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 · Catalogue · 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#
{
"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#
{
"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#
{
"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 review register for the checks and decisions.