manakov_1986#
N. L. Manakov, V. D. Ovsiannikov and L. P. Rapoport, “Atoms in a laser field”, Phys. Rep. 141, 320-433 (1986)
Source record · Catalogue · Review register
DOI: 10.1016/s0370-1573(86)80001-1
Source kind: theory
Recorded technique: Review of the theory of atoms in a monochromatic field: quasienergy states (Floquet) and their perturbation theory, the Coulomb, quantum-defect and Fues model-potential (FMP) Green functions for composite matrix elements (Secs. 3-4), the dynamic Stark effect, polarizability and hyperpolarizability tensors (Sec. 5), nonresonant and resonant multiphoton ionisation, photon statistics, photoelectron angular distributions and spin polarisation (Sec. 6), and collisions in a field (Sec. 7). The noble-gas values relevant to two-photon processes are those of Table 5.3, quoted from the authors’ earlier paper (Ref. [78]), whose method the review does not state for that table (Sec. 5.1, p. 374, lists [78] among the FMP calculations of polarizabilities), and three He 2 3S1 polarizabilities in the text (p. 376), quoted from a measurement [134] and a calculation [137].
Materials in structured entries: He, Xe
Dataset quantities: hyperpolarizability, level_polarizability, polarizability
Contents: 9 datasets; 0 formulas.
Curation notes#
IDENTITY: checked on PDF pages 1-2 on 2026-10-09: ‘PHYSICS REPORTS (Review Section of Physics Letters) 141, No. 6 (1986) 319-433. North-Holland, Amsterdam’; N.L. Manakov, V.D. Ovsiannikov and L.P. Rapoport, Voronezh State University; received March 1986. Journal page = PDF page + 318 (PDF p. 58 is p. 376; p. 319 is the title page). Crossref gives pages 320-433; the printed range is 319-433. The PDF is the publisher’s with a text layer; numbers were taken from the library’s cells and checked against the table images and the rendered pages.
WHAT IS NOT HERE: no two-photon ionisation cross section, no two-photon bound-bound strength or excitation cross section, no oscillator strength or transition probability, and no figure of any of these, for any noble gas. For krypton (OEP 6, Q2) the review gives neither a table nor a vector nor a raster figure of two-photon ionisation. Nothing can be compared with the curated two-photon ionisation references (TC-943) or with NIST’s near-infrared lines (TC-983).
TABLE 5.3 (p. 381; cells checked cell by cell against the image and the page): scalar polarizability alpha^S(omega) and hyperpolarizability components gamma_0^l(omega) and gamma_0^c(omega) ‘of the ground-state atoms at the pump-laser frequencies (in atomic units)’, omega_N = 0.043 a.u. and omega_R = 0.0656 a.u. (the text’s 1.17 and 1.78 eV, p. 376; 1059.6 and 694.6 nm, computed here). The values are ‘presented in table 5.3 [78]’ (p. 381): Ref. [78], N.L. Manakov, V.D. Ovsiannikov and L.P. Rapoport, Zh. Eksp. Teor. Fiz. 70 (1976) 1697, is not in the library, so they are use = ‘reproduced’. No uncertainty is stated. Taken: the He and Xe rows. NOT TAKEN (no material): H, 4.55, 1434.5, 845.6 at omega_N and 4.618, 1587.7, 1029.4 at omega_R; the Li, Na, K and Cs rows (Cs has no gamma at omega_R, printed ‘-’).
CONVENTION (from the paper’s own definitions): the field is F(t) = Re{F e exp(-i omega t)}, F the amplitude (p. 322). The second-order shift is Delta epsilon = -(1/4) alpha F^2 (Eq. 5.7, p. 373) and the fourth-order shift of an S state is epsilon^(4) = -(1/64) gamma_0 F^4 (Eqs. 5.16-5.19 and p. 380); the static expansion is epsilon = E - alpha E^2/2 - gamma E^4/4! (Eq. 5.15, p. 378), the Taylor-series (T) convention, which the omega -> 0 limit of -(1/64) gamma F^4 reproduces (<cos^4> = 3/8). So gamma_0^l is gamma_T(-w; w, -w, w), the intensity-dependent index (process kerr, component parallel), as the paper’s chi_par = chi_xxxx = gamma_0^l / 6 (p. 381) also states in Ward’s per-molecule chi (gamma_T = 6 chi). gamma_0^c is the same coefficient for circular polarization of the same amplitude F (component ‘circular’, not the mean gamma): chi_perp = (1/2)(chi_xxxx - chi_xyxy) = chi_xxyy = gamma_0^c / 12 (p. 381), so gamma_0^c = 2 gamma_T,xxyy in the paper’s index order, and 2/3 of gamma_0^l where Kleinman symmetry holds. The printed gamma_0^c / gamma_0^l is 0.6667 (He, omega_N), 0.664 (He, omega_R), 0.656 (Xe, omega_N) and 0.650 (Xe, omega_R). ‘epsilon^(4)l has the two-photon singularities on the excited S states, while epsilon^(4)c remains smooth’ (p. 380). alpha^S of an S state is its whole polarizability (no vector or tensor part, p. 374). The table’s values are electronic (atoms).
TWO-PHOTON IONISATION FROM GAMMA (p. 382): for |E_n|/2 < hbar omega < |E_n|, the total two-photon ionisation rate of a level is W^(2) = Im gamma_0^(l,c) F^4 / (32 hbar) (Eq. 5.21), against W^(1) = Im alpha^S F^2 / (2 hbar) for one photon (Eq. 5.14a): W^(2) depends on the polarization, W^(1) does not. Above threshold Im gamma_0 is the F^2 correction to the one-photon rate (Eq. 5.21a), with a re-emission term besides two-photon absorption (p. 382). The optical theorem sigma = 4 pi (omega / c) Im alpha (Gaussian units, p. 377) is OEP 8’s Im alpha = eps0 c sigma / omega in SI.
THE TWO-PHOTON AMPLITUDE (Sec. 6.1, pp. 386-389), initial S state, fine structure neglected: W_N(omega, l) = W_N^c + sum_k A_N^(k) l^(2k), l the degree of linear polarization (Eq. 6.6); W_N^c = (2 pi / hbar)(eF/2)^(2N) N!/(2N+1)!! |rho_(N,...,2)|^2 (Eq. 6.7); W_N^l = (2 pi / hbar)(eF/2)^(2N) sum_L |B_L|^2 / (2L+1) (Eq. 6.9), B_L from Eq. 6.10, rho the radial composite matrix element of Eq. 6.8 (the radial Green functions g_l at E_n + k hbar omega). For N = 2 these give W^c proportional to (2/15) |rho_2|^2 and W^l to |rho_0|^2/9 + 4 |rho_2|^2/45 (evaluated here from Eqs. 6.7, 6.9, 6.10), rho_L the s -> p -> L amplitude; A_2^(1) = W^l - W^c (Eq. 6.11). The ratio R = W^c / W^l is at most (2N-1)!!/N! (Eq. 6.14, Klarsfeld and Maquet [164]), 3/2 for N = 2, reached when rho_0 = 0; at large N linear polarization ionises more. Composite matrix elements from discrete oscillator strengths alone (no continuum) ‘are correct only for the two-photon transitions’, the discrete sum diverging for N >= 3 (p. 358). Angular distributions (p. 398): circular, from an S state, Eq. 6.35, beta_2^c = -10/7 and beta_4^c = 3/7 for N = 2; linear, beta_2^l = (40 - 140 x cos(delta_2 - delta_0))/(35 x^2 + 28) and beta_4^l = 72/(35 x^2 + 28), x = rho_0/rho_2 (Eq. 6.36). Hydrogen, notes only: near the 2p resonance beta_2^l = 12/7, beta_4^l = 16/7, against 16/17 for one-photon ionisation of 2p at the same frequency (p. 399); the analytic two-photon rate of H(1s) through Appell functions (Eqs. 6.12-6.13, Refs. [36, 39]).
RESONANT (2+1) IONISATION (Sec. 6.2, pp. 391-393): the weak-field Breit-Wigner rate W_N = (2 pi / hbar) |V_E1^(N2)|^2 |V_10^(N1)|^2 / (Delta^2 + Gamma_s^2/4) (Eq. 6.16), Delta = E_1 - E_0 - N_1 hbar omega; with N_1 >= 2 and one-photon ionisation of the resonant level its width Gamma_i = 2 pi |V_E1^(1)|^2 (Eq. 6.17) replaces Gamma_s; for N_1 <= N_2 the field width Gamma_f = 4 hbar omega_R, omega_R = |V_10^(N1)|/hbar the two-level Rabi frequency. The time-dependent two-level solution with an ionisation-broadened upper level (Eqs. 6.18-6.19, from [165]-[167]), its short-time limit (Eq. 6.20, the width set by the pulse’s spectrum, Eq. 6.21) and long-time limit W(t) = 1 - exp(-Gamma_i Gamma_f^2 t / (16 hbar Delta^2)) (Eq. 6.23): the two-level reduction of OEP 8’s Eq. 7. Photon statistics (p. 394): <I^N> = N! <I>^N for chaotic light (Eq. 6.27), a factor 2 for N = 2; for N_1 = N_2 = 1 ‘the statistical properties of radiation are not pronounced’ [174] (p. 395).
LIGHT SHIFTS OF A LEVEL f (pp. 372-374): linear, Delta epsilon_fM = -(F^2/4)[alpha^S + alpha^T (3M^2 - f(f+1))/(f(2f-1))] (Eq. 5.7), M along e; circular, -(F^2/4){alpha^S + A alpha^a M/(2f) - alpha^T (3M^2 - f(f+1))/(2f(2f-1))} (Eq. 5.8), M along the propagation, A = +-1; elliptical off-diagonal terms Eq. 5.9; alpha^S, alpha^a, alpha^T from the irreducible alpha_p (Eqs. 5.5-5.6). A J = 0 level has only alpha^S; a J = 2 level (Xe 6p[3/2]2, 6p[5/2]2) shifts by M through alpha^T. OEP 8’s -alpha_f |E^+|^2 is -(1/4) alpha F^2 with |E^+| = F/2, the same normalisation. Above threshold an excited level’s alpha^S tends to -e^2/(m omega^2) for hbar omega >= 2|E_nl|, and alpha^T ~ |E_nl / hbar omega|^2 alpha^S (Eq. 5.13, pp. 376-377).
HELIUM 2 3S1 (p. 376; taken under level_polarizability, TC-1011): the tensor polarizability measured in a dc field [134] (M.A. Player and P.G.H. Sandars, Phys. Lett. 30A (1969) 475), ‘alpha^T_{2 3S1}(0) = (3.53 +- 0.14) x 10^-2 atomic units’, and the dynamic vector and tensor polarizabilities at the neodymium frequency calculated in [137] (N.L. Manakov and V.D. Ovsiannikov, Zh. Eksp. Teor. Fiz. 75 (1978) 803), ‘alpha^a_{2 3S1}(omega_N) = -12.1; alpha^T_{2 3S1}(omega_N) = 4.04 a.u.’ Both are quoted from other papers, so use = reproduced; the level is NIST’s 1s.2s 3S J = 1. Definition (parameters.definition): the review’s Eqs. 5.6-5.8 (p. 373), the shift of sublevel M in an oscillating field of amplitude F being -(F^2/4)[alpha^S + alpha^T (3M^2 - J(J+1))/(J(2J-1))] for linear and -(F^2/4){alpha^S + A alpha^a M/(2J) - alpha^T (3M^2 - J(J+1))/(2J(2J-1))} for circular polarization (A = +-1, M along the propagation), and -(1/2)E^2 times the linear bracket in a static field E. The review quotes Player and Sandars’s value in its own notation without restating their definition; that it is the same normalisation is the review’s statement, not checked against the original (not in the library). The level of the +- 0.14 is not stated. The scalar alpha^S of 2 3S1 is not printed. The review’s point: the light-field splitting of 2 3S1 is ‘three or four orders of magnitude larger than in a d.c. field with the same strength’.
NOT TAKEN (not two-photon data): Table 5.1 (p. 375, the dc Stark coefficient of the alkali hyperfine transitions) and Table 5.2 (p. 375, alpha^S and alpha^a of Cs and Rb at omega_N and omega_R): no material. The unlabelled table on p. 412: N2+/N+ at the one-electron saturation intensity for Xe, Kr, Ar, Ne and He, ‘measured in the work [217]’ (A. L’Huillier, L.A. Lompre, G. Mainfray and C. Manus, J. Phys. B 16 (1983) 1363; Phys. Rev. A 27 (1983) 2503): reproduced, and no quantity holds a double-to-single ion ratio. Figures: 6.1 (K four-photon), 6.2 (scheme), 6.3 (Kr 4s one-photon beta, ‘Taken from [182]’), 6.4-6.5 (Rb), 6.6 (Xe 11-photon above-threshold photoelectron yields, from [212]), 7.1-7.4 (collisions): none is noble-gas two-photon data.
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
manakov_1986/he_alpha#
{
"id": "he_alpha",
"material": "He",
"file": "He/manakov_1986__alpha.csv",
"table": "tbl_4be3eb1d2dd5",
"quantity": "polarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"N. L. Manakov, V. D. Ovsiannikov and L. P. Rapoport, Zh. Eksp. Teor. Fiz. 70, 1697 (1976) [Ref. 78]"
]
}
Table 5.3, He alpha^S(omega) of the ground state at omega_N = 0.043 and omega_R = 0.0656 a.u.; printed 1.49 at both. No uncertainty stated; the method of Ref. [78] is not stated in the review (FMP, p. 374). 7.5 % above fit/He at these frequencies.
manakov_1986/xe_alpha#
{
"id": "xe_alpha",
"material": "Xe",
"file": "Xe/manakov_1986__alpha.csv",
"table": "tbl_4be3eb1d2dd5",
"quantity": "polarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"N. L. Manakov, V. D. Ovsiannikov and L. P. Rapoport, Zh. Eksp. Teor. Fiz. 70, 1697 (1976) [Ref. 78]"
]
}
Table 5.3, Xe alpha^S(omega) of the ground state at omega_N = 0.043 and omega_R = 0.0656 a.u. No uncertainty stated. Within 0.3 and 0.9 % of fit/Xe.
manakov_1986/he_gamma_linear#
{
"id": "he_gamma_linear",
"material": "He",
"file": "He/manakov_1986__gamma_linear.csv",
"table": "tbl_4be3eb1d2dd5",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"N. L. Manakov, V. D. Ovsiannikov and L. P. Rapoport, Zh. Eksp. Teor. Fiz. 70, 1697 (1976) [Ref. 78]"
],
"parameters": {
"process": "kerr",
"convention": "T",
"part": "electronic",
"component": "parallel"
}
}
Table 5.3, He gamma_0^l(omega): the fourth-order quasienergy coefficient for linear polarization, epsilon^(4) = -gamma_0^l F^4 / 64, which is gamma_T(-w; w, -w, w) (record notes). No uncertainty stated. 1.31 times OEP 5’s fitted He gamma at both frequencies.
manakov_1986/he_gamma_circular#
{
"id": "he_gamma_circular",
"material": "He",
"file": "He/manakov_1986__gamma_circular.csv",
"table": "tbl_4be3eb1d2dd5",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"N. L. Manakov, V. D. Ovsiannikov and L. P. Rapoport, Zh. Eksp. Teor. Fiz. 70, 1697 (1976) [Ref. 78]"
],
"parameters": {
"process": "kerr",
"convention": "T",
"part": "electronic",
"component": "circular"
}
}
Table 5.3, He gamma_0^c(omega): the same coefficient for circular polarization of the same amplitude, epsilon^(4) = -gamma_0^c F^4 / 64, = 12 chi_xxyy = 2 gamma_T,xxyy (p. 381); not the mean gamma. No uncertainty stated.
manakov_1986/xe_gamma_linear#
{
"id": "xe_gamma_linear",
"material": "Xe",
"file": "Xe/manakov_1986__gamma_linear.csv",
"table": "tbl_4be3eb1d2dd5",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"N. L. Manakov, V. D. Ovsiannikov and L. P. Rapoport, Zh. Eksp. Teor. Fiz. 70, 1697 (1976) [Ref. 78]"
],
"parameters": {
"process": "kerr",
"convention": "T",
"part": "electronic",
"component": "parallel"
}
}
Table 5.3, Xe gamma_0^l(omega), gamma_T(-w; w, -w, w) as for he_gamma_linear. No uncertainty stated. 1.76 and 1.81 times OEP 5’s fitted Xe gamma at omega_N and omega_R.
manakov_1986/xe_gamma_circular#
{
"id": "xe_gamma_circular",
"material": "Xe",
"file": "Xe/manakov_1986__gamma_circular.csv",
"table": "tbl_4be3eb1d2dd5",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"N. L. Manakov, V. D. Ovsiannikov and L. P. Rapoport, Zh. Eksp. Teor. Fiz. 70, 1697 (1976) [Ref. 78]"
],
"parameters": {
"process": "kerr",
"convention": "T",
"part": "electronic",
"component": "circular"
}
}
Table 5.3, Xe gamma_0^c(omega), circular polarization as for he_gamma_circular; not the mean gamma. No uncertainty stated.
manakov_1986/he_2s3s1_tensor_static#
{
"id": "he_2s3s1_tensor_static",
"material": "He",
"table": "text",
"quantity": "level_polarizability",
"unit": "au",
"scale": 0.01,
"abscissa_unit": "nm",
"wavelength_medium": "vacuum",
"use": "reproduced",
"reproduced_from": [
"M. A. Player and P. G. H. Sandars, Phys. Lett. 30A, 475 (1969) [Ref. 134]"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"configuration": "1s.2s",
"term": "3S",
"j": "1",
"component": "tensor",
"complex_part": "real",
"method": "measured",
"definition": "Manakov et al. 1986, Eqs. 5.6-5.8 (p. 373): static shift -(1/2) E^2 [alpha^S + alpha^T (3M^2 - J(J+1))/(J(2J-1))]"
}
}
1 inline points in the source record.
p. 376: alpha^T_{2 3S1}(0) = (3.53 +- 0.14) x 10^-2 atomic units, the tensor polarizability of He 1s2s 3S1 measured in a dc field (quoted; printed scale 10^-2). Uncertainty level not stated.
manakov_1986/he_2s3s1_vector_omega_n#
{
"id": "he_2s3s1_vector_omega_n",
"material": "He",
"table": "text",
"quantity": "level_polarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"N. L. Manakov and V. D. Ovsiannikov, Zh. Eksp. Teor. Fiz. 75, 803 (1978) [Ref. 137]"
],
"parameters": {
"configuration": "1s.2s",
"term": "3S",
"j": "1",
"component": "vector",
"complex_part": "real",
"method": "calculated",
"definition": "Manakov et al. 1986, Eqs. 5.6-5.8 (p. 373): circular polarization, shift -(F^2/4){alpha^S + A alpha^a M/(2J) - alpha^T (3M^2 - J(J+1))/(2J(2J-1))}, A = +-1, M along the propagation; alpha^a = -alpha_1 sqrt(2J/(J+1))"
}
}
1 inline points in the source record.
p. 376: alpha^a_{2 3S1}(omega_N) = -12.1, the vector (axial) dynamic polarizability of He 1s2s 3S1 at the neodymium frequency omega_N = 0.043 a.u. (1.17 eV), calculated (quoted). No uncertainty stated.
manakov_1986/he_2s3s1_tensor_omega_n#
{
"id": "he_2s3s1_tensor_omega_n",
"material": "He",
"table": "text",
"quantity": "level_polarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"N. L. Manakov and V. D. Ovsiannikov, Zh. Eksp. Teor. Fiz. 75, 803 (1978) [Ref. 137]"
],
"parameters": {
"configuration": "1s.2s",
"term": "3S",
"j": "1",
"component": "tensor",
"complex_part": "real",
"method": "calculated",
"definition": "Manakov et al. 1986, Eqs. 5.6-5.8 (p. 373): linear polarization, shift -(F^2/4)[alpha^S + alpha^T (3M^2 - J(J+1))/(J(2J-1))], M along the polarization; alpha^T = -alpha_2 [2J(2J-1)/(3(J+1)(2J+3))]^(1/2)"
}
}
1 inline points in the source record.
p. 376: alpha^T_{2 3S1}(omega_N) = 4.04 a.u., the tensor dynamic polarizability of He 1s2s 3S1 at omega_N = 0.043 a.u. (1.17 eV), calculated (quoted). No uncertainty stated.
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.