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 `__ · :doc:`Catalogue ` · :doc:`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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 :doc:`review register ` for the checks and decisions.