bahl_2016#
A. Bahl, E. M. Wright and M. Kolesik, “Nonlinear optical response of noble gases via the metastable electronic state approach”, Phys. Rev. A 94, 023850 (2016)
Source record · Catalogue · Review register
DOI: 10.1103/PhysRevA.94.023850
Source kind: theory
Recorded technique: Static-field resonance (Stark-resonance) energies of single-active-electron models of He, Ne, Ar, Kr and Xe: the Hamiltonian H = -Delta/2 + V(r) - F x (Eq. (1)) with the field axis continued into the complex plane far from the atom (‘a version of the exterior complex scaling’, p. 2), so that the metastable ground state psi_0(F), the Stark resonance that tends to the field-free ground state, has the complex energy E_0(F) whose imaginary part gives the ionisation rate (Eq. (4), p. 2; Eq. (32), p. 5). ‘we utilized SAE potentials specified in Refs. [18-20], and used the FEAST eigenvalue solver [21] to obtain the metastable wave functions’ (p. 5). The data are tabulated for the paper’s metastable electronic state approach (MESA) to the nonlinear response of the gases in pulse propagation, and compared there with the authors’ TDSE in the same potentials (Sec. IV).
Materials in structured entries: Ar, Kr, Ne, Xe
Dataset quantities: ionization_rate
Contents: 4 datasets; 0 formulas.
Curation notes#
Journal pp. 023850-1 to -10 = PDF pages 1-10. Identity checked against the first page (A. Bahl, E. M. Wright, and M. Kolesik, Phys. Rev. A 94, 023850 (2016)).
THE DATA FILES. ‘We have tabulated quantities D_NL(F), E_0(F), and M(F,0) for the single-active-electron (SAE) models of He, Ne, Ar, Kr, and Xe atoms ... the Supplemental Material [22] includes these data sets’ (p. 5). The ten files of the Supplemental Material are attached to the paper in the library byte for byte, with their URL and SHA-256: per atom <ATOM>_imE_nlp.dat and <ATOM>_pa_corr.dat. An _imE_nlp file has three columns and no header: F (au), Im E_0(F) (au) and D_NL(F) (Eq. (31), au). The paper does not describe the files’ columns; the reading follows the file names and the paper’s list, and is checked: Im E_0 is never positive and |Im E_0| rises with F; D_NL/F^3 is constant at low field (Ne 11.3, Ar 159, Kr 355, Xe 1275 au between 0.001 and 0.003 au), as a third-order response must be. Fields every 0.001 au from 0 to 0.150 (Ne, Ar), 0.130 (Kr) and 0.100 au (Xe); Ne lacks 0.061 and 0.091 au, Xe 0.017 and 0.027 au.
WHAT IS TAKEN. The rate Gamma = -2 Im E_0 against F, for Ne, Ar, Kr and Xe: the file keeps Im E_0 as printed and scale = -2 makes it the rate (au). ‘imposing the outgoing boundary conditions shifts the eigenvalues into the lower half of the complex plane, where the imaginary parts reflect the lifetimes and can be interpreted as the ionization rates’ (p. 2); the ionised fraction obeys d rho/dt = 2 Im{E_R(F(t))}[1 - rho] (Eq. (32), p. 5; E_R = E_0 in the adiabatic limit, Eq. (29)): the population decays as exp(2 Im E_0 t), so the rate is -2 Im E_0, the sign of Eq. (32) being that of a decay. Confirmed for Ar: the file’s -2 Im E_0, interpolated in log Gamma, is 0.998-1.000 times the rate of the 3p, m = 0 electron in Tong and Lin’s potential computed with tRecX (travers_2026_trecx/static_Ar_m0) at 0.053, 0.094, 0.122 and 0.144 au, and 0.999-1.000 times zhang_2014’s Tong-Lin rates (Table IX, 2 x the printed Gamma/2) at 0.053, 0.094 and 0.144 au (at 0.122 au it is 1.19 times the Tong-Lin cell and 1.000 times the Muller cell, the displaced row of that table) (computed 2026-10-01). Gamma, not Gamma/2: -Im E_0 alone would be half the tRecX rate.
WHAT THE RATES COUNT. One active electron in a model potential, in the state that continues the field-free ground state of the model: one electron, no factor for the other electrons of the shell. For Ne, Ar, Kr and Xe that state is the p orbital with m = 0 along the field. The paper does not state m; it is implied by the method (the authors’ TDSE, which ‘represents exactly the same open (i.e., norm nonconserving) system as the one used to extract all MESA-related quantities’, p. 5, runs on a grid ‘along z and radial dimensions’, so in cylindrical symmetry, m = 0) and confirmed for Ar by the agreement with the m = 0 tRecX rate above (the m = 1 rate in that potential is 2 to 22 % of it, travers_2026_trecx/static_Ar_m1). The atom’s rate in this model would add the other p electrons (the m = 0 partner of opposite spin, and the m = +-1 electrons); the paper uses the one-electron rate as the rate of the atom (Eq. (32)).
THE POTENTIALS. ‘SAE potentials specified in Refs. [18-20]’: Tong and Lin 2005 (tong_2005), Cloux, Fabre and Pons, Phys. Rev. A 91, 023415 (2015) (not in the library), and Zhao, Liu and Zhou 2014 (zhao_2014). The paper does not say which atom takes which. tong_2005 tabulates He, Ne and Ar; zhao_2014 (p. 75) gives Xe’s parameters in the Tong-Lin form and uses Garvey et al.’s potential for Kr. Ar is Tong and Lin’s (the check above). For Ne, Tong and Lin’s is the only one of the three in the library that gives Ne (zhao_2014 takes He, Ne and Ar from it; Cloux et al. not checked), but the Ne rates were not checked against it. For Kr and Xe the potential is not identified (zhao_2014 or Cloux et al.). Each dataset names what is known in parameters.potential.
THE USABLE RANGE (decided 2026-10-01). At low field the files are not rates. Each dataset keeps the rows from the first field F0 from which on the rate rises monotonically and its logarithmic slope d ln Gamma/dF (between consecutive rows) never increases, the first row’s slope from its lower neighbour included (a tunnelling rate’s ln Gamma is concave in F): F0 = 0.043 au (Ne), 0.025 (Ar), 0.020 (Kr), 0.018 (Xe), where Gamma is 1.8e-12, 1.0e-12, 3.8e-13 and 3.3e-11 au. Below F0 there are isolated glitches (Ar: 1.15e-14 au at 0.020 au, 7.4e-16 at 0.021; Ne: 8.4e-15 at 0.036, 1.5e-15 at 0.037; Kr: 0.018 and 0.019 au at 2.0 and 0.91 times the zeroth-order WFAT shape described below, against 1.04-1.15 from 0.020 to 0.025 au), an absolute noise of about 1e-14 au in Gamma; and below the glitches the values are smooth but on a branch that does not continue the rates above F0: relative to the zeroth-order WFAT rate |g00|^2 W00(F) with trinh_2013’s coefficients (a different potential, used only for the shape, whose ratio to an exact rate must tend to a constant as F -> 0), the file’s rate is 0.93-0.95 (Ne, 0.043-0.050 au), 0.70-0.83 (Ar, 0.025-0.050), 0.70-1.15 (Kr, 0.020-0.050) and 0.53-1.06 (Xe, 0.018-0.050), but at 0.010 au 0.0012 (Ne), 18 (Ar), 2.0 (Kr) and 8e-82 (Xe) (computed 2026-10-01). The rows are kept in the files and excluded with their reasons (excluded_rows). A reviewer’s reading (Ar from 0.023, Kr from 0.020, Xe from 0.018 au) agrees except for Ar, where d ln Gamma/dF rises at 0.024 au, a row 9 % below the cubic through its four neighbours, so 0.023 and 0.024 au are excluded too. Within the kept range a scatter of a few per cent remains near F0: the deviation of a row from the cubic through its four neighbours exceeds 1 % up to 0.043 (Ne), 0.027 (Ar), 0.026 (Kr) and 0.026 au (Xe), and is below 0.1 % above 0.048, 0.036, 0.035 and 0.034 au.
ACCURACY. No uncertainty is stated for the tabulated quantities. The Ar check above (0.2 % against tRecX) shows the rates at 0.05-0.15 au are converged to that level.
He IS NOT TAKEN. Its field column is printed to three decimals while its grid is (k - 1/2) x 0.001 au, k = 1-225: D_NL/F^3 is constant only with that grid (4.67-4.75 au over rows 2-30, against 0.6-4.5 with the printed fields), and 20 printed fields occur twice (0.004, 0.009, 0.011, ... 0.203). Every printed field is 0.0005 au off, which changes a tunnelling rate by d ln Gamma/d ln F x 0.0005/F (about 8 % at 0.1 au) and leaves rows with the same field. Taking He would need the grid as an erratum of every row; the rates are not taken. (On the reconstructed grid the rate is smooth, and its logarithm concave in F, from 0.0035 au on, without the glitches of the other files.)
NOT TAKEN. The nonlinear dipole D_NL(F) (third column; the model’s, kept in the printed cells). The _pa_corr files (the post-adiabatic correction M(F,0), Eq. (26), not documented column by column). The effective energies E_eff (p. 5: 0.17, 0.14, 0.12, 0.11, 0.10 au for He-Xe, adjusted to TDSE yields). The ionised fractions of Figs. 2-6 (figures; MESA and TDSE in pulses).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
bahl_2016/rate_Ne#
{
"id": "rate_Ne",
"material": "Ne",
"file": "Ne/bahl_2016__rate_Ne.csv",
"table": "data/NE_imE_nlp.dat",
"quantity": "ionization_rate",
"unit": "au",
"scale": -2,
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"excluded_rows": {
"0.000": "F = 0: no field, Im E_0 = 0",
"0.001": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.002": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.003": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.004": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.005": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.006": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.007": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.008": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.009": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.010": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.011": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.012": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.013": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.014": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.015": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.016": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.017": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.018": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.019": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.020": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.021": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.022": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.023": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.024": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.025": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.026": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.027": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.028": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.029": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.030": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.031": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.032": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.033": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.034": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.035": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.036": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.037": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.038": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.039": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.040": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.041": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)",
"0.042": "below 0.043 au, the usable range: glitches at 0.036-0.042 au and below them a branch that departs from the tunnelling law (record notes)"
},
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"orbital": "2p",
"m": 0,
"potential": "SAE model of refs. [18-20], not stated; of these only Tong and Lin's (tong_2005) is known to give Ne",
"method": "exterior complex scaling, FEAST eigenvalue solver (SAE)"
}
}
File NE_imE_nlp.dat of the Supplemental Material (record notes), column 2: Im E_0(F) of the metastable ground state of the single-active-electron model of Ne, the 2p electron with m = 0 (implied by the method, record notes), against the static field F (au); scale = -2 makes it the rate Gamma = -2 Im E_0 (au) of that one electron, with no factor for the other electrons of the atom. Potential: SAE model of refs. [18-20], not stated; of these only Tong and Lin’s (tong_2005) is known to give Ne. 149 rows from 0 to 0.150 au; the 43 rows below 0.043 au are excluded (excluded_rows; the usable range, record notes), leaving 106 rows from 0.043 to 0.150 au, Gamma 1.8e-12 to 0.00221 au. No uncertainty is stated.
bahl_2016/rate_Ar#
{
"id": "rate_Ar",
"material": "Ar",
"file": "Ar/bahl_2016__rate_Ar.csv",
"table": "data/AR_imE_nlp.dat",
"quantity": "ionization_rate",
"unit": "au",
"scale": -2,
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"excluded_rows": {
"0.000": "F = 0: no field, Im E_0 = 0",
"0.001": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.002": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.003": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.004": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.005": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.006": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.007": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.008": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.009": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.010": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.011": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.012": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.013": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.014": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.015": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.016": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.017": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.018": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.019": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.020": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.021": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.022": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.023": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)",
"0.024": "below 0.025 au, the usable range: glitches at 0.020-0.024 au and below them a branch that departs from the tunnelling law (record notes)"
},
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"orbital": "3p",
"m": 0,
"potential": "Tong and Lin's (tong_2005), identified by the rates; the paper cites refs. [18-20] without assigning them",
"method": "exterior complex scaling, FEAST eigenvalue solver (SAE)"
}
}
File AR_imE_nlp.dat of the Supplemental Material (record notes), column 2: Im E_0(F) of the metastable ground state of the single-active-electron model of Ar, the 3p electron with m = 0 (implied by the method, record notes), against the static field F (au); scale = -2 makes it the rate Gamma = -2 Im E_0 (au) of that one electron, with no factor for the other electrons of the atom. Potential: Tong and Lin’s (tong_2005), identified by the rates; the paper cites refs. [18-20] without assigning them. 151 rows from 0 to 0.150 au; the 25 rows below 0.025 au are excluded (excluded_rows; the usable range, record notes), leaving 126 rows from 0.025 to 0.150 au, Gamma 1e-12 to 0.0565 au. No uncertainty is stated. Within 0.2 % of the Tong-Lin m = 0 rates of travers_2026_trecx/static_Ar_m0 at 0.053-0.144 au.
bahl_2016/rate_Kr#
{
"id": "rate_Kr",
"material": "Kr",
"file": "Kr/bahl_2016__rate_Kr.csv",
"table": "data/KR_imE_nlp.dat",
"quantity": "ionization_rate",
"unit": "au",
"scale": -2,
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"excluded_rows": {
"0.000": "F = 0: no field, Im E_0 = 0",
"0.001": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.002": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.003": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.004": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.005": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.006": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.007": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.008": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.009": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.010": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.011": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.012": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.013": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.014": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.015": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.016": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.017": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.018": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)",
"0.019": "below 0.020 au, the usable range: glitches at 0.018-0.019 au and below them a branch that departs from the tunnelling law (record notes)"
},
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"orbital": "4p",
"m": 0,
"potential": "SAE model of refs. [18-20] (zhao_2014 or Cloux et al. 2015); not identified",
"method": "exterior complex scaling, FEAST eigenvalue solver (SAE)"
}
}
File KR_imE_nlp.dat of the Supplemental Material (record notes), column 2: Im E_0(F) of the metastable ground state of the single-active-electron model of Kr, the 4p electron with m = 0 (implied by the method, record notes), against the static field F (au); scale = -2 makes it the rate Gamma = -2 Im E_0 (au) of that one electron, with no factor for the other electrons of the atom. Potential: SAE model of refs. [18-20] (zhao_2014 or Cloux et al. 2015); not identified. 131 rows from 0 to 0.130 au; the 20 rows below 0.020 au are excluded (excluded_rows; the usable range, record notes), leaving 111 rows from 0.020 to 0.130 au, Gamma 3.8e-13 to 0.0671 au. No uncertainty is stated.
bahl_2016/rate_Xe#
{
"id": "rate_Xe",
"material": "Xe",
"file": "Xe/bahl_2016__rate_Xe.csv",
"table": "data/XE_imE_nlp.dat",
"quantity": "ionization_rate",
"unit": "au",
"scale": -2,
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"excluded_rows": {
"0.000": "F = 0: no field, Im E_0 = 0",
"0.001": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.002": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.003": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.004": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.005": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.006": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.007": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.008": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.009": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.010": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.011": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.012": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.013": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.014": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.015": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)",
"0.016": "below 0.018 au, the usable range: values 1e-31 to 1e-228 of the tunnelling law, not a rate (record notes)"
},
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"orbital": "5p",
"m": 0,
"potential": "SAE model of refs. [18-20] (zhao_2014 or Cloux et al. 2015); not identified",
"method": "exterior complex scaling, FEAST eigenvalue solver (SAE)"
}
}
File XE_imE_nlp.dat of the Supplemental Material (record notes), column 2: Im E_0(F) of the metastable ground state of the single-active-electron model of Xe, the 5p electron with m = 0 (implied by the method, record notes), against the static field F (au); scale = -2 makes it the rate Gamma = -2 Im E_0 (au) of that one electron, with no factor for the other electrons of the atom. Potential: SAE model of refs. [18-20] (zhao_2014 or Cloux et al. 2015); not identified. 99 rows from 0 to 0.100 au; the 17 rows below 0.018 au are excluded (excluded_rows; the usable range, record notes), leaving 82 rows from 0.018 to 0.100 au, Gamma 3.3e-11 to 0.0822 au. 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.