perelomov_1967

A. M. Perelomov and V. S. Popov, “Ionization of atoms in an alternating electrical field. III”, Sov. Phys. JETP 25, 336 (1967) [J. Exptl. Theoret. Phys. (U.S.S.R.) 52, 514 (1967)]

Source record · Catalogue · Review register

No DOI is recorded.

Source kind: theory

Recorded technique: The quasiclassical (‘imaginary time’) method for the penetration of a time-varying barrier: the Coulomb interaction between the electron and the atomic remainder is taken as a perturbation of the action along the sub-barrier trajectory of the short-range problem (Sect. 4, pp. 340-341).

Materials in structured entries: None recorded.

Dataset quantities: None recorded.

Contents: 0 datasets; 2 formulas.

Curation notes

Pages are journal pages (pdf page 1 is p. 336). Identity checked on the first page (title, authors, volume 25, number 2, August 1967); the library’s automatic check of the identity is ‘review’, the paper having no DOI. This is the third paper of the series; the first is Perelomov, Popov & Terent’ev (Sov. Phys. JETP 23, 924 (1966)), whose eq. (54) is the short-range rate, and the second (Sov. Phys. JETP 24, 207 (1967)) is in the library as Perelomov_1967_IonizationAtomsAlternating.

No tables and no data: the record holds the formulas on which optmat’s Coulomb factor rests (TC-670). Everything was read on the page images (pp. 340-342).

THE FACTOR (1 + gamma^2)^(-n*) IS NOT IN THIS PAPER. Ilkov et al. (ilkov_1992, eq. 8) and Bergé et al. (2007, eq. B14) cite this paper for a Coulomb factor that they write (2F_0/(F sqrt(1 + gamma^2)))^(2n*). Here the factor is (2F_0/F)^(2 lambda) for linear polarisation at any gamma within the range of validity (eq. 42, and C(gamma, 0) = 1 in eq. 45).

VALIDITY. The abstract: formulas ‘for the Coulomb correction in the case of not too high frequencies (gamma << gamma_c, where gamma_c is defined in (51))’. The condition is made exact in perelomov_1968.

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

Datasets

No datasets are recorded.

Formulas

perelomov_1967/eq42_coulomb

{
  "id": "eq42_coulomb",
  "equation": "Eq. (42), p. 341",
  "printed": "delta S(t_0, 0) = -i lambda ln(2F_0/F); exp{-2 Im delta S} = (2F_0/F)^(2 lambda)",
  "variable": "Atomic units. F: amplitude of the linearly polarised field; F_0 = kappa^3, kappa^2/2 the binding energy; lambda = kappa_c/kappa = Z/kappa, the Coulomb parameter (optmat's n*)",
  "range": "Linear polarisation; gamma << gamma_c (the abstract), made exact in perelomov_1968",
  "coefficients": {},
  "check": "Checked against the page image (p. 341), 2026-09-28."
}

‘The dependence of delta S on the frequency has dropped out, i.e., the Coulomb correction in the ionization probability w(F, omega) has the same form as for a static field (see (31))’ (p. 341). optmat’s static Coulomb factor (coulomb = ‘static’).

perelomov_1967/eq45_coulomb_elliptic

{
  "id": "eq45_coulomb_elliptic",
  "equation": "Eqs. (45)-(48), p. 341",
  "printed": "w(F, omega, epsilon) = [2F_0 C(gamma, epsilon)/F]^(2 lambda) w_s.r.(F, omega, epsilon) (45); C(gamma, epsilon) = (tau_0/(2 gamma)) exp{int_0^tau_0 d tau [gamma/F(gamma, epsilon) - 1/(tau_0 - tau)]} (46); F(gamma, epsilon) = [(ch tau_0 - ch tau)^2 - epsilon^2 tau^2 (sh tau_0/tau_0 - sh tau/tau)^2]^(1/2) (47); sh^2 tau_0 - epsilon^2 (ch tau_0 - sh tau_0/tau_0)^2 = gamma^2 (48)",
  "variable": "epsilon: the ellipticity (0 linear, 1 circular); w_s.r.: the rate in a short-range potential (lambda = 0); tau_0 = omega t_0, t_0 the time of motion under the barrier",
  "range": "As Eq. (42)",
  "coefficients": {},
  "check": "Checked against the page image (p. 341), 2026-09-28. For epsilon = 0, tau_0 = arsinh gamma and the integrand is gamma/(ch tau_0 - ch tau) - 1/(tau_0 - tau); C(gamma, 0) = 1.0000 at gamma = 0.5, 1, 2, 3, 5, 10, 20 and 30 by numerical quadrature (computed 2026-09-28), so that (45) is (42) for linear polarisation at every gamma."
}

‘In the adiabatic region (gamma << 1) the Coulomb correction does not depend on epsilon’ (p. 341). Ilkov et al.’s footnote (ilkov_1992, p. 4007) quotes this factor with ‘C = 1 for gamma << 1 and linear polarisation’; for linear polarisation C is 1 at any gamma.

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.