zhao_2014

S.-F. Zhao, L. Liu and X.-X. Zhou, “Multiphoton and tunneling ionization probability of atoms and molecules in an intense laser field”, Opt. Commun. 313, 74 (2014); corrigendum Opt. Commun. 355, 615 (2015)

Source record · Catalogue · Review register

DOI: 10.1016/j.optcom.2013.09.074

Source kind: theory

Recorded technique: Ionisation probabilities of atoms from the authors’ time-dependent Schroedinger equation with one active electron (H, He, Ne, Ar, Kr, Xe; model potentials, Eq. (3)) against the rates of Perelomov, Popov & Terent’ev and of Ammosov, Delone & Krainov; and of molecules (H2, NO, Cl2, N2, O2) from a molecular PPT rate (after benis_2004) and the molecular tunnelling rate of Tong, Zhao & Lin, against others’ calculations and measurements. 266 to 1200 nm; 15 to 30 fs; 1e13 to 1e15 W/cm^2.

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 2 formulas.

Curation notes

Pages are journal pages 74-79; the corrigendum (one page, Opt. Commun. 355, 615 (2015), doi 10.1016/j.optcom.2015.09.005) is bound in the library’s file as its last pages. Identity checked on the first page of each. There are no tables, and every comparison is of probabilities or signals normalised to 1 at saturation, to the calculation at one intensity, or to the measurement at its highest intensity (pp. 3-4): they test the dependence on intensity, not the magnitude. No dataset is taken.

THE ATOMIC AND THE MOLECULAR RATE OF THE PAPER DIFFER IN THEIR COULOMB FACTOR. Eq. (8) (atoms) has (2F_0/F)^(2n* - |m| - 1) (1 + gamma^2)^(|m|/2 + 3/4): Perelomov & Popov’s static Coulomb factor. Eq. (13) (molecules), as corrected, has (2 kappa^3/(F sqrt(1 + gamma^2)))^(2Z_c/kappa - |m| - 1). For one partial wave the second is the first times (1 + gamma^2)^(-n* - 1/4). The paper does not remark on it.

WHAT IS NOT IN THE FORMULAS. A_m ‘can be found in Refs. [21,24,25]’; no structure coefficients are given; the molecule is aligned (‘We assume that the molecular axis is aligned along the external field direction’, p. 2) though the measurements compared with are of unaligned gases; no sum over m, no count of electrons, no factor of the cycle average (the rates are called static and used at |F(t)|, Eq. (16)); no correction at finite field.

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

Datasets

No datasets are recorded.

Formulas

zhao_2014/eq8_ppt

{
  "id": "eq8_ppt",
  "equation": "Eqs. (8)-(11), p. 75",
  "printed": "w_PPT(F, omega) = |C_n*l*|^2 f(l, m) E_0 (2F_0/F)^(2n* - |m| - 1) (1 + gamma^2)^(|m|/2 + 3/4) A_m(omega, gamma) exp(-(2F_0/3F) g(gamma)); |C_n*l*|^2 = 2^(2n*)/(n* Gamma(n* + l* + 1) Gamma(n* - l*)); f(l, m) = (2l + 1)(l + |m|)!/(2^|m| |m|! (l - |m|)!); g(gamma) = (3/2 gamma)[(1 + 1/(2 gamma^2)) sinh^-1 gamma - sqrt(1 + gamma^2)/(2 gamma)]",
  "variable": "Atomic units. E_0: the ionisation energy; F_0 = (2E_0)^(3/2); n* = Z_c (2E_0)^(-1/2); l* = n* - 1; gamma = omega sqrt(2 E_0)/F",
  "range": "Any gamma",
  "coefficients": {},
  "reproduced_from": [
    "A. M. Perelomov, V. S. Popov and M. V. Terent'ev, Sov. Phys. JETP 23, 924 (1966)"
  ],
  "check": "Checked against the page image (p. 75), 2026-09-28. It is the rate of larochelle_1998's eq. (10) without the factor (3F/pi F_0)^(1/2) of the cycle average: optmat's short-range rate times the static Coulomb factor, divided by that factor."
}

Called ‘the ionization rate in a static field’ and used at the instantaneous |F(t)| in Eq. (16).

zhao_2014/eq13_mo_ppt

{
  "id": "eq13_mo_ppt",
  "equation": "Eq. (13), p. 76, and the corrigendum",
  "printed": "w_MO-PPT(F, omega, 0) = [B^2(m)/(2^|m| |m|!)] [A_m(omega, gamma)/kappa^(2Z_c/kappa - 1)] (2 kappa^3/(F (1 + gamma^2)))^(2Z_c/kappa - |m| - 1) e^(-(2 kappa^3/3F) g(gamma)); B(m) = sum_l C_l Q(l, m) (14); Q(l, m) = (-1)^((m + |m|)/2) sqrt((2l + 1)(l + |m|)!/(2 (l - |m|)!)) (15)",
  "variable": "As Eq. (8); kappa = sqrt(2 I_p); C_l: the structure coefficients of a linear molecule with its axis along the field",
  "range": "Not stated",
  "coefficients": {
    "coulomb_bracket": "2 kappa^3/(F (1 + gamma^2))"
  },
  "reproduced_from": [
    "benis_2004"
  ],
  "check": "Checked against the page image (p. 76) and the image of the corrigendum, 2026-09-28.",
  "corrections": [
    {
      "term": "coulomb_bracket",
      "printed": "2 kappa^3/(F (1 + gamma^2))",
      "corrected": "2 kappa^3/(F sqrt(1 + gamma^2))",
      "reason": "The authors' corrigendum: 'There is a printing error in Eq. (13), the corrected formula for calculating the static ionization rate with the MO-PPT model should be as follows', with the square root.",
      "evidence": "Opt. Commun. 355, 615 (2015), read on its page image; benis_2004's eq. (2), which the paper follows, has the square root."
    }
  ]
}

‘Based on the MO-PPT model [41]’ (p. 76; [41] is benis_2004). As corrected it is benis_2004’s eq. (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.