santra_2006#
R. Santra, R. W. Dunford and L. Young, “Spin-orbit effect on strong-field ionization of krypton”, Phys. Rev. A 74, 043403 (2006)
Source record · Catalogue · Review register
DOI: 10.1103/PhysRevA.74.043403
Source kind: theory
Recorded technique: Static-field tunnel ionisation rates of the Kr 4p orbitals in an effective one-electron model with spin-orbit coupling: H = -nabla^2/2 + V_HS(r) + (alpha^2/2)(1/r) dV_HS/dr l.s - z E - i eta W(r) (Eq. (1), p. 043403-2). V_HS is the Hartree-Fock-Slater potential of Herman and Skillman’s code, its exchange parameter chosen as 1.1035 so that the spin-orbit-free 4p level is E_4p = -14.222 eV, and the 4p fine-structure splitting is set to 0.666 eV (higher levels by the hydrogenic formula, Eq. (7), constant 85.248 eV), so that the model’s 4p_3/2 and 4p_1/2 binding energies are the measured ones (14.0 and 14.7 eV, p. -2); spin-orbit coupling in first-order degenerate perturbation theory within each n, l subshell (Eqs. (4)-(6)). Radial finite elements (3001 functions, quadratic grid to 60 a.u.), l = 0-11, the 75 lowest radial functions per l; the field couples them by Eq. (8); a complex absorbing potential W = (r - c)^2 beyond c = 4 a.u. (Eq. (2)), its strength eta optimised; the complex Siegert energy E of each resonance from the matrix of H in a subspace of 300 eigenvectors, ‘the ionization rate gamma = -2 Im(E)’ (p. -3). Only m, the projection of the total angular momentum, is conserved; each resonance is labelled by m and by the field-free j it overlaps most. ‘All numerical parameters here and in the following are chosen such as to ensure converged tunnel ionization rates’ (p. -3).
Materials in structured entries: Kr
Dataset quantities: ionization_rate
Contents: 4 datasets; 0 formulas.
Curation notes#
Journal pp. 043403-1 to -9 = PDF pages 1-9. Identity checked against the first page (Robin Santra, Robert W. Dunford, and Linda Young, Phys. Rev. A 74, 043403 (2006)).
WHAT IS TAKEN. Table I (p. -3, tbl_f7044803390d; every cell checked against the table image and the PDF text): the tunnel ionisation rates gamma (au) of the three 4p resonance states at the static field E = 0.10 au (the caption), one dataset per channel: 4p_1/2 with |m| = 1/2 (gamma = 4.89e-3 au), 4p_3/2 with |m| = 1/2 (1.18e-2) and 4p_3/2 with |m| = 3/2 (1.41e-3). The rows print m only (+1/2, +1/2, +3/2); j is read from the squared overlaps with the field-free 4p_j states (0.976 with j = 1/2; 0.957 and 0.970 with j = 3/2), as the text names them: ‘gamma_{3/2,+-1/2} is greater than gamma_{3/2,+-3/2} by more than a factor of 8 and greater than gamma_{1/2,+-1/2} by 2.4’ (p. -4; the table gives 8.37 and 2.41). ‘Data were calculated for positive m. Replacing m with -m yields identical results’ (caption). And the total of the atom, a text value (total_Kr, p. -4).
WHAT THE RATES COUNT. Each gamma is the rate of ONE electron, the one in the 4p_j, m spin-orbital (an effective one-electron model: no factor for the other electrons). ‘The total atomic ionization rate is obtained as the sum over all gamma_{j,m} weighted by the number of electrons in the respective j,m subshell. Combining the data in Table I, the ionization rate of Kr, at E = 0.10 a.u., is 0.036 a.u., which corresponds to a tunneling lifetime of 0.67 fs’ (p. -4). Each (j, m) state holds one electron and m and -m have the same rate, so the six 4p electrons give 2 x (4.89e-3 + 1.18e-2 + 1.41e-3) = 2 x 0.01810 = 0.03620 au: the printed 0.036 au (checked 2026-10-01), and 1/0.0362 au = 27.6 au of time = 0.668 fs, the printed 0.67 fs. The 4s electrons are not included. The rates are static (a field, not a laser intensity): ‘E in Eq. (1) represents a static field along the z axis’ (p. -2); the paper’s cycle averages (Eq. (10), Fig. 1) are not taken. As a laser amplitude, 0.10 au is 3.5e14 W/cm^2 (p. -3).
ACCURACY. No uncertainty is stated; the numerical parameters were ‘chosen such as to ensure converged tunnel ionization rates’ (p. -3). The model’s approximations are the Hartree-Fock-Slater mean field, which the field is assumed not to modify (‘At field strengths of 0.1 a.u. or less, this approximation should be reasonable’, p. -2), and the first-order spin-orbit coupling within a subshell. Printed to three digits.
NOT TAKEN. The Stark shifts and the overlaps of Table I (no quantity; kept in the printed cells). Table II (p. -7: spin-orbit periods and x-ray transition energies of the Ne-Xe ions, reproduced from refs. [79-84]). Fig. 1 (cycle-averaged rates against intensity) and Fig. 2 (Kr+ state populations): figures.
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
santra_2006/tableI_j12_m12_Kr#
{
"id": "tableI_j12_m12_Kr",
"material": "Kr",
"file": "Kr/santra_2006__tableI_j12_m12_Kr.csv",
"table": "tbl_f7044803390d",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"orbital": "4p_1/2",
"m_j": "+-1/2",
"potential": "Herman-Skillman (Hartree-Fock-Slater, exchange parameter 1.1035) with spin-orbit coupling, 4p_j energies tuned to the measured ones",
"method": "complex absorbing potential, finite-element basis"
}
}
Table I (p. 043403-3), row 1 (m = +1/2, |c(j=1/2)|^2 = 0.976), column gamma (au): the static-field tunnel ionisation rate gamma = -2 Im E of the 4p_1/2 resonance state with |m| = 1/2 at E = 0.10 au (the caption), in the Herman-Skillman potential with spin-orbit coupling. The rate of the ONE electron in that spin-orbital; m = -1/2 has the same rate (caption), so the 4p_1/2 subshell’s two electrons give twice it. No uncertainty is stated.
santra_2006/tableI_j32_m12_Kr#
{
"id": "tableI_j32_m12_Kr",
"material": "Kr",
"file": "Kr/santra_2006__tableI_j32_m12_Kr.csv",
"table": "tbl_f7044803390d",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"orbital": "4p_3/2",
"m_j": "+-1/2",
"potential": "Herman-Skillman (Hartree-Fock-Slater, exchange parameter 1.1035) with spin-orbit coupling, 4p_j energies tuned to the measured ones",
"method": "complex absorbing potential, finite-element basis"
}
}
Table I (p. 043403-3), row 2 (m = +1/2, |c(j=3/2)|^2 = 0.957), column gamma (au): the static-field tunnel ionisation rate gamma = -2 Im E of the 4p_3/2 resonance state with |m| = 1/2 at E = 0.10 au (the caption), in the Herman-Skillman potential with spin-orbit coupling. The rate of the ONE electron in that spin-orbital; m = -1/2 has the same rate (caption). The fastest channel: 8.37 times the |m| = 3/2 rate and 2.41 times the 4p_1/2 rate (‘more than a factor of 8’ and ‘2.4’, p. -4). No uncertainty is stated.
santra_2006/tableI_j32_m32_Kr#
{
"id": "tableI_j32_m32_Kr",
"material": "Kr",
"file": "Kr/santra_2006__tableI_j32_m32_Kr.csv",
"table": "tbl_f7044803390d",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"orbital": "4p_3/2",
"m_j": "+-3/2",
"potential": "Herman-Skillman (Hartree-Fock-Slater, exchange parameter 1.1035) with spin-orbit coupling, 4p_j energies tuned to the measured ones",
"method": "complex absorbing potential, finite-element basis"
}
}
Table I (p. 043403-3), row 3 (m = +3/2, |c(j=3/2)|^2 = 0.970, |c(j=1/2)|^2 printed 0), column gamma (au): the static-field tunnel ionisation rate gamma = -2 Im E of the 4p_3/2 resonance state with |m| = 3/2 at E = 0.10 au (the caption), in the Herman-Skillman potential with spin-orbit coupling. The rate of the ONE electron in that spin-orbital (no m_l = 0 component: ‘has no overlap with |4p, m_l = 0, m_s>’, p. -4); m = -3/2 has the same rate (caption). No uncertainty is stated.
santra_2006/total_Kr#
{
"id": "total_Kr",
"material": "Kr",
"table": "text",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"orbital": "4p (all six electrons)",
"potential": "Herman-Skillman (Hartree-Fock-Slater, exchange parameter 1.1035) with spin-orbit coupling, 4p_j energies tuned to the measured ones",
"method": "complex absorbing potential, finite-element basis"
}
}
1 inline points in the source record.
Text, p. 043403-4: ‘the ionization rate of Kr, at E = 0.10 a.u., is 0.036 a.u., which corresponds to a tunneling lifetime of 0.67 fs’: the rate of the atom, the sum of the Table I rates over the six 4p electrons, 2 x (4.89e-3 + 1.18e-2 + 1.41e-3) = 0.03620 au (checked 2026-10-01). Static field. Printed to two significant digits; 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.