saenz_2002#

A. Saenz, “Behavior of molecular hydrogen exposed to strong dc, ac, or low-frequency laser fields. II. Comparison of ab initio and Ammosov-Delone-Krainov rates”, Phys. Rev. A 66, 063408 (2002)

Source record · Catalogue · Review register

DOI: 10.1103/physreva.66.063408

Source kind: theory

Recorded technique: Static (dc) field ionisation rates of H2 oriented parallel to the field from a three-dimensional, fully correlated ab initio method (paper I of the series): nonrelativistic Born-Oppenheimer, explicitly correlated basis in prolate spheroidal coordinates, energies and widths by complex scaling at each internuclear distance R; the rotationless nuclear Hamiltonian solved in a B-spline basis. Vibrational motion enters through limits: frozen nuclei (the R-dependent width averaged over the field-free vibrational wave function), fully adiabatic (vibrational states of the complex in-field potential curve), fixed nuclei (R = 1.40 a0). Compared with the ADK rate (Eq. (1) of Walsh et al. 1993, walsh_1993) and Krainov’s modified ADK (MADK, Eqs. (1)-(2)) (pp. 1-2).

Materials in structured entries: H2

Dataset quantities: ionization_rate

Contents: 24 datasets; 1 formula.

Curation notes#

The citation first requested was Phys. Rev. A 66, 063407; the paper and its DOI are Phys. Rev. A 66, 063408 (2002), part II of a series; part I, the ‘preceding paper’ that describes the method, is not in the reference list and not in the library. Pages are pdf pages (1-9 = 063408-1 to -9).

WHAT IS TAKEN. Table I (p. 7), ‘Ionization rates (in a.u.) of different vibrational states v of H2 exposed to an electric field’, F = 0.05338, 0.06, 0.08, 0.10, 0.12 and 0.18 au (0.05338 au is 1.0e14 W/cm^2), v = 0, 1, 2, 4, 9, 14; four rows per entry, one dataset per row type and v (24 datasets): (a) ‘the result obtained in the frozen-nuclei limit using the ab initio ionization rates’; (b) ‘the corresponding results obtained with the ADK model’ (frozen-nuclei average of the ADK rate with the R-dependent ionisation potential I_P(R) = E_0,H2+(R) - E_0,H2(R), pp. 2-3, 6); (c) ‘the fully adiabatic limit, using the complex ab initio energies’; (d) ‘the ADK model with the corresponding R-independent ionization potential’, ‘the (field-free) energy difference between the corresponding vibrational state of H2 and the rovibrational ground-state energy of H2+’ (p. 6). ‘Values in brackets indicate the power of 10’. Blank (c) cells: no bound vibrational state in that limit (‘No data point is given for F = 0.18 a.u. in the fully adiabatic limit, because for that field the adiabatic potential curve does not support any bound vibrational states anymore’, p. 6). Image checked; no erratum, no structural fix beyond the spanned field cell.

ORIENTATION AND WHAT THE RATE COUNTS. The molecule is oriented parallel to the field (angle_deg = 0, p. 1); the paper argues for, but did not compute, a nearly isotropic rate (Sect. VII, pp. 7-8). The rate is the width of the two-electron state of the molecule (the whole molecule, both electrons), in au, rotationless (J = 0); rotational excitation would raise the frozen-nuclei rates (p. 8). The ADK rows use the one-electron ADK formula of Walsh et al. (walsh_1993 Eq. (1), the Ilkov-modified form, ilkov_1992 Eq. (7); l is not stated); no occupancy factor is mentioned. For review: majety_2015 Table 2’s benchmark [18] (Saenz 2000, fixed nuclei at R = 1.4 a0; saenz_2000 prints it in no table, its rates being in figures only) is 3.36e-5 au at F = 0.06, against 5.248e-5 here for v = 0 frozen nuclei: the vibrational average raises the rate by 56 % at 0.06 au (the fixed-nuclei rates are in Fig. 4 only).

USE. (a) v = 0 is primary (the frozen-nuclei limit is the one for a laser whose field peaks quickly compared with nuclear motion: ‘the with respect to ionization rates equivalent non-moving-nuclei limit is, e.g., valid in the case of a linearly polarized low-frequency laser field’, p. 4); (c) and the excited states v > 0 are check; (b) and (d) are formula evaluations (use = check). ACCURACY: no number is stated. ‘the ab initio calculation has problems to accurately predict the small ionization rates, due to the numerical difficulties discussed in the preceding paper. The small wiggles seen on the calculated curves give an indication of the numerical precision’ (p. 3, about the R-dependent rates of Figs. 1-2). Uncertainty left unstated.

FORMULA. MADK, Eqs. (1)-(2) (p. 2), recorded below; the ADK rows use Walsh et al.’s formula (walsh_1993 record). Text values (not taken, not H2 in a molecular state): ‘The ab initio ionization rate of a hydrogen atom at F = 0.08 a.u. is about 1.85 x 10^14 s^-1 (using the width given in Ref. [25])’ (Scrinzi 2000), two H atoms 3.7e14 s^-1, H2 at large R about 3.5e14 s^-1, ADK about 6e14 s^-1 (p. 3). The tunnel-to-barrier-suppression field F_BSI = I_P^2/4 (p. 4): 0.0625 au for hydrogenic Ip, 0.0775 au for I_P(R = 1.80 a0) = 0.556 au (p. 3). ‘Using the experimental ionization potential (15.4 eV) in the MADK calculation leads to much higher ionization rates’ (p. 4); Figs. 1-5 (R-dependent rates at F = 0.06 and 0.08 au; He and H2 against F/F_BSI; fixed- against frozen-nuclei; fully adiabatic) are figures only. The one-centre expansion of the H2 ground state at equilibrium has ‘more than 88%’ l = 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#

saenz_2002/tableI_a_v0#

{
  "id": "tableI_a_v0",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_a_v0.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "primary",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 0,
    "method": "ab initio, frozen nuclei"
  }
}

Table I (p. 7), row (a) frozen-nuclei limit, ab initio: the R-dependent ab initio width averaged over the field-free vibrational wave function of v; H2 in vibrational state v = 0, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_a_v1#

{
  "id": "tableI_a_v1",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_a_v1.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 1,
    "method": "ab initio, frozen nuclei"
  }
}

Table I (p. 7), row (a) frozen-nuclei limit, ab initio: the R-dependent ab initio width averaged over the field-free vibrational wave function of v; H2 in vibrational state v = 1, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_a_v2#

{
  "id": "tableI_a_v2",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_a_v2.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 2,
    "method": "ab initio, frozen nuclei"
  }
}

Table I (p. 7), row (a) frozen-nuclei limit, ab initio: the R-dependent ab initio width averaged over the field-free vibrational wave function of v; H2 in vibrational state v = 2, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_a_v4#

{
  "id": "tableI_a_v4",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_a_v4.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 4,
    "method": "ab initio, frozen nuclei"
  }
}

Table I (p. 7), row (a) frozen-nuclei limit, ab initio: the R-dependent ab initio width averaged over the field-free vibrational wave function of v; H2 in vibrational state v = 4, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_a_v9#

{
  "id": "tableI_a_v9",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_a_v9.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 9,
    "method": "ab initio, frozen nuclei"
  }
}

Table I (p. 7), row (a) frozen-nuclei limit, ab initio: the R-dependent ab initio width averaged over the field-free vibrational wave function of v; H2 in vibrational state v = 9, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_a_v14#

{
  "id": "tableI_a_v14",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_a_v14.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 14,
    "method": "ab initio, frozen nuclei"
  }
}

Table I (p. 7), row (a) frozen-nuclei limit, ab initio: the R-dependent ab initio width averaged over the field-free vibrational wave function of v; H2 in vibrational state v = 14, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_b_v0#

{
  "id": "tableI_b_v0",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_b_v0.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 0,
    "method": "ADK, frozen nuclei (R-dependent Ip)"
  }
}

Table I (p. 7), row (b) frozen-nuclei limit, ADK: the ADK rate with the R-dependent ionisation potential, averaged in the same way; a formula evaluation; H2 in vibrational state v = 0, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_b_v1#

{
  "id": "tableI_b_v1",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_b_v1.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 1,
    "method": "ADK, frozen nuclei (R-dependent Ip)"
  }
}

Table I (p. 7), row (b) frozen-nuclei limit, ADK: the ADK rate with the R-dependent ionisation potential, averaged in the same way; a formula evaluation; H2 in vibrational state v = 1, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_b_v2#

{
  "id": "tableI_b_v2",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_b_v2.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 2,
    "method": "ADK, frozen nuclei (R-dependent Ip)"
  }
}

Table I (p. 7), row (b) frozen-nuclei limit, ADK: the ADK rate with the R-dependent ionisation potential, averaged in the same way; a formula evaluation; H2 in vibrational state v = 2, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_b_v4#

{
  "id": "tableI_b_v4",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_b_v4.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 4,
    "method": "ADK, frozen nuclei (R-dependent Ip)"
  }
}

Table I (p. 7), row (b) frozen-nuclei limit, ADK: the ADK rate with the R-dependent ionisation potential, averaged in the same way; a formula evaluation; H2 in vibrational state v = 4, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_b_v9#

{
  "id": "tableI_b_v9",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_b_v9.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 9,
    "method": "ADK, frozen nuclei (R-dependent Ip)"
  }
}

Table I (p. 7), row (b) frozen-nuclei limit, ADK: the ADK rate with the R-dependent ionisation potential, averaged in the same way; a formula evaluation; H2 in vibrational state v = 9, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_b_v14#

{
  "id": "tableI_b_v14",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_b_v14.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 14,
    "method": "ADK, frozen nuclei (R-dependent Ip)"
  }
}

Table I (p. 7), row (b) frozen-nuclei limit, ADK: the ADK rate with the R-dependent ionisation potential, averaged in the same way; a formula evaluation; H2 in vibrational state v = 14, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_c_v0#

{
  "id": "tableI_c_v0",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_c_v0.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 0,
    "method": "ab initio, fully adiabatic"
  }
}

saenz_2002/tableI_c_v1#

{
  "id": "tableI_c_v1",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_c_v1.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 1,
    "method": "ab initio, fully adiabatic"
  }
}

saenz_2002/tableI_c_v2#

{
  "id": "tableI_c_v2",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_c_v2.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 2,
    "method": "ab initio, fully adiabatic"
  }
}

saenz_2002/tableI_c_v4#

{
  "id": "tableI_c_v4",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_c_v4.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 4,
    "method": "ab initio, fully adiabatic"
  }
}

saenz_2002/tableI_c_v9#

{
  "id": "tableI_c_v9",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_c_v9.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 9,
    "method": "ab initio, fully adiabatic"
  }
}

saenz_2002/tableI_c_v14#

{
  "id": "tableI_c_v14",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_c_v14.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 14,
    "method": "ab initio, fully adiabatic"
  }
}

Table I (p. 7), row (c) fully adiabatic limit, ab initio: the width of the vibrational state v of the complex in-field potential curve; only states that remain bound; H2 in vibrational state v = 14, parallel to the field, rate of the molecule in au against F in au. At F = 0.05338 au the frozen-nuclei rate (a) exceeds this one because the in-field curve supports more bound states (up to v = 16) than the field-free one (p. 6).

saenz_2002/tableI_d_v0#

{
  "id": "tableI_d_v0",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_d_v0.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 0,
    "method": "ADK, R-independent Ip"
  }
}

Table I (p. 7), row (d) ADK with the R-independent ionisation potential of v (field-free energy of v minus the H2+ rovibrational ground state); a formula evaluation; H2 in vibrational state v = 0, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_d_v1#

{
  "id": "tableI_d_v1",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_d_v1.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 1,
    "method": "ADK, R-independent Ip"
  }
}

Table I (p. 7), row (d) ADK with the R-independent ionisation potential of v (field-free energy of v minus the H2+ rovibrational ground state); a formula evaluation; H2 in vibrational state v = 1, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_d_v2#

{
  "id": "tableI_d_v2",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_d_v2.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 2,
    "method": "ADK, R-independent Ip"
  }
}

Table I (p. 7), row (d) ADK with the R-independent ionisation potential of v (field-free energy of v minus the H2+ rovibrational ground state); a formula evaluation; H2 in vibrational state v = 2, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_d_v4#

{
  "id": "tableI_d_v4",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_d_v4.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 4,
    "method": "ADK, R-independent Ip"
  }
}

Table I (p. 7), row (d) ADK with the R-independent ionisation potential of v (field-free energy of v minus the H2+ rovibrational ground state); a formula evaluation; H2 in vibrational state v = 4, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_d_v9#

{
  "id": "tableI_d_v9",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_d_v9.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 9,
    "method": "ADK, R-independent Ip"
  }
}

Table I (p. 7), row (d) ADK with the R-independent ionisation potential of v (field-free energy of v minus the H2+ rovibrational ground state); a formula evaluation; H2 in vibrational state v = 9, parallel to the field, rate of the molecule in au against F in au.

saenz_2002/tableI_d_v14#

{
  "id": "tableI_d_v14",
  "material": "H2",
  "file": "H2/saenz_2002__tableI_d_v14.csv",
  "table": "tbl_b2f3d07790b3",
  "quantity": "ionization_rate",
  "unit": "au",
  "abscissa": "field",
  "abscissa_unit": "au",
  "use": "check",
  "parameters": {
    "wavelength_nm": Infinity,
    "polarization": "static",
    "angle_deg": 0,
    "vibrational_state_v": 14,
    "method": "ADK, R-independent Ip"
  }
}

Table I (p. 7), row (d) ADK with the R-independent ionisation potential of v (field-free energy of v minus the H2+ rovibrational ground state); a formula evaluation; H2 in vibrational state v = 14, parallel to the field, rate of the molecule in au against F in au.

Formulas#

saenz_2002/madk#

{
  "id": "madk",
  "material": "H2",
  "equation": "Eqs. (1)-(2), p. 2",
  "printed": "Gamma^MADK = Z (2F)^(1/3) D^2 / (2 (n*)^2) {[Ai'(k)]^2 - k Ai^2(k)}, D = (4 e Z^3/(F (n*)^4))^(n*), k = (Z/n*)^2 (2F)^(-2/3), n* = Z/sqrt(2 I_p)",
  "variable": "F: static field (au); Z: the charge seen by the escaping electron; I_p: ionisation potential (au); Ai, Ai': the Airy function and its derivative; Gamma in au",
  "range": "not stated; meant to cover the barrier-suppression regime",
  "coefficients": {},
  "reproduced_from": [
    "V. P. Krainov, J. Opt. Soc. Am. B 14, 425 (1997)"
  ],
  "check": "Not checkable: the MADK rates are in figures only (Figs. 3-5)."
}

Krainov’s modified ADK [4]. ‘Note the error in Eq. (15) in Ref. [4] where instead of the derivative of the Airy function the Airy function occurs twice’ (p. 2): the form here is Saenz’s correction of Krainov’s printed formula. ‘In Eq. (1) the original main quantum number n has been substituted by an effective value n* = Z/sqrt(2 I_p)’ (p. 2).

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.