is epsilon^R = -12.27 eV, Gamma = -1.07e-5 eV); scale = -2/27.211386245981 (the hartree in eV, CODATA 2022) turns it into the orbital’s rate w_i = -2 Gamma_i/hbar in atomic units (Eq. (10), p. -2: ‘The ionization rate of the orbital i, w_i ... = -(2/hbar) Gamma_i’). Gamma_i is the imaginary part of the energy, not a width: the rate is twice |Gamma_i|/hbar. The real parts are kept in the printed cells. The library’s cells are scrambled (rows merged); the script transcribes the table from the image, and checks the transcription against the library’s cells; the image and the PDF’s text layer agree (checked 2026-10-01). The columns are headed ‘2p_x’, ‘2p_y’, ‘2p_z’: for Xe the orbitals are 5p (the text, p. -6, says ‘p_x, p_y, and p_z orbitals’); the label is a misprint of the heading and changes no value.
THE ABSCISSA. The fields are static; the table labels each by the intensity of a linearly polarised laser whose peak field it is, I = c eps0 F^2/2: ‘5 x 10^13 W/cm^2 (1.94 eV/Angstrom)’ (p. -5), and 5e13 W/cm^2 gives F = 1.941 V/Angstrom by that relation. The intensities 4-9 x 10^13 W/cm^2 are F = 0.03376, 0.03775, 0.04135, 0.04466, 0.04774 and 0.05064 au. The datasets keep the printed intensity.
WHAT THE RATES COUNT. Each w_i is the rate of one electron in the Kohn-Sham orbital i (the flux through a large sphere over the orbital’s norm, Eq. (10)). The atom’s rate is the sum over the occupied orbitals: ‘The total ionization rate w is given by summing up the rates of all occupied orbitals’ (p. -4; Eq. (23), w = -(2/hbar) sum_i Gamma_i = (2/hbar) integral n W, n the total electron density), and ‘Summing up the ionization rates of all orbitals, we obtain the total ionization rate. In Fig. 4, we show the calculated ionization rate of the Xe and Ar atoms’ (p. -6). Xe is closed-shell, each spatial orbital holding two electrons, so the 5p contribution is 2 x (w_px + w_py + w_pz); ‘The eigenvalue of the s orbital is not shown, since the imaginary part of the eigenvalue of the s orbital is very small’ (p. -6). That total is 1.34e-3 fs^-1 at 4e13 and 7.47e-2 fs^-1 at 9e13 W/cm^2; Fig. 4’s open squares (read by eye, not digitised) lie near 1.5e-3 and 8e-2 fs^-1 there, and not at the half: the plotted total includes the factor 2 for spin. p_x and p_y are equal (‘reflecting the axial symmetry’); p_z, along the field, is 19 to 36 times faster.
DOUBT: THE 8e13 ROW. Gamma of p_z grows by 3.54, 2.63, 1.99, 2.35 and 1.28 from one intensity to the next, and that of p_x by 2.07, 2.31, 2.57, 1.93 and 2.33: a smooth tunnelling rate grows by a factor that falls steadily with the field. The p_z value at 8e13 W/cm^2 (8.65e-3 eV) is high against its neighbours (2.35 after 1.99, then 1.28), and the p_x values at 7e13 and 8e13 are irregular too. The paper says nothing about it; the values are as printed, nothing is excluded.
ACCURACY. No uncertainty is stated. ‘we examined carefully that the calculated ionization rates are not sensitive to the change of W0’ (p. -6), and the spatial parameters were checked (p. -4). The method is a static, adiabatic one (‘the Keldysh parameter ... is assumed to be much smaller than unity’, p. -2; ‘This trend may be attributed to the effect of the multiphoton process’, p. -6, of the fall of the calculated rate below the measured one under 3 x 10^13 W/cm^2 for Xe). ‘Comparing our calculation with the ADK formula, the absolute values of the ionization rate are slightly higher (about a factor of 2)’ (p. -6). The field-free p orbital energy of the calculation is 12.07 eV against the measured ionisation potential of 12.13 eV (p. -6, Table II).
NOT TAKEN. The real parts (Stark-shifted orbital energies) and the measured ionisation potential (12.13 eV) of Table II. Ar’s rates (Figs. 4 and 5, figures only, with and without the static polarisation). Table III (orbital energies of N2, O2, F2) and the molecular rates (figures).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
otobe_2004/tableII_px_Xe#
{
"id": "tableII_px_Xe",
"material": "Xe",
"file": "Xe/otobe_2004__tableII_px_Xe.csv",
"table": "tbl_a857b4484f15",
"quantity": "ionization_rate",
"unit": "au",
"scale": -0.0734986443513289,
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"orbital": "5p_x (printed 2p_x)",
"method": "Gamow states of the KLI-SIC Kohn-Sham equation, absorbing potential, pseudopotentials"
}
}
Table II (p. 053404-6), column ‘2p_x (eV)’ (Xe 5p_x, perpendicular to the field): Gamma_x, the imaginary part of the complex Kohn-Sham (KLI-SIC) orbital energy in a static field, eV as printed, against the ‘laser intensity’ of the field (I = c eps0 F^2/2: 4-9e13 W/cm^2 are F = 0.0338-0.0506 au). scale = -2/27.211386245981 makes it the rate of the orbital w = -2 Gamma/hbar in atomic units (Eq. (10)): the rate of ONE electron in that orbital; the atom’s 5p rate is 2 x (w_px + w_py + w_pz) (record notes). Equal to p_y. No uncertainty is stated.
otobe_2004/tableII_py_Xe#
{
"id": "tableII_py_Xe",
"material": "Xe",
"file": "Xe/otobe_2004__tableII_py_Xe.csv",
"table": "tbl_a857b4484f15",
"quantity": "ionization_rate",
"unit": "au",
"scale": -0.0734986443513289,
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"orbital": "5p_y (printed 2p_y)",
"method": "Gamow states of the KLI-SIC Kohn-Sham equation, absorbing potential, pseudopotentials"
}
}
Table II (p. 053404-6), column ‘2p_y (eV)’ (Xe 5p_y, perpendicular to the field): Gamma_y, the imaginary part of the complex Kohn-Sham (KLI-SIC) orbital energy in a static field, eV as printed, against the ‘laser intensity’ of the field (I = c eps0 F^2/2: 4-9e13 W/cm^2 are F = 0.0338-0.0506 au). scale = -2/27.211386245981 makes it the rate of the orbital w = -2 Gamma/hbar in atomic units (Eq. (10)): the rate of ONE electron in that orbital; the atom’s 5p rate is 2 x (w_px + w_py + w_pz) (record notes). Equal to p_x (‘reflecting the axial symmetry’, p. -6). No uncertainty is stated.
otobe_2004/tableII_pz_Xe#
{
"id": "tableII_pz_Xe",
"material": "Xe",
"file": "Xe/otobe_2004__tableII_pz_Xe.csv",
"table": "tbl_a857b4484f15",
"quantity": "ionization_rate",
"unit": "au",
"scale": -0.0734986443513289,
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"orbital": "5p_z (printed 2p_z)",
"method": "Gamow states of the KLI-SIC Kohn-Sham equation, absorbing potential, pseudopotentials"
}
}
Table II (p. 053404-6), column ‘2p_z (eV)’ (Xe 5p_z, along the field, the m = 0 orbital): Gamma_z, the imaginary part of the complex Kohn-Sham (KLI-SIC) orbital energy in a static field, eV as printed, against the ‘laser intensity’ of the field (I = c eps0 F^2/2: 4-9e13 W/cm^2 are F = 0.0338-0.0506 au). scale = -2/27.211386245981 makes it the rate of the orbital w = -2 Gamma/hbar in atomic units (Eq. (10)): the rate of ONE electron in that orbital; the atom’s 5p rate is 2 x (w_px + w_py + w_pz) (record notes). The 8e13 W/cm^2 value is irregular against its neighbours (growth 2.35 from 7e13, then 1.28 to 9e13; record notes); kept as printed. No uncertainty is stated.
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.