trinh_2013 ========== V\. H\. Trinh, O\. I\. Tolstikhin, L\. B\. Madsen and T\. Morishita, "First\-order correction terms in the weak\-field asymptotic theory of tunneling ionization", Phys\. Rev\. A 87, 043426 \(2013\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/PhysRevA\.87\.043426 `__ **Source kind:** theory **Recorded technique:** The weak\-field asymptotic theory \(WFAT\) of tunnelling ionisation in a static field, carried to first order in F, for one electron in a potential with a Coulomb tail \(single\-active\-electron and frozen\-nuclei approximations\), in parabolic coordinates \(Secs\. II\-III\)\. Illustrated for H and for Ne\(2p\), Ar\(3p\), Kr\(4p\), Xe\(5p\) \(m = 0\) in the Green\-Sellin\-Zachor model potential\: E0 and psi\_0 from a Laguerre discrete\-variable representation, alpha and psi\_1 by spectral perturbation sums, g00, g10, a00 by fitting Eqs\. \(37\)\-\(38\) at large eta; the 'exact' rates for comparison by the Siegert\-state method of batishchev\_2010 \(Sec\. IV\)\. **Materials in structured entries:** Ar, Kr, Ne, Xe **Dataset quantities:** ionization\_model\_parameter, tunnelling\_structure\_coefficient **Contents:** 16 datasets; 0 formulas. Curation notes -------------- Journal pp\. 043426\-1 to \-14 = PDF pages 1\-14 \(pages cited as \-n\)\. Identity checked on the first page\. WHAT IS TABULATED AND WHICH QUANTITY \(the question asked when the paper was requested\)\. Table I \(p\. \-9, tbl\_44397cd5a3f8, image checked\), 'Characteristics of noble\-gas atoms \.\.\. All values are given in atomic units'\: N, u, v, E0, alpha, g00, g10, a00, A00, B00 per atom\. \- g00 and g10 ARE structure factors\: the asymptotic coefficients g\_nu of the parabolic channels nu = \(0, 0\) and \(1, 0\) \(Eq\. \(37\)\), with G\_nu = e^\(\-kappa mu\_z\) g\_nu the WFAT structure factor \(Eq\. \(50\)\) and mu\_z = 0 for these atoms, so G00 = g00 \(p\. \-10\)\: recorded as tunnelling\_structure\_coefficient, model = wfat \(wfat\_\\)\. The row label is the parabolic channel \(n\_xi, m\), not a partial wave l as for MO\-ADK\: the vocabulary's 'one per partial wave l' does not fit WFAT exactly \(for review\)\. \- a00, A00 and B00 are NOT structure factors\: a00 is the first\-order distortion coefficient of the asymptotic solution \(Eqs\. \(34\), \(38\)\), A00 and B00 the first\-order correction coefficients of the rate, Gamma = \|G00\|^2 W00\(F\) \[1 \+ A00 F ln\(F/\(4 kappa^2\)\) \+ B00 F\] \(Eqs\. \(49\), \(53\)\)\: recorded as ionization\_model\_parameter, model = wfat \(correction\_\\)\. \- N, u, v define the model potential \(potential\_\\); E0 and alpha are the model state's energy and polarizability \(state\_\\)\: ionization\_model\_parameter\. All use = check\: properties of one\-electron model states, which the paper uses to illustrate the theory\. CHECKS \(computed 2026\-09\-27\)\: \(1\) A00 from Eq\. \(40a\) with beta^\(0\) = 1 \- kappa/2 \(Eq\. \(30a\)\), beta^\(1\) = \-1/\(2 kappa^2\) \(Eq\. \(31a\)\), gamma\_0 = 1/4 \(Eq\. \(16\), D = 0\), mu\_z = 0\: Ne 0\.2456, Ar 0\.1582, Kr 0\.0415, Xe \-0\.2217, against 0\.246, 0\.158, 0\.042, \-0\.222 printed \(all agree to the printed digits; A00 = 0 at kappa = 1, E0 = \-0\.5, as p\. \-10 says\)\. \(2\) B00 from Eq\. \(40b\) with the printed E0, alpha and a00\: Ne \-2\.62, Ar \-7\.58, Kr \-10\.42, Xe \-16\.48, against \-2\.6, \-7\.7, \-10\.5, \-16\.4\: within the \+\-0\.1 that a00's one printed decimal allows \(2 Re a00 enters B00\), Ar by 0\.12\. \(3\) The model potential's bound states, by finite differences on a 60 a0 radial grid\: the lowest, second, third and fourth l = 1 levels with Trinh's N, u, v are \-0\.7934 \(Ne\), \-0\.5791 \(Ar\), \-0\.5152 \(Kr\), \-0\.4460 \(Xe\), reproducing E0 to the printed three decimals\. The same code gives Kr's 4p at \-0\.4589 with Garvey et al\.'s a = 1\.351, b = 4\.418 and \-0\.5139 with batishchev\_2010's modified a = 1\.320, b = 4\.355, reproducing that paper's 0\.459 and 0\.514\: Trinh's Kr parameters \(u = 1\.340, v = 4\.311\) are a third set, and all four of Trinh's sets are tuned so that E0 is minus the atom's ionisation energy \(batishchev\_2010 quotes 0\.793, 0\.579, 0\.515, 0\.446 as 'exact'\)\. ACCURACY\: no uncertainty is stated for Table I; g00, g10, a00 are printed to one decimal\. The WFAT\(1\) rates agree with the exact Siegert\-state rates up to about F\_c, the field where the WFAT\(1\) rate turns zero\: F\_c ~ 0\.3, 0\.12, 0\.095, 0\.065 for Ne, Ar, Kr, Xe \(Eq\. \(62\) gives 0\.4, 0\.18, 0\.13, 0\.09\); second\-order perturbation theory for the energy holds up to F ~ 0\.1, 0\.05, 0\.05, 0\.03 \(pp\. \-10, \-11\)\. For H\(1s\) the paper compares with the exact rates and with higher\-order expansions \(Figs\. 1\-3, pp\. \-7 and \-8\)\. FIGURES \(not digitised\)\: Fig\. 1, H\(1s\) Gamma/W00 against F; Fig\. 2, excited H states; Figs\. 3, 8\-11, transverse momentum distributions; Figs\. 4\-7, the energy, the rate and its ratio to the field factor for Ne\(2p\), Ar\(3p\), Kr\(4p\), Xe\(5p\) \(exact, WFAT\(0\), WFAT\(1\)\)\: the exact SAE static rates of these model atoms are in figures only\. FOR REVIEW\: solprop uses ADK/PPT and MO\-ADK, not WFAT; these are the atoms' weak\-field asymptotic coefficients the roadmap asks for \(Trinh et al\.\), in the WFAT's own normalisation \(the parameters' normalisation field\), with the first\-order corrections\. **Recorded bibliographic identity status:** VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- trinh\_2013/wfat\_Ne ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "wfat_Ne", "material": "Ne", "file": "Ne/trinh_2013__wfat_Ne.csv", "table": "tbl_44397cd5a3f8", "quantity": "tunnelling_structure_coefficient", "unit": "1", "abscissa": "label", "use": "check", "parameters": { "model": "wfat", "orbital": "2p", "m": 0, "normalisation": "Trinh et al. 2013 Eq. (37): g_nu = eta^(1/2 - beta_nu^(0)/kappa) e^(kappa eta/2) as eta -> inf, psi_0 the real normalised bound state, Phi_nu^(0) the parabolic channel functions of Eq. (30b), beta_nu^(0) = Z - kappa(n_xi + (|m| + 1)/2), kappa = (2|E0|)^(1/2); G_nu = e^(-kappa mu_z) g_nu (Eq. (50)); the rate Gamma = (2 - delta_m0)|G_0m|^2 W_0m(F)(1 + A_0m F ln(F/(4 kappa^2)) + B_0m F) (Eq. (53)) with W_nu(F) = (kappa/2)(4 kappa^2/F)^(2Z/kappa - 2 n_xi - |m| - 1) exp(-2 kappa^3/(3F)) (Eq. (51)), Z = 1" } } Table I, p\. 043426\-9\: g00 and g10, the asymptotic coefficients of the parabolic channels nu = \(n\_xi, m\) = \(0, 0\) and \(1, 0\) of the 2p \(m = 0\) orbital in the model potential of Eqs\. \(63\)\-\(64\) \(potential\_Ne\); the rows are the channel, not a partial wave l\. G\_00 = g00 is the WFAT structure factor of the dominant channel \(mu\_z = 0\); g10 enters the transverse momentum distribution\. Printed to two digits\. Values of the SAE model state, not of the many\-electron atom\: use = check \(record notes\)\. trinh\_2013/correction\_Ne ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "correction_Ne", "material": "Ne", "file": "Ne/trinh_2013__correction_Ne.csv", "table": "tbl_44397cd5a3f8", "quantity": "ionization_model_parameter", "unit": "au", "abscissa": "label", "use": "check", "parameters": { "model": "wfat", "parameter": "a00, A00, B00 of Eqs. (38), (40), the row label" } } Table I, p\. 043426\-9\: a00 \(Eq\. \(38\), the coefficient of the first\-order distortion of the orbital in the asymptotic expansion, Eq\. \(34\)\) and the first\-order correction coefficients A00 and B00 \(Eqs\. \(40\)\) of the dominant channel \(0, 0\), for the 2p \(m = 0\) SAE state\. Units\: atomic units of inverse field \(they multiply F\)\. A00 reproduced from E0 \(record notes\)\. trinh\_2013/potential\_Ne ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "potential_Ne", "material": "Ne", "file": "Ne/trinh_2013__potential_Ne.csv", "table": "tbl_44397cd5a3f8", "quantity": "ionization_model_parameter", "unit": "1", "abscissa": "label", "use": "check", "parameters": { "model": "gsz_sae_potential", "parameter": "N, u, v of Eqs. (63)-(64), the row label" } } Table I, p\. 043426\-9\: N \(the nuclear charge, Z\_eff\(0\)\), u and v of the effective charge Z\_eff\(r\) = N \- \(N \- 1\){1 \- \[\(v/u\)\(e^\(u r\) \- 1\) \+ 1\]^\(\-1\)} \(Eq\. \(64\)\) of the SAE potential V = \-Z\_eff\(r\)/r \(Eq\. \(63\)\), 'the recommended values' \(p\. \-9, citing Green et al\. 1969 and Garvey et al\. 1975\); u and v in inverse bohr\. They reproduce E0 \(checked, record notes\)\. trinh\_2013/state\_Ne ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "state_Ne", "material": "Ne", "file": "Ne/trinh_2013__state_Ne.csv", "table": "tbl_44397cd5a3f8", "quantity": "ionization_model_parameter", "unit": "au", "abscissa": "label", "use": "check", "parameters": { "model": "gsz_sae_potential", "parameter": "E0, alpha of the model's active electron, the row label" } } Table I, p\. 043426\-9\: E0, the unperturbed energy of the 2p \(m = 0\) state in the model potential, and alpha, 'its polarizability' \(alpha\_zz of the active electron in the model, which enters B00 through Eq\. \(40b\)\)\. Properties of the SAE model state, not of the atom\: E0 equals minus the atom's first ionisation energy to the printed digits \(by the choice of u, v\), but alpha is the one\-electron model's, not the atom's dipole polarizability, and must not be read as one\. trinh\_2013/wfat\_Ar ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "wfat_Ar", "material": "Ar", "file": "Ar/trinh_2013__wfat_Ar.csv", "table": "tbl_44397cd5a3f8", "quantity": "tunnelling_structure_coefficient", "unit": "1", "abscissa": "label", "use": "check", "parameters": { "model": "wfat", "orbital": "3p", "m": 0, "normalisation": "Trinh et al. 2013 Eq. (37): g_nu = eta^(1/2 - beta_nu^(0)/kappa) e^(kappa eta/2) as eta -> inf, psi_0 the real normalised bound state, Phi_nu^(0) the parabolic channel functions of Eq. (30b), beta_nu^(0) = Z - kappa(n_xi + (|m| + 1)/2), kappa = (2|E0|)^(1/2); G_nu = e^(-kappa mu_z) g_nu (Eq. (50)); the rate Gamma = (2 - delta_m0)|G_0m|^2 W_0m(F)(1 + A_0m F ln(F/(4 kappa^2)) + B_0m F) (Eq. (53)) with W_nu(F) = (kappa/2)(4 kappa^2/F)^(2Z/kappa - 2 n_xi - |m| - 1) exp(-2 kappa^3/(3F)) (Eq. (51)), Z = 1" } } Table I, p\. 043426\-9\: g00 and g10, the asymptotic coefficients of the parabolic channels nu = \(n\_xi, m\) = \(0, 0\) and \(1, 0\) of the 3p \(m = 0\) orbital in the model potential of Eqs\. \(63\)\-\(64\) \(potential\_Ar\); the rows are the channel, not a partial wave l\. G\_00 = g00 is the WFAT structure factor of the dominant channel \(mu\_z = 0\); g10 enters the transverse momentum distribution\. Printed to two digits\. Values of the SAE model state, not of the many\-electron atom\: use = check \(record notes\)\. trinh\_2013/correction\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "correction_Ar", "material": "Ar", "file": "Ar/trinh_2013__correction_Ar.csv", "table": "tbl_44397cd5a3f8", "quantity": "ionization_model_parameter", "unit": "au", "abscissa": "label", "use": "check", "parameters": { "model": "wfat", "parameter": "a00, A00, B00 of Eqs. (38), (40), the row label" } } Table I, p\. 043426\-9\: a00 \(Eq\. \(38\), the coefficient of the first\-order distortion of the orbital in the asymptotic expansion, Eq\. \(34\)\) and the first\-order correction coefficients A00 and B00 \(Eqs\. \(40\)\) of the dominant channel \(0, 0\), for the 3p \(m = 0\) SAE state\. Units\: atomic units of inverse field \(they multiply F\)\. A00 reproduced from E0 \(record notes\)\. trinh\_2013/potential\_Ar ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "potential_Ar", "material": "Ar", "file": "Ar/trinh_2013__potential_Ar.csv", "table": "tbl_44397cd5a3f8", "quantity": "ionization_model_parameter", "unit": "1", "abscissa": "label", "use": "check", "parameters": { "model": "gsz_sae_potential", "parameter": "N, u, v of Eqs. (63)-(64), the row label" } } Table I, p\. 043426\-9\: N \(the nuclear charge, Z\_eff\(0\)\), u and v of the effective charge Z\_eff\(r\) = N \- \(N \- 1\){1 \- \[\(v/u\)\(e^\(u r\) \- 1\) \+ 1\]^\(\-1\)} \(Eq\. \(64\)\) of the SAE potential V = \-Z\_eff\(r\)/r \(Eq\. \(63\)\), 'the recommended values' \(p\. \-9, citing Green et al\. 1969 and Garvey et al\. 1975\); u and v in inverse bohr\. They reproduce E0 \(checked, record notes\)\. trinh\_2013/state\_Ar ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "state_Ar", "material": "Ar", "file": "Ar/trinh_2013__state_Ar.csv", "table": "tbl_44397cd5a3f8", "quantity": "ionization_model_parameter", "unit": "au", "abscissa": "label", "use": "check", "parameters": { "model": "gsz_sae_potential", "parameter": "E0, alpha of the model's active electron, the row label" } } Table I, p\. 043426\-9\: E0, the unperturbed energy of the 3p \(m = 0\) state in the model potential, and alpha, 'its polarizability' \(alpha\_zz of the active electron in the model, which enters B00 through Eq\. \(40b\)\)\. Properties of the SAE model state, not of the atom\: E0 equals minus the atom's first ionisation energy to the printed digits \(by the choice of u, v\), but alpha is the one\-electron model's, not the atom's dipole polarizability, and must not be read as one\. trinh\_2013/wfat\_Kr ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "wfat_Kr", "material": "Kr", "file": "Kr/trinh_2013__wfat_Kr.csv", "table": "tbl_44397cd5a3f8", "quantity": "tunnelling_structure_coefficient", "unit": "1", "abscissa": "label", "use": "check", "parameters": { "model": "wfat", "orbital": "4p", "m": 0, "normalisation": "Trinh et al. 2013 Eq. (37): g_nu = eta^(1/2 - beta_nu^(0)/kappa) e^(kappa eta/2) as eta -> inf, psi_0 the real normalised bound state, Phi_nu^(0) the parabolic channel functions of Eq. (30b), beta_nu^(0) = Z - kappa(n_xi + (|m| + 1)/2), kappa = (2|E0|)^(1/2); G_nu = e^(-kappa mu_z) g_nu (Eq. (50)); the rate Gamma = (2 - delta_m0)|G_0m|^2 W_0m(F)(1 + A_0m F ln(F/(4 kappa^2)) + B_0m F) (Eq. (53)) with W_nu(F) = (kappa/2)(4 kappa^2/F)^(2Z/kappa - 2 n_xi - |m| - 1) exp(-2 kappa^3/(3F)) (Eq. (51)), Z = 1" } } Table I, p\. 043426\-9\: g00 and g10, the asymptotic coefficients of the parabolic channels nu = \(n\_xi, m\) = \(0, 0\) and \(1, 0\) of the 4p \(m = 0\) orbital in the model potential of Eqs\. \(63\)\-\(64\) \(potential\_Kr\); the rows are the channel, not a partial wave l\. G\_00 = g00 is the WFAT structure factor of the dominant channel \(mu\_z = 0\); g10 enters the transverse momentum distribution\. Printed to two digits\. Values of the SAE model state, not of the many\-electron atom\: use = check \(record notes\)\. trinh\_2013/correction\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "correction_Kr", "material": "Kr", "file": "Kr/trinh_2013__correction_Kr.csv", "table": "tbl_44397cd5a3f8", "quantity": "ionization_model_parameter", "unit": "au", "abscissa": "label", "use": "check", "parameters": { "model": "wfat", "parameter": "a00, A00, B00 of Eqs. (38), (40), the row label" } } Table I, p\. 043426\-9\: a00 \(Eq\. \(38\), the coefficient of the first\-order distortion of the orbital in the asymptotic expansion, Eq\. \(34\)\) and the first\-order correction coefficients A00 and B00 \(Eqs\. \(40\)\) of the dominant channel \(0, 0\), for the 4p \(m = 0\) SAE state\. Units\: atomic units of inverse field \(they multiply F\)\. A00 reproduced from E0 \(record notes\)\. trinh\_2013/potential\_Kr ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "potential_Kr", "material": "Kr", "file": "Kr/trinh_2013__potential_Kr.csv", "table": "tbl_44397cd5a3f8", "quantity": "ionization_model_parameter", "unit": "1", "abscissa": "label", "use": "check", "parameters": { "model": "gsz_sae_potential", "parameter": "N, u, v of Eqs. (63)-(64), the row label" } } Table I, p\. 043426\-9\: N \(the nuclear charge, Z\_eff\(0\)\), u and v of the effective charge Z\_eff\(r\) = N \- \(N \- 1\){1 \- \[\(v/u\)\(e^\(u r\) \- 1\) \+ 1\]^\(\-1\)} \(Eq\. \(64\)\) of the SAE potential V = \-Z\_eff\(r\)/r \(Eq\. \(63\)\), 'the recommended values' \(p\. \-9, citing Green et al\. 1969 and Garvey et al\. 1975\); u and v in inverse bohr\. They reproduce E0 \(checked, record notes\)\. trinh\_2013/state\_Kr ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "state_Kr", "material": "Kr", "file": "Kr/trinh_2013__state_Kr.csv", "table": "tbl_44397cd5a3f8", "quantity": "ionization_model_parameter", "unit": "au", "abscissa": "label", "use": "check", "parameters": { "model": "gsz_sae_potential", "parameter": "E0, alpha of the model's active electron, the row label" } } Table I, p\. 043426\-9\: E0, the unperturbed energy of the 4p \(m = 0\) state in the model potential, and alpha, 'its polarizability' \(alpha\_zz of the active electron in the model, which enters B00 through Eq\. \(40b\)\)\. Properties of the SAE model state, not of the atom\: E0 equals minus the atom's first ionisation energy to the printed digits \(by the choice of u, v\), but alpha is the one\-electron model's, not the atom's dipole polarizability, and must not be read as one\. trinh\_2013/wfat\_Xe ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "wfat_Xe", "material": "Xe", "file": "Xe/trinh_2013__wfat_Xe.csv", "table": "tbl_44397cd5a3f8", "quantity": "tunnelling_structure_coefficient", "unit": "1", "abscissa": "label", "use": "check", "parameters": { "model": "wfat", "orbital": "5p", "m": 0, "normalisation": "Trinh et al. 2013 Eq. (37): g_nu = eta^(1/2 - beta_nu^(0)/kappa) e^(kappa eta/2) as eta -> inf, psi_0 the real normalised bound state, Phi_nu^(0) the parabolic channel functions of Eq. (30b), beta_nu^(0) = Z - kappa(n_xi + (|m| + 1)/2), kappa = (2|E0|)^(1/2); G_nu = e^(-kappa mu_z) g_nu (Eq. (50)); the rate Gamma = (2 - delta_m0)|G_0m|^2 W_0m(F)(1 + A_0m F ln(F/(4 kappa^2)) + B_0m F) (Eq. (53)) with W_nu(F) = (kappa/2)(4 kappa^2/F)^(2Z/kappa - 2 n_xi - |m| - 1) exp(-2 kappa^3/(3F)) (Eq. (51)), Z = 1" } } Table I, p\. 043426\-9\: g00 and g10, the asymptotic coefficients of the parabolic channels nu = \(n\_xi, m\) = \(0, 0\) and \(1, 0\) of the 5p \(m = 0\) orbital in the model potential of Eqs\. \(63\)\-\(64\) \(potential\_Xe\); the rows are the channel, not a partial wave l\. G\_00 = g00 is the WFAT structure factor of the dominant channel \(mu\_z = 0\); g10 enters the transverse momentum distribution\. Printed to two digits\. Values of the SAE model state, not of the many\-electron atom\: use = check \(record notes\)\. trinh\_2013/correction\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "correction_Xe", "material": "Xe", "file": "Xe/trinh_2013__correction_Xe.csv", "table": "tbl_44397cd5a3f8", "quantity": "ionization_model_parameter", "unit": "au", "abscissa": "label", "use": "check", "parameters": { "model": "wfat", "parameter": "a00, A00, B00 of Eqs. (38), (40), the row label" } } Table I, p\. 043426\-9\: a00 \(Eq\. \(38\), the coefficient of the first\-order distortion of the orbital in the asymptotic expansion, Eq\. \(34\)\) and the first\-order correction coefficients A00 and B00 \(Eqs\. \(40\)\) of the dominant channel \(0, 0\), for the 5p \(m = 0\) SAE state\. Units\: atomic units of inverse field \(they multiply F\)\. A00 reproduced from E0 \(record notes\)\. trinh\_2013/potential\_Xe ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "potential_Xe", "material": "Xe", "file": "Xe/trinh_2013__potential_Xe.csv", "table": "tbl_44397cd5a3f8", "quantity": "ionization_model_parameter", "unit": "1", "abscissa": "label", "use": "check", "parameters": { "model": "gsz_sae_potential", "parameter": "N, u, v of Eqs. (63)-(64), the row label" } } Table I, p\. 043426\-9\: N \(the nuclear charge, Z\_eff\(0\)\), u and v of the effective charge Z\_eff\(r\) = N \- \(N \- 1\){1 \- \[\(v/u\)\(e^\(u r\) \- 1\) \+ 1\]^\(\-1\)} \(Eq\. \(64\)\) of the SAE potential V = \-Z\_eff\(r\)/r \(Eq\. \(63\)\), 'the recommended values' \(p\. \-9, citing Green et al\. 1969 and Garvey et al\. 1975\); u and v in inverse bohr\. They reproduce E0 \(checked, record notes\)\. trinh\_2013/state\_Xe ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "state_Xe", "material": "Xe", "file": "Xe/trinh_2013__state_Xe.csv", "table": "tbl_44397cd5a3f8", "quantity": "ionization_model_parameter", "unit": "au", "abscissa": "label", "use": "check", "parameters": { "model": "gsz_sae_potential", "parameter": "E0, alpha of the model's active electron, the row label" } } Table I, p\. 043426\-9\: E0, the unperturbed energy of the 5p \(m = 0\) state in the model potential, and alpha, 'its polarizability' \(alpha\_zz of the active electron in the model, which enters B00 through Eq\. \(40b\)\)\. Properties of the SAE model state, not of the atom\: E0 equals minus the atom's first ionisation energy to the printed digits \(by the choice of u, v\), but alpha is the one\-electron model's, not the atom's dipole polarizability, and must not be read as one\. 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.