parker_2007#
J. S. Parker, K. J. Meharg, G. A. McKenna and K. T. Taylor, “Single-ionization of helium at Ti:Sapphire wavelengths: rates and scaling laws”, J. Phys. B: At. Mol. Opt. Phys. 40, 1729 (2007)
Source record · Catalogue · Review register
DOI: 10.1088/0953-4075/40/10/008
Source kind: theory
Recorded technique: Full-dimensional time-dependent numerical integration (TDNI) of the two-electron helium-laser Schrodinger equation (the HELIUM code, smyth_1998: finite differences in the radial variables, coupled spherical harmonics), infinite nuclear mass, linear polarization; field ramped on over eight periods and held for up to 200 periods; the rate is the steady exponential decay of the population within 20 au of the nucleus (pp. 4-5). 390 nm at 60 intensities, 0.25-34.0e14 W/cm^2 (grid 0.2 au); 780 nm at 24 intensities, 0.33-14.0e14 W/cm^2 (grids 0.2 and 0.29 au). A single-active-electron model tuned to the two-electron results refines and interpolates them (p. 5).
Materials in structured entries: He
Dataset quantities: ionization_rate
Contents: 2 datasets; 4 formulas.
Curation notes#
Pages are pdf pages: pdf page 1 is the IOPscience download cover, so the journal page is 1727 + n (pdf p. 13 is p. 1740). Identity checked against pdf p. 2. UNMAPPED_GLYPHS on pdf pp. 6, 7, 8, 12, 13 and 15 (symbols such as Gamma lost in the text); the formulas below were checked against the page images of pp. 12-13.
WHY ALMOST NOTHING IS TAKEN. The rates are in figures only (Figs. 1-8: He single ionisation at 390 and 780 nm against intensity, and as 1/log^2(rate)); there is no table. The two text values that are rates at a stated intensity are recorded as inline points (use = check, ‘typical’ values amid resonances); the fits are recorded as formulas. The rates count the ionisation of the atom (single ionisation from the 1s1s ground state, both electrons in the calculation).
ACCURACY (p. 5): ‘we believe uncertainty in the 390 nm results to be under 2%, and those of the 780 nm results to be under 4%’; the SAE extrapolation changes the two-electron results by 1-3 % and rarely the 390 nm results by more than 1 %; for smoothed data ‘we believe the uncertainty in this case to be lower than the estimates given above’. Grid: at delta r = 0.1 au the 390 nm rates are within 0.25 % of those at 0.2 au (p. 4); 780 nm corrections from the 0.2/0.29 au comparison are typically below 1 %, rarely above 3 % (p. 4).
VALUES IN THE TEXT (not taken): Ip = 0.903724 au, ‘the helium ionization potential for single-electron ionization’ (p. 6), the value for the infinite nuclear mass the calculation assumes (p. 3) (smyth_1998 quotes the He ground state as -2.9037 au): 24.5916 eV with 27.2114 eV/au, against solprop’s 3.939465e-18 J = 24.5882 eV = 0.9036 au; a model input, no kind stated, so no ionization_energy dataset; omega_390 = 0.11683 au, omega_780 = 0.058415 au; U_p = 0.05336^2 I/(4 omega^2) (I in 1e14 W/cm^2, p. 6); 4.1341e16 converts au to s^-1 (p. 6); the Keldysh parameter is 1 at 2.16e14 W/cm^2 (780 nm) and 8.66e14 W/cm^2 (390 nm) (p. 14); AC-ADK is too small against the 780 nm rates by four orders of magnitude at 0.5e14, two at 0.9e14 and a factor 10 at 1.5e14 W/cm^2 (p. 15).
FORMULAS. Eq. (3) (and (1)), Eq. (4), Eq. (5) and the AC-ADK rate are recorded below. Eq. (2): N(I, omega) = [(K + Ip + U_p(Ibar, omega_390))/omega_390] omega_390/omega = N0(Ibar) R, K = 0 (p. 8).
Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
parker_2007/text_390nm#
{
"id": "text_390nm",
"material": "He",
"table": "text",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"parameters": {
"wavelength_nm": 390,
"polarization": "linear",
"method": "full-dimensional TDSE (HELIUM)"
}
}
1 inline points in the source record.
p. 6: ‘total ionization rates Gamma_390 are calculated to a maximum intensity of I = 34.2 x 10^14 W cm^-2. Despite the extreme intensity, in the I = 30 x 10^14 W cm^-2 limit the decay of the initial (ground) state is to good approximation exponential. At this extreme, a typical value of Gamma_390 is 0.013 au, which implies roughly 50% ionization of the helium atom per field period’. A ‘typical’ value near 30e14 W/cm^2, where the rates fluctuate with resonances; Eq. (5) gives 0.0107 au there (computed 2026-09-26). Intensity as the paper’s I (the laser’s peak intensity is not distinguished from the mean).
parker_2007/text_780nm#
{
"id": "text_780nm",
"material": "He",
"table": "text",
"quantity": "ionization_rate",
"unit": "au",
"abscissa": "intensity",
"abscissa_unit": "W/cm2",
"use": "check",
"parameters": {
"wavelength_nm": 780,
"polarization": "linear",
"method": "full-dimensional TDSE (HELIUM)"
}
}
1 inline points in the source record.
p. 6: ‘At 780 nm ... the total ionization rates Gamma_780 are calculated to a maximum intensity of I = 14.5 x 10^14 W cm^-2. At this intensity, a typical value of Gamma_780 is 0.0013 au, which implies 13% ionization of the atom per field period’. (p. 4 gives the 780 nm range as 0.33-14.0e14 W/cm^2.) Eq. (5) gives 0.00142 au there (computed 2026-09-26).
Formulas#
parker_2007/eq5_intense_field#
{
"id": "eq5_intense_field",
"material": "He",
"equation": "Eq. (5), p. 13",
"printed": "Gamma(Ibar, R) = exp(-R/sqrt(a0 + a1 Ibar + a2 Ibar^2 + a3 Ibar^3)); 390 nm (R = 1): a0 = 0.001 10, a1 = 0.001 630, a2 = 4.43 x 10^-6, a3 = -2.033 x 10^-7; 780 nm (R = 2): a0 = 0.001 14, a1 = 0.001 424, a2 = 4.49 x 10^-6, a3 = -2.960 x 10^-8",
"variable": "R = omega_390/omega (wavelength in units of 390 nm); Ibar = I R^2, I in 1e14 W/cm^2; Gamma in au",
"range": "Least-squares fits to the smoothed 390 nm (to Ibar = 34.2) and 780 nm (I to 14.5e14 W/cm^2) rates; the fits hold down to Ibar = 0.3e14 W/cm^2 (p. 12)",
"coefficients": {
"a0_390": "0.00110",
"a1_390": "0.001630",
"a2_390": "4.43e-6",
"a3_390": "-2.033e-7",
"a0_780": "0.00114",
"a1_780": "0.001424",
"a2_780": "4.49e-6",
"a3_780": "-2.960e-8"
},
"check": "Checked against the page image (p. 13). The data are in figures only; consistent with the two text values: 0.0107 au at 30e14 W/cm^2, 390 nm ('typical' 0.013) and 0.00142 au at 14.5e14 W/cm^2, 780 nm ('typical' 0.0013) (computed 2026-09-26)."
}
‘the fits were designed to pass through the centre of the fluctuating data sets (in a least-squares sense)’ (p. 13), unlike Eqs. (3)-(4), which lie at the base of the non-resonant data; ‘This latter type of fit is expected to be of greater use to experimentalists’ (p. 9). The data are smoothed over 0.4e14 (390 nm) and 0.04e14 W/cm^2 (780 nm) before fitting.
parker_2007/eq3_perturbative#
{
"id": "eq3_perturbative",
"material": "He",
"equation": "Eqs. (1)-(3), pp. 6-8",
"printed": "Gamma(Ibar, R) = [(A/R)(d0^2 Ibar)^(N0(Ibar))]^R, A = 548 000.0, d0(R = 1) = 0.136 57, d0(R = 2) = 0.137 84; N0(Ibar) = (Ip + U_p(Ibar, omega_390))/omega_390, Ip = 0.903 724 au, omega_390 = 0.116 83 au",
"variable": "R = omega_390/omega; Ibar = I R^2, I in 1e14 W/cm^2; U_p = 0.05336^2 Ibar/(4 omega_390^2) au; Gamma in au",
"range": "Non-resonant rates up to about 8e14 W/cm^2 (390 nm) and 9e14 W/cm^2 (780 nm) (pp. 7, 11)",
"coefficients": {
"A": "548000.0",
"d0_390": "0.13657",
"d0_780": "0.13784",
"Ip": "0.903724",
"omega_390": "0.11683"
},
"check": "Not checkable: the data are in figures only. N0(0) = 7.735 at 390 nm (p. 7) is reproduced (0.903724/0.11683 = 7.7354)."
}
‘the parameters A and d0 are best regarded as curve-fit parameters’ (p. 8). Eq. (1) is the R = 1 case.
parker_2007/eq4_perturbative_quadratic#
{
"id": "eq4_perturbative_quadratic",
"material": "He",
"equation": "Eq. (4), p. 9",
"printed": "Gamma(Ibar, R) = [(A/R)(d0^2 (1 - b1 Ibar + b2 Ibar^2) Ibar)^(N0(Ibar))]^R, A = 10 300.0; 390 nm (R = 1): d0 = 0.1751, b1 = 0.019 25, b2 = 0.000 1625; 780 nm (R = 2): d0 = 0.1767, b1 = 0.019 25, b2 = 0.000 1655",
"variable": "as for eq3_perturbative",
"range": "390 nm up to Ibar = 34.2e14 W/cm^2; fails at 780 nm above I = 9e14 W/cm^2 (Ibar = 36e14) (p. 10)",
"coefficients": {
"A": "10300.0",
"d0_390": "0.1751",
"b1_390": "0.01925",
"b2_390": "0.0001625",
"d0_780": "0.1767",
"b1_780": "0.01925",
"b2_780": "0.0001655"
},
"check": "Not checkable: the data are in figures only."
}
A curve fit to the base of the non-resonant data (p. 9).
parker_2007/ac_adk#
{
"id": "ac_adk",
"material": "He",
"equation": "text, p. 12",
"printed": "Gamma(I) = 5.053 (0.053 36^2 I)^0.006 18 exp(-1/sqrt(0.001 085 I))",
"variable": "I in 1e14 W/cm^2; Gamma in au",
"range": "not stated",
"coefficients": {
"prefactor": "5.053",
"field_au_per_sqrtI": "0.05336",
"exponent": "0.00618",
"c": "0.001085"
},
"check": "Reproduced (computed 2026-09-26): the cycle-averaged static ADK rate C^2 Ip (2 kappa^3/E)^(2n*-1) exp(-2 kappa^3/(3E)) sqrt(3E/(pi kappa^3)) with Ip = 0.903724 au (kappa = 1.34445, n* = 0.74382), l = m = 0 and the Stirling form C^2 = (2e/n*)^(2n*)/(2 pi n*) = 4.1253 gives the prefactor 5.0525; the field power E^(3/2 - 2n*) = (E^2)^0.00618 with E = 0.05336 sqrt(I) au; and 2 kappa^3/(3 x 0.05336) = 30.359 = 1/sqrt(0.001085). With the Gamma-function C^2 = 3.3300 the prefactor would be 4.078."
}
‘The cycle-averaged ADK ionization rate (AC-ADK) for a ground state one-electron atom with ionization potential 0.903724 au ... The cycle-averaged ADK ionization rate of a two-electron atom is twice that of the one-electron atom’ (p. 12): the formula is per electron; the paper’s He comparison (Fig. 6) doubles it. parker_2009 uses ‘the ADK formula ... discussed in [1]’ (this paper) for its static ADK column.
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.