sato_2016

T. Sato, K. L. Ishikawa, I. Brezinova, F. Lackner, S. Nagele and J. Burgdorfer, “Time-dependent complete-active-space self-consistent-field method for atoms: Application to high-order harmonic generation”, Phys. Rev. A 94, 023405 (2016)

Source record · Catalogue · Review register

DOI: 10.1103/PhysRevA.94.023405

Source kind: theory

Recorded technique: Time-dependent complete-active-space self-consistent-field (TD-CASSCF) method (Sec. II-III): the wave function a configuration-interaction expansion in Slater determinants of time-dependent orbitals, split into frozen-core, dynamical-core and active orbitals, (n_fc, n_dc, n_a); for helium, (0,0,n) is the multiconfiguration time-dependent Hartree-Fock (MCTDHF) method with both electrons active, (0,0,1) is TDHF. Orbitals on a spherical finite-element discrete-variable-representation (FEDVR) radial grid times spherical harmonics, L_max = L_ee; nonrelativistic, dipole approximation; the initial state the ground state by imaginary-time propagation (p. 023405-4). A split-operator propagator (Sec. III B): the stiff one-electron part by an implicit method (Eqs. 26), the nonlinear part and the CI coefficients by fourth-order Runge-Kutta. He at 800 nm (Sec. IV A, pp. 023405-5 to -7): velocity gauge, d_FE = 2, L_max = L_ee = 71, 20 000 steps per cycle, (0,0,14), ‘converged, up to the cutoff frequencies, in radial resolution (d_FE = 2), angular resolution (L_max = L_ee = 71) temporal resolution (20 000 steps per cycle), and number of orbitals (n = 14)’ (p. 023405-5, of the HHG spectra of Fig. 5; Fig. 6 uses ‘the same computational condition’). The radial box and absorber of the 800 nm runs are not restated: at 400 nm, R_max = 320 with orbitals masked beyond 256 by a cos^1/4 function (p. 023405-5). At 400 nm, 4e14 W/cm2, 12 cycles, the (0,0,14) survival probability is ‘indistinguishable’ from the full two-electron TDSE of the Vienna code (Fig. 2(b), p. 023405-5); at 800 nm the TDSE ‘is still difficult’ to converge and no TDSE is shown.

Materials in structured entries: He

Dataset quantities: ionization_yield

Contents: 1 dataset; 0 formulas.

Curation notes

Journal pp. 023405-1 to -14 = PDF pages 1 to 14 (the journal’s page n is PDF page n). Identity checked on the first page (PDF p. 1: ‘PHYSICAL REVIEW A 94, 023405 (2016)’, Takeshi Sato, Kenichi L. Ishikawa, Iva Brezinova, Fabian Lackner, Stefan Nagele and Joachim Burgdorfer; received 2 May 2016, published 9 August 2016) on 2026-10-06.

THE PULSE (Eq. 27, p. 023405-4): ‘E(t) = E0 sin(omega0 t) sin^2(pi t/tau), 0 <= t <= tau, with total duration tau, peak intensity I0 = E0^2, wavelength lambda = 2 pi/omega0, and period T = 2 pi/omega0’. The envelope is on the electric field; the carrier a sine from the pulse’s start, so the field is zero at the envelope’s peak (t = tau/2); the intensity is that of the envelope’s amplitude E0 in atomic units (E0^2 times 3.50945e16 W/cm2), the largest |E(t)| being 0.983 E0 for six cycles (computed). Velocity gauge, A(t) = -integral of E(t) dt (Eq. 6b); with Eq. 27, A(tau) = 0. The 800 nm runs: ‘(lambda = 800 nm, I0 = 8 x 10^14 W/cm2, and tau = 6T)’ (p. 023405-5, for Figs. 3 and 4); Fig. 5 (4, 8 and 14 x 10^14 W/cm2) and Fig. 6 (‘the same computational condition as for Fig. 5, a wavelength of 800 nm’) do not restate tau: their time axes end at 6 optical cycles, and Fig. 4(c), the 8 x 10^14 W/cm2 survival against time in atomic units, ends at 661.9 au = 6T (read). tau = 6T = 16.01 fs at 800 nm (T = 2.6685 fs); the intensity envelope, sin^4, is 0.364 tau = 5.83 fs wide at half maximum (computed).

THE MEASURE (p. 023405-5): ‘the probability of finding both two electrons inside a sphere of radius R0 = 20 a.u. (referred to as survival probability hereafter) measuring the temporal evolution of the complement to ionization or formation of Rydberg states’. Its complement, 1 - S, is the probability that at least one electron is beyond 20 au: single and double ionisation together, and bound (Rydberg) population beyond 20 au; electrons ionised but still inside 20 au at t = 6T count as surviving. The paper does not separate single from double ionisation for helium.

EXTRACTED (tools/extract/sato_2016.py). The paper prints no number of these probabilities and has no supplement: they are given only in Fig. 6 (p. 023405-7), a vector drawing, read from the PDF by data rule 8 (TC-699): the (0,0,14) curve’s last vertex, at t = 6T (the 6-cycle tick, the pulse’s end), in each of the three panels. The data file holds 1 - S; the survival S as read is in each row’s printed cell. Axes calibrated from the drawing’s own ticks, labelled by the text objects at them: x 0 to 6 cycles (worst tick residual 0.016 pt), y 0.9996 to 1.0000, 0.980 to 1.000 and 0.80 to 1.00 (worst 0.0007 pt), each on 90.4 pt; the drawing’s coordinates step by 0.055 pt. Read: S = 0.9996971 (4e14 W/cm2), 0.9841076 (8e14), 0.8392404 (1.4e15); 1 - S = 3.029e-4, 0.01589, 0.1608.

DIGITISING UNCERTAINTY: 0.06 pt on the y axis (one quantum: half a quantum plus the worst tick residual, and the last vertices stepping one quantum up and down on the flat end): 2.7e-7, 1.3e-5 and 1.3e-4 in S, absolute, at 4e14, 8e14 and 1.4e15 W/cm2, the same on 1 - S (the sigma column), 0.088, 0.084 and 0.083 % of it: the axes’ spans scale with 1 - S. The paper states no uncertainty of the calculation; its convergence statements are quoted in the technique.

THE CHECKS (the script fails if one is missed). (1) Fig. 4(c) (p. 023405-6), the same calculation at 8e14 W/cm2 with L_max = 59, ends at S = 0.9841062, 1.4e-6 below Fig. 6(b) (0.009 % of 1 - S), at 661.93 au (6T = 661.92 au). (2) The caption’s multipliers, verbatim: ‘For the survival probabilities to match those of TD-CASSCF the ADK rates must be scaled by 2.55, 1.35, and 0.96 for the three intensities in ascending order. The analogous factors for the PPT rates are 1.24, 1.27, and 1.24. The ADK and PPT probabilities are shifted in time to take into account the time required for an ejected electron to propagate classically to R0 = 20 a.u.’ Read as ln S(TD-CASSCF) / ln S(model) at 6T from the drawn ADK and PPT curves: ADK 2.546, 1.353, 0.955; PPT 1.236, 1.267, 1.260 (within 0.5 %, and PPT at 1.4e15 1.6 %): the drawn curves are the unscaled models, with S = exp(-integral of the rate). The overlay of the read vertices on the rendered page matches the curves’ ends (inspected 2026-10-06).

ADK AND PPT, NOT TAKEN: the curves are the authors’ evaluation of Ammosov, Delone and Krainov, Sov. Phys. JETP 64, 1191 (1986) [53] and Perelomov, Popov and Terent’ev, Sov. Phys. JETP 23, 924 (1966) [54], ‘calculated by integrating over the temporal profile of the laser electric field’ (p. 023405-5). The paper gives no formula, no ionisation energy, no asymptotic coefficient, no orbital quantum numbers and no number of electrons (one, or two equivalent 1s electrons) for either model (checked in the text, captions and appendices, 2026-10-06), so the multipliers cannot be reinterpreted between those conventions. The text: ‘The ADK model fails to reproduce the intensity dependence of the survival probability, underestimating the ionization probability at moderate intensity while approaching the TD-CASSCF result at high intensity. The PPT model, on the other hand, consistently underestimates the ionization by a nearly constant factor independent of the intensity’ (pp. 023405-5, -6).

ALSO NOT TAKEN: Fig. 2(b) (He, 400 nm, 4e14 W/cm2, 12 cycles: (0,0,n) and the TDSE), Fig. 4(c) (He, 800 nm, 8e14, n = 1 to 14 at L_max = 59; read only for the check), and Fig. 9(b) (Be, 800 nm, 3e14 W/cm2, 3 cycles, the probability of all electrons inside 20 au; TDHF and TD-CASSCF): no one-electron run is matched to them. The HHG spectra (Figs. 2-5, 9, 10) and the dipole moments of Be (Figs. 7, 8) are not quantities of the vocabulary.

Recorded bibliographic identity status: VALIDATED. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets

sato_2016/fig6_casscf_He_800nm

{
  "id": "fig6_casscf_He_800nm",
  "material": "He",
  "file": "He/sato_2016__fig6_casscf_He_800nm.csv",
  "table": "fig_13d7c9bcd599",
  "digitised": "vector",
  "quantity": "ionization_yield",
  "unit": "1",
  "abscissa": "intensity",
  "abscissa_unit": "W/cm2",
  "use": "check",
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "wavelength_nm": 800,
    "pulse_fs": 16.01,
    "pulse_fs_definition": "total (foot-to-foot) duration tau = 6T of Eq. 27's sin^2 envelope of the field, T = 2.6685 fs; the intensity envelope (sin^4) is 5.83 fs wide at half maximum (computed); tau = 6T as the text states for 800 nm, 8e14 W/cm2 (p. 023405-5), Fig. 6's time axis (0 to 6 cycles) and Fig. 4(c)'s curve ending at 6T",
    "pulse_cycles": 6,
    "polarization": "linear",
    "pulse_envelope": "sin^2 on the electric field: E(t) = E0 sin(omega0 t) sin^2(pi t/tau), 0 <= t <= tau (Eq. 27)",
    "cep": "sine",
    "cep_definition": "E(t) = E0 sin(omega0 t) sin^2(pi t/tau) (Eq. 27): a sine carrier from the pulse's start, the field zero at the envelope's peak (t = tau/2 = 3T)",
    "intensity_definition": "I0 = E0^2 in atomic units (Eq. 27's text; 3.50945e16 W/cm2 per au^2): the envelope's amplitude, the largest |E(t)| being 0.983 E0 (computed)",
    "gauge": "velocity",
    "measure": "1 - the survival probability of both electrons inside R0 = 20 a.u., at t = 6T",
    "method": "TD-CASSCF (0,0,14) = MCTDHF: both electrons active in 14 time-dependent orbitals, no core; spherical FEDVR, d_FE = 2, L_max = L_ee = 71, 20 000 steps per cycle, velocity gauge (pp. 023405-5 to -7); box and absorber at 800 nm not restated",
    "electrons": "two, both active (all electrons; no frozen or dynamical core)"
  }
}

Fig. 6 (p. 023405-7), the TD-CASSCF (0,0,14) curves (black, thick): 1 - S, S the survival probability of both electrons inside R0 = 20 au, at t = 6T, the end of the six-cycle sin^2 pulse (Eq. 27), against the peak intensity I0 = E0^2, 4, 8 and 14e14 W/cm2; for He, (0,0,14) is MCTDHF with both electrons active, equal to the full two-electron TDSE where that converges (400 nm, Fig. 2(b)). The values are 1 - S; the survival read (0.9996971, 0.9841076, 0.8392404) is in the printed cells. Read from the vector drawing, the curves’ last vertices (the record’s notes). sigma: the digitising uncertainty, absolute, 0.06 pt on each panel’s y axis (2.7e-7, 1.3e-5, 1.3e-4; 0.08 to 0.09 % of 1 - S); the calculation’s own is not stated. Fig. 4(c), the same at L_max = 59, agrees at 8e14 within 1.4e-6 in S. Not the ADK or PPT curves (the record’s notes).

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.