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 <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/perelomov_1967.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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 :doc:`review register </register>` for the checks and decisions.