parker_2009#
J. S. Parker, G. S. J. Armstrong, M. Boca and K. T. Taylor, “From the UV to the static-field limit: rates and scaling laws of intense-field ionization of helium”, J. Phys. B: At. Mol. Opt. Phys. 42, 134011 (2009)
Source record · Catalogue · Review register
DOI: 10.1088/0953-4075/42/13/134011
Source kind: theory
Recorded technique: Full-dimensional integration of the two-electron helium time-dependent Schrodinger equation (the HELIUM code: finite differences in the radial variables, coupled spherical harmonics; Smyth et al. 1998, smyth_1998), infinite nuclear mass. Laser-driven single-ionisation rates at 195 nm up to 32e14 W/cm^2, and static-field rates for E < 0.4 au: the field is ramped on smoothly, E = E_max (1 - cos(Omega t))/2 for 0 < t < pi/Omega, and the rate is the exponential decay of the population within 18 Bohr of the nucleus (p. 8).
Materials in structured entries: He
Dataset quantities: ionization_rate
Contents: 4 datasets; 2 formulas.
Curation notes#
Pages are pdf pages: pdf page 1 is the IOPscience download cover, so the article page is 134011-(n-1). Identity checked against pdf p. 2.
WHAT IS TAKEN. Table 1 (p. 8), ‘Static-field ionization rates from the ground state of helium as a function of peak electric field strength E’: Gamma (au) against E (au) for ‘Present work’, ‘Scrinzi et al [3]’, ‘Themelis et al [4]’ and ‘ADK theory [9]’, one dataset per column (wavelength_nm = inf, polarization = static). The library’s table is scrambled (the characters of every row interleaved in one cell per column): the script transcribes it from the image and checks each column’s characters against the scrambled cell (structural fix, no erratum). The rate is that of the atom: the decay of the two-electron ground-state population (single ionisation), not per electron.
CONVERGENCE (p. 8, quoted; no overall uncertainty is stated, so none is recorded): ‘The integrations were repeated with increasingly large values for the maximum angular momenta L_max and ramp-on times T, until no change was observed in the final results’ (L_max 12 at low field, 24 for E > 0.25 au); ‘Reducing delta r to 0.2 au altered ionization rates by 0.3% at E = 0.1 au and by 0.03% at E = 0.3 au’. ‘No adiabatic response was observed for E > 0.38 au ... Despite this source of uncertainty, at E = 0.40 au the measured ionization rate differed from Scrinzi’s by only a few per cent’ (p. 8); the table has no present-work value at 0.40. A change of functional form at E = 0.175 au, a component scaling as E^4 (p. 3, p. 8).
REPRODUCED AND CHECK COLUMNS. [3] = A. Scrinzi, M. Geissler and T. Brabec, Phys. Rev. Lett. 83, 706 (1999) and [4] = S. I. Themelis, T. Mercouris and C. A. Nicolaides, Phys. Rev. A 61, 024101 (1999), full-dimensional time-independent methods (p. 9); neither is in the library. [9] ADK: ‘The ADK formula used here is discussed in [1]’ (parker_2007, p. 9), whose AC-ADK is for ‘a ground state one-electron atom with ionization potential 0.903724 au’ and says that of the two-electron atom is twice it (parker_2007 p. 12). Not reproduced exactly (computed 2026-09-26): the static ADK rate with the Gamma-function C_n*l^2 (n* = 0.7438, l = m = 0), Ip = 0.903724 au and two electrons is 0.783 +- 0.001 of the printed column at every E except 0.20 au; with Stirling’s C_n*l^2 = (2e/n*)^(2n*) /(2 pi n*) it is 0.970 +- 0.001. At E = 0.20 au the ratio is 0.809 (Gamma form) and 1.003 (Stirling): the printed 1.07e-2 departs by +3.3 % from the smooth trend of its neighbours, which gives about 1.11e-2; probably a misprint of the ADK cell, not corrected (a formula evaluation, use = check). majety_2015 Table 1 reprints this ADK column digit for digit, 1.07e-2 at 0.20 included, as it reprints the other three columns (at the 13 fields 0.06-0.20 au).
FORMULAS. Eq. (8) (static fit) and Eq. (7) (the laser-driven fits of Figs. 3-5) are recorded below. The empirical cycle-averaged static rate (p. 9): ‘multiplying equation (8) by 0.146 I^0.25 works well for I < 50.0 x 10^14 W cm^-2, (E < 0.3773)’, with I = 14.0484 (E/0.2)^2 (I in 1e14 W/cm^2, E in au).
195 nm AND THE SCALING LAWS (figures only, not taken). Fig. 1 (p. 3): rates at 195, 390 and 780 nm and the cycle-averaged static rates, 0 < I < 16e14 W/cm^2; Fig. 5 (p. 5): 195 nm, 1/ln^2(Gamma) against I, data up to I = 32.0e14 W/cm^2. Text values (pp. 3, 6-7): the 780 nm rates exceed the static rates by factors 100, 8, 3 and 2 at I = 1, 2, 3 and 4e14 W/cm^2; Eq. (2) with A = 548000.0, d0 = 0.138, n = 7.735, xi = 0.456 (ponderomotive shift xi0 = 0.4464 plus Stark xi2 = 0.0096, 390 nm units); b0 from the figures 0.000247 (780 nm), 0.000990 (390 nm), 0.003920 (195 nm) against Eq. (6) 0.000250, 0.000989, 0.003856; b1 from the figures 0.001485, 0.001630, 0.001750 against Eq. (5) 0.001470, 0.001680, 0.001930 (‘the 10% error at R = 0.5 stands out’); a0 = b0 R^2 from Eq. (6) 0.000993 (3120 nm), 0.001000 (1560 nm), 0.001000 (780 nm), 0.000989 (390 nm), 0.000964 (195 nm); for neon’s n = 6.7832, a0 = 0.00139 at R = 2. At 195 nm Eq. (7) fails for I < 1.0e14 W/cm^2 (0.25e14 at 390 nm). The ABI onset: Scrinzi’s 14e14 W/cm^2 (E = 0.2 au) (p. 3, p. 9). None of these is a quantity: notes only. At 195 nm (omega = 2 x 0.11683 = 0.23366 au, parker_2007’s omega_390) single ionisation of He needs four photons (Ip/omega = 0.903724/0.23366 = 3.87 at zero intensity; computed 2026-10-08): it is not two-photon ionisation, and no 195 nm rate is held.
UNMAPPED_GLYPHS on p. 4 touch the ponderomotive-shift text; the Table 1 values do not depend on it.
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
parker_2009/table1_present#
{
"id": "table1_present",
"material": "He",
"file": "He/parker_2009__table1_present.csv",
"table": "tbl_f4122d1f56cb",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "primary",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"method": "full-dimensional TDSE (HELIUM)"
}
}
Table 1 (p. 8), ‘Present work’: full-dimensional time-dependent static-field rates of He, 26 fields 0.045-0.3773 au (none at 0.40). Eq. (8) reproduces them within 2.6 % except at 0.05 au (+7.3 %) and 0.067 au (-6.5 %) (computed 2026-09-26). Convergence statements in the record’s notes; uncertainty not stated.
parker_2009/table1_scrinzi_1999#
{
"id": "table1_scrinzi_1999",
"material": "He",
"file": "He/parker_2009__table1_scrinzi_1999.csv",
"table": "tbl_f4122d1f56cb",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "reproduced",
"reproduced_from": [
"scrinzi_1999"
],
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"method": "full-dimensional complex scaling (Scrinzi et al. 1999)"
}
}
Table 1 (p. 8), ‘Scrinzi et al [3]’: full-dimensional time-independent (complex-scaling) He rates, 15 fields 0.08-0.40 au. majety_2015 reprints the 0.08-0.20 au values identically. The original, scrinzi_1999/table1_He (Table I), prints all 15 identically (checked 2026-09-27).
parker_2009/table1_themelis_1999#
{
"id": "table1_themelis_1999",
"material": "He",
"file": "He/parker_2009__table1_themelis_1999.csv",
"table": "tbl_f4122d1f56cb",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "reproduced",
"reproduced_from": [
"S. I. Themelis, T. Mercouris and C. A. Nicolaides, Phys. Rev. A 61, 024101 (1999)"
],
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"method": "full-dimensional state-specific (Themelis et al. 1999)"
}
}
Table 1 (p. 8), ‘Themelis et al [4]’: full-dimensional time-independent He rates, 19 fields 0.067-0.40 au. majety_2015 reprints the 0.07-0.20 au values identically.
parker_2009/table1_adk#
{
"id": "table1_adk",
"material": "He",
"file": "He/parker_2009__table1_adk.csv",
"table": "tbl_f4122d1f56cb",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "field",
"abscissa_unit": "au",
"use": "check",
"parameters": {
"wavelength_nm": Infinity,
"polarization": "static",
"method": "ADK formula"
}
}
Table 1 (p. 8), ‘ADK theory [9]’: a formula evaluation, 27 fields 0.045-0.40 au. The E = 0.20 au cell (1.07e-2) is +3.3 % off the smooth trend of the rest (see the record’s notes); not corrected.
Formulas#
parker_2009/static_fit#
{
"id": "static_fit",
"material": "He",
"equation": "Eq. (8), pp. 8-9",
"printed": "Gamma(E) = (1/E^2) exp(-1/(1.47 x 10^-5 + 0.577 E)) + 6.183 (E - 0.1755)^4 Step(E - 0.1755)",
"variable": "E: static field in au (E < 0.4 au); Gamma in au; Step(x) = 1 for x > 0, else 0",
"range": "E < 0.4 au",
"coefficients": {
"c0": "1.47e-5",
"c1": "0.577",
"A4": "6.183",
"E0": "0.1755"
},
"check": "Reproduces Table 1 'Present work' within 2.6 % at 24 of 26 fields; +7.3 % at 0.05 au and -6.5 % at 0.067 au; +0.2 % at 0.3773 au (computed 2026-09-26)."
}
‘the E^4 model is based on only five data points’ (p. 9). Times 0.146 I^0.25 (I in 1e14 W/cm^2, I = 14.0484 (E/0.2)^2) it gives the cycle-averaged static rate of Fig. 1 for I < 50e14 W/cm^2 (p. 9).
parker_2009/laser_fit#
{
"id": "laser_fit",
"material": "He",
"equation": "Eq. (7), p. 7",
"printed": "Gamma(Ibar, R) = exp(-R / sqrt(a0 + a1 Ibar)); 780 nm (R = 2.0): a0 = 0.0009882, a1 = 0.001485; 390 nm (R = 1.0): a0 = 0.0009900, a1 = 0.001630; 195 nm (R = 0.5): a0 = 0.0009800, a1 = 0.001750",
"variable": "R: wavelength in units of 390 nm; Ibar = I R^2, I the (cycle-averaged) intensity in 1e14 W/cm^2; Gamma in au",
"range": "Ibar < 16 (390 and 780 nm), Ibar < 8 (195 nm); fails at 195 nm below I = 1.0e14 W/cm^2 (p. 7)",
"coefficients": {
"a0_780": "0.0009882",
"a1_780": "0.001485",
"a0_390": "0.0009900",
"a1_390": "0.001630",
"a0_195": "0.0009800",
"a1_195": "0.001750"
},
"check": "Not checkable: the laser-driven rates are in figures only."
}
Fits (the dashed lines of Figs. 3-5) to the non-resonant trend of the TDSE rates; resonances smoothed away. ‘Over higher intensity ranges, the curves given in equation (5) of [1] may be used’ (parker_2007).
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.