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 `__ · :doc:`Catalogue ` · :doc:`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 ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 :doc:`review register ` for the checks and decisions.