batishchev_2010 =============== P\. A\. Batishchev, O\. I\. Tolstikhin and T\. Morishita, "Atomic Siegert states in an electric field\: Transverse momentum distribution of the ionized electrons", Phys\. Rev\. A 82, 023416 \(2010\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevA\.82\.023416 `__ **Source kind:** theory **Recorded technique:** Siegert states \(regular, outgoing\-wave solutions of the stationary Schrodinger equation\) of one electron in an atomic potential and a static uniform field, in parabolic coordinates\: slow\-variable discretisation in eta with an adiabatic basis in xi and R\-matrix propagation to the asymptotic region, where the outgoing\-wave condition is imposed in the separable asymptotic form \(Secs\. II\-III, Appendix\)\. The complex eigenvalue is E = script\-E \- i Gamma/2 \(Eq\. \(7\)\)\: Gamma is the ionisation width \(rate\) of the state\. Single\-active\-electron \(SAE\) potentials\: pure Coulomb \(H\), the Green\-Sellin\-Zachor form \(Eqs\. \(46\)\-\(47\)\) with Garvey, Jackman & Green's \(1975\) parameters for Ne, Ar, Kr, Xe, and a finite\-range model for H\- \(Eq\. \(48\)\)\. **Materials in structured entries:** Ar, Kr **Dataset quantities:** ionization\_model\_parameter, ionization\_rate **Contents:** 3 datasets; 0 formulas. Curation notes -------------- Journal pp\. 023416\-1 to \-12 = PDF pages 1\-12 \(pages cited as \-n\)\. Identity checked on the first page\. EXTRACTED\: Table I \(p\. \-8, tbl\_c150ef90d0bb, JSON cells, image checked\), the convergence of the Siegert eigenvalue of Ar\(3p, m = 0\) with the number of adiabatic channels N\_ch, at F = 0, 0\.05, 0\.1, 0\.2, 0\.5 and 1\.0 au\. 'All digits in the last line for each value of F are converged' \(caption\)\: the last line's Gamma at each F \> 0 is the dataset table1\_Ar \(5 fields\)\. Gamma is the width of one electron's Siegert state \(the 3p, m = 0 orbital, SAE\)\: the rate per electron in that orbital, not per atom, with no sum over m or over the six 3p electrons\. The converged values \(au\)\: F = 0\.05, \-script\-E 0\.607144, Gamma 0\.236633e\-5 \(N\_ch = 20\); 0\.1, 0\.614961, 0\.537961e\-2 \(20\); 0\.2, 0\.616812, 0\.931215e\-1 \(20\); 0\.5, 0\.523588, 0\.241714 \(15\); 1\.0, 0\.464172, 0\.585482 \(15\)\. The Stark\-shifted energy \-script\-E has no quantity \(it is the Siegert state's real energy, not an ionisation energy\)\: notes only\. F = 0\: \-script\-E = 0\.605685 \(N\_ch = 30\), Gamma = 0, the model's bound\-state energy\. The rows with fewer channels are the convergence study \(e\.g\. at F = 0\.05\: Gamma 0\.270883e\-5 with 5 channels, 0\.237055e\-5 with 10, 0\.236645e\-5 with 15\)\. ACCURACY\: Fig\. 3's results \(Ne, Ar, Kr, Xe\) 'are converged to about six significant digits' \(p\. \-8\); the H results of Fig\. 1 'to at least ten significant digits' and coincide with the literature \(p\. \-6\)\. The model potential, not the numerics, limits the physics\: its binding energies \|E0\| are 0\.811 \(Ne\), 0\.606 \(Ar\), 0\.459 \(Kr\) and 0\.486 \(Xe\) au 'while the exact ionization potentials are 0\.793, 0\.579, 0\.515, and 0\.446' \(p\. \-7, uncited\)\: 'The error varies from 2% for Ne to 11% for Kr', 'a price for simplicity of this model potential'\. So these are SAE\-model rates of a model atom whose binding energy is 4\.6 % \(Ar\) too large\: validators of an SAE rate at the model's own \|E0\|, not of argon's rate\. THE POTENTIAL \(Eqs\. \(46\)\-\(47\), p\. \-7\)\: V\(r\) = \-Z\_eff\(r\)/r, Z\_eff\(r\) = Z \- \(Z \- 1\){1 \- \[\(b/a\)\(e^\(a r\) \- 1\) \+ 1\]^\(\-1\)} \(Green, Sellin & Zachor 1969 \[57\]\), with 'the recommended values of the parameters a and b for the different atoms' of Garvey, Jackman & Green, Phys\. Rev\. A 12, 1144 \(1975\) \[58\]; the paper prints them only for Kr\: a = 1\.351, b = 4\.418 from \[58\], and modified values a = 1\.320, b = 4\.355 that give \|E0\| ~ 0\.514 'much closer to the exact value 0\.515' \(p\. \-8; recorded as datasets, ionization\_model\_parameter of the model 'gsz\_sae\_potential'\)\. Ne's, Ar's and Xe's a, b are not printed\: Garvey et al\. 1975 is not in the library \(missing\)\. FIGURES \(not digitised\)\: Fig\. 1, script\-E and Gamma of the four lowest Siegert states of H against F \(exact, second\-order perturbation theory, semiclassical asymptotics\); Figs\. 2, 4, 7, the transverse momentum distributions of H, the noble gases and H\-; Fig\. 3, script\-E and Gamma of Ne\(2p\), Ar\(3p\), Kr\(4p\), Kr'\(4p\) \(modified parameters\) and Xe\(5p\) against F \(Xe's energy has a maximum near F ~ 0\.37, Kr's near 0\.94, pp\. \-7 and \-8\); Fig\. 5, the asymptotic coefficients f\_nu of Ar\(3p\); Fig\. 6, H\-\. WEAK\-FIELD LIMIT \(Eqs\. \(40\)\-\(42\), p\. \-5\)\: Gamma ~ F^\(1 \+ \|m\| \- 2 Z\_as/kappa\) exp\(\-2 kappa^3/\(3F\)\), kappa = \(2\|E0\|\)^\(1/2\), the leading asymptotic channel nu = 0; the coefficients are 'not given explicitly' \(the weak\-field asymptotic theory is trinh\_2013's subject\)\. H\- model \(Eq\. \(48\), p\. \-9\)\: V0 = 0\.383 1087, r0 = 2\.5026, \|E0\| = 0\.027 7510 \(not curated\)\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- batishchev\_2010/table1\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "table1_Ar", "material": "Ar", "file": "Ar/batishchev_2010__table1_Ar.csv", "table": "tbl_c150ef90d0bb", "quantity": "ionization_rate", "unit": "au", "abscissa": "field", "abscissa_unit": "au", "use": "check", "parameters": { "wavelength_nm": Infinity, "polarization": "static", "method": "SAE Siegert state (slow-variable discretisation, R-matrix propagation), Green-Sellin-Zachor potential with Garvey et al. 1975 parameters", "orbital": "3p, m = 0" } } Table I, p\. \-8\: the converged width Gamma \(the last line of each block, 'All digits \.\.\. are converged'\) of the Ar\(3p, m = 0\) Siegert state in the SAE model potential of Eqs\. \(46\)\-\(47\) with Garvey et al\.'s parameters, whose binding energy is 0\.605685 au \(0\.606 in the text\) against argon's 0\.579\: a model atom\. Per electron in the m = 0 orbital\. use = check\: a validator of an SAE rate at the model's \|E0\| \(record notes\)\. batishchev\_2010/potential\_garvey\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "potential_garvey_Kr", "material": "Kr", "table": "text", "quantity": "ionization_model_parameter", "unit": "1", "abscissa": "label", "use": "reproduced", "reproduced_from": [ "R. H. Garvey, C. H. Jackman and A. E. S. Green, Phys. Rev. A 12, 1144 (1975)" ], "parameters": { "model": "gsz_sae_potential", "parameter": "a, b of Eq. (47)" } } 2 inline points in the source record. p\. \-8\: 'By slightly modifying the parameters in Eq\. \(47\) for Kr \(1\.320 and 4\.355 instead of 1\.351 and 4\.418 for a and b, respectively\)'\: the recommended values of \[58\] \(Garvey et al\. 1975\), which give Kr's \|E0\| = 0\.459 au \(exact 0\.515\), below Xe's 0\.486\. a in inverse bohr \(e^\(a r\), r in au\); b likewise \(the ratio b/a is dimensionless\)\. batishchev\_2010/potential\_modified\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "potential_modified_Kr", "material": "Kr", "table": "text", "quantity": "ionization_model_parameter", "unit": "1", "abscissa": "label", "use": "check", "parameters": { "model": "gsz_sae_potential", "parameter": "a, b of Eq. (47)" } } 2 inline points in the source record. p\. \-8\: this paper's modification of Eq\. \(47\)'s parameters for Kr, which gives \|E0\| ~ 0\.514 au, 'much closer to the exact value 0\.515 and restores the correct order of the binding energies' \(the Kr'\(4p\) curves of Fig\. 3\)\. A model input chosen by the authors; units as potential\_garvey\_Kr\. 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.