zon_1972#
B. A. Zon, N. L. Manakov and L. P. Rapoport, “Perturbation theory for the multiphoton ionization of atoms”, Sov. Phys. JETP 34, 515-519 (1972) [Zh. Eksp. Teor. Fiz. 61, 968-975 (1971)]
Source record · Catalogue · Review register
No DOI is recorded.
Source kind: theory
Recorded technique: Lowest-order perturbation theory of N-photon ionisation (nonrelativistic, dipole) with the infinite sums over intermediate states, continuum included, done through the Green’s function of the optical electron in the quantum-defect method (Eq. 2 for E > 0, the expression after Eq. 8 for E < 0): its poles are the atom’s measured levels (quantum defects interpolated from Moore’s tables), its radial part built from regular and irregular Coulomb functions. Continuum functions in the quantum-defect method (Eq. 6) with phases delta_l = pi mu_l(E) extrapolated above threshold, the irregular function cut off by Seaton’s factor (1 - exp(-10 r / l(l + 1)))^(2l + 1). Three-photon ionisation by linearly and circularly polarised light of H 1s and 2s and of He 2 3S1 and 2 1S0 (Figs. 1-4).
Materials in structured entries: He
Dataset quantities: level_polarizability
Contents: 3 datasets; 0 formulas.
Curation notes#
Journal pp. 515-519 = PDF pages 1-5. Identity checked on the first page (PDF p. 1: Soviet Physics JETP, Volume 34, Number 3, March 1972; ‘Perturbation Theory for the Multiphoton Ionization of Atoms’, B. A. Zon, N. L. Manakov and L. P. Rapoport, Voronezh State University; submitted March 24, 1971; Zh. Eksp. Teor. Fiz. 61, 968-975 (September, 1971)) on 2026-10-09; the translation has no DOI (library identity ASSERTED). The PDF is a scan (one page image, 4961 x 7014 pixels, with an OCR text layer, per page); Figs. 1-4 are raster. Taken: the three level polarisabilities of p. 518 (TC-1011’s level_polarizability; below).
DEFINITIONS (pp. 515-517, image checked). Atomic units. Eq. (1): dw/dOmega = 2 pi (omega F / F0)^N |K_fi^(N)(omega)|^2, ‘F denotes the photon flux in units of cm^-2 sec’ (read cm^-2 s^-1, as p. 517 writes it), F0 = c / 2 pi a^3 = 3.22 x 10^34 cm^-2 s^-1 (a the Bohr radius); K_fi^(N) the chain of Green’s functions between the dipole operators (e.r). From an s state, integrated over the electron’s direction: linear polarisation, Eq. (10), a sum over channels; circular, Eq. (11), w = 2 pi (omega F/F0)^N N!/(2N + 1)!! |T_(N, N-1, ..., 2)|^2, the one path that raises l by one per photon. For N = 3 (p. 517): w^(l) = 2 pi (omega F/F0)^3 {(1/27)[T_10 + (4/5) T_12]^2 + (4/175) T_32^2}, w^(c) = 2 pi (omega F/F0)^3 (2/35) T_32^2: so w^(c) has a zero between each pair of poles and w^(l) has none. Eq. (13) splits w = B eta, B = (alpha c / a)(1/8 pi^2)(F/F0)^N 2^N / I_n^(N-2) [(n + N)!/n!]^4 an order-of-magnitude factor and eta (Figs. 1-4) the structure. The optical theorem (Eqs. 7-8): the dynamic polarisability alpha_n(omega) = <n|(e.r){G_(E_n + omega) + G_(E_n - omega)}(e.r)|n>, Im f(0) = (alpha omega / 4 pi) sigma_nl(E_n + omega), relating Im alpha_n above threshold to the one-photon photoionisation cross section; Re(Delta E) = -(1/4) E^2 Re alpha and Im(Delta E) = -(1/4) E^2 Im alpha (p. 518), E the field amplitude.
VALUES PRINTED. Hydrogen: B_1s = 0.833 x 10^-82 F^3 s^-1, B_2s = 1.30 x 10^-80 F^3 s^-1 (p. 517); ‘the 2s-state of hydrogen can be ionized by two quanta of a ruby laser (omega = 14402.2 cm^-1) or by three quanta of a neodymium laser (omega = 9433 cm^-1)’, with equal rates at F ~ 10^31 cm^-2 s^-1. Helium: B_(2 3S1) = 0.927 x 10^-80 F^3 s^-1, B_(2 1S0) = 1.11 x 10^-80 F^3 s^-1 (p. 517); at the ruby frequency, linear polarisation, w_(2 3S1)^(l) = 3.09 x 10^-81 F^3 s^-1 and w_(2 1S0)^(l) = 3.30 x 10^-78 F^3 s^-1 (p. 518), the latter three orders larger because two ruby photons lie within ‘<~ 30 cm^-1’ of 2 1S0 -> 6 1S0. Light shifts at the ruby frequency (p. 518): ‘alpha_(2 1S0) = 270 atomic units’ (the shift of 2 1S0, ‘calculated by the method described in [14]’, Davydkin et al.; that it is the dynamic value at the ruby frequency is implied by the paragraph, not written), ‘Re alpha_(6 1S0) = 300 a.u., Im alpha_(6 1S0) = 35 a.u.’, so that below ~10^6 V/cm the shift and broadening ‘cannot substantially change the probability’. Through Eq. (8), Im alpha = 35 au at omega = 14402.2 cm^-1 (0.06562 au) is a 6 1S0 photoionisation cross section of 4 pi alpha omega Im alpha = 0.211 a0^2 = 5.9e-18 cm^2 (derived here, not printed; not data). Measured upper limit (Bakos, Kantor and Kish, JETP Lett. 12, 255 (1970), Ref. 17) for three-photon ionisation of metastable He (singlet and triplet together) at 2 x 10^5 V/cm: 4.7 x 10^-71 F^3 s^-1.
NOT TAKEN (no quantity; declined, TC-1011): the He 2 3S1 and 2 1S0 three-photon generalised cross sections at the ruby frequency, 3.09e-81 and 3.30e-78 cm6 s2 (linear; p. 518), and Figs. 3-4’s eta(omega) (raster): the multiphoton cross section of an excited level; multiphoton_ionization_cross_section names no initial level and every curated value is from the ground state.
TAKEN (level_polarizability, TC-1011; inline points, p. 518, use check: calculations by the authors’ quantum-defect Green’s function, no uncertainty stated). NIST labels: 2 1S0 = 1s.2s 1S J = 0; 6 1S0 = 1s.6s 1S J = 0; scalar parts (J = 0). (a) alpha_1s2s = ‘270 atomic units’, real: the wavelength cell is ‘not stated’, because the paper does not write the frequency of this value; the paragraph (the shift of 2 1S0 in the ruby field, ‘calculated by the method described in [14]’) implies the ruby frequency, 14402.2 cm^-1 (p. 517), but a static value cannot be excluded from the text alone. (b) 1s6s: ‘Re alpha_(6 1S0) = 300 a.u., Im alpha_(6 1S0) = 35 a.u.’ ‘For the frequency corresponding to a ruby laser’, at omega = 14402.2 cm^-1 as printed on p. 517 (an energy, i.e. a vacuum wavenumber; 694.34 nm); real and imaginary parts as separate datasets. Their shift convention is Re(Delta E) = -(1/4) E^2 Re alpha, Im(Delta E) = -(1/4) E^2 Im alpha (E the field amplitude), the quantity’s -(1/4) alpha F^2. NOT TAKEN (other reasons): hydrogen (not a material); the B factors (scales, not values); Bakos et al.’s limit (reproduced; singlet and triplet mixed).
TWO-PHOTON IONISATION OF THE NOBLE GASES (OEP 6): none; the paper treats three-photon ionisation of H and of metastable He only. KRYPTON: not treated. For OEP 8 the He 2 1S0 dynamic polarisability (the 1s2s level’s light shift) is relevant, but at 694 nm, not at the two-photon resonance’s 120 nm.
INCONSISTENCIES: ‘cm^-2 sec’ for the flux and for F0 (p. 516) against ‘cm^-2 sec^-1’ (p. 517): F0 = c / 2 pi a^3 is 3.22e34 cm^-2 s^-1 with a = 0.529e-8 cm, so s^-1 is meant.
FURTHER SOURCES CITED (not in the library): L. P. Rapoport, B. A. Zon and N. L. Manakov, Sov. Phys. JETP 29, 220 (1969) (analytic two-photon ionisation of H, Ref. 11); B. A. Zon, N. L. Manakov and L. P. Rapoport, Sov. Phys. Doklady 14, 904 (1970) (the quantum-defect Green’s function, Ref. 12); V. A. Davydkin, B. A. Zon, N. L. Manakov and L. P. Rapoport, Sov. Phys. JETP 33, 70 (1971) (the algorithm and polarisabilities, Ref. 14); Y. Gontier and M. Trahin, Phys. Rev. 172, 83 (1968) (H three-photon, Ref. 5); G. A. Delone, N. B. Delone, N. L. Manakov and G. A. Piskova (K four-photon, Ref. 18, in press).
Recorded bibliographic identity status: ASSERTED. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
zon_1972/alpha_1s2s_1S0#
{
"id": "alpha_1s2s_1S0",
"material": "He",
"table": "text",
"quantity": "level_polarizability",
"unit": "au",
"abscissa_unit": "cm-1",
"use": "check",
"parameters": {
"configuration": "1s.2s",
"term": "1S",
"j": "0",
"component": "scalar",
"complex_part": "real",
"method": "calculated: quantum-defect Green's function of the optical electron (Davydkin, Zon, Manakov and Rapoport, Sov. Phys. JETP 33, 70 (1971), Ref. 14)",
"frequency_doubt": "probably the ruby frequency, 14402.2 cm^-1 (p. 517), from the paragraph; not written"
}
}
1 inline points in the source record.
p. 518: ‘The shift of the 2 1S0 level has been calculated by the method described in [14]: alpha_(2 1S0) = 270 atomic units.’ The frequency is not written; the context (the level’s shift in the ruby field) implies 14402.2 cm^-1, a doubt (the record’s notes). A calculation; no uncertainty stated.
zon_1972/alpha_1s6s_1S0_real#
{
"id": "alpha_1s6s_1S0_real",
"material": "He",
"table": "text",
"quantity": "level_polarizability",
"unit": "au",
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "check",
"parameters": {
"configuration": "1s.6s",
"term": "1S",
"j": "0",
"component": "scalar",
"complex_part": "real",
"method": "calculated: quantum-defect Green's function, Eqs. (7) and (4)"
}
}
1 inline points in the source record.
p. 518: ‘Re alpha_(6 1S0) = 300 a.u.’ ‘For the frequency corresponding to a ruby laser’, omega = 14402.2 cm^-1 as printed on p. 517; from their Eqs. (7) and (4). Above the level’s ionisation threshold, so complex (see alpha_1s6s_1S0_imaginary). A calculation; no uncertainty stated.
zon_1972/alpha_1s6s_1S0_imaginary#
{
"id": "alpha_1s6s_1S0_imaginary",
"material": "He",
"table": "text",
"quantity": "level_polarizability",
"unit": "au",
"abscissa_unit": "cm-1",
"wavelength_medium": "vacuum",
"use": "check",
"parameters": {
"configuration": "1s.6s",
"term": "1S",
"j": "0",
"component": "scalar",
"complex_part": "imaginary",
"method": "calculated: quantum-defect continuum, through the optical theorem, Eq. (8)"
}
}
1 inline points in the source record.
p. 518: ‘Im alpha_(6 1S0) = 35 a.u.’ at the ruby frequency (14402.2 cm^-1, p. 517), ‘expressed in terms of the cross section for one-photon ionization, given by Eq. (8)’: sigma = 4 pi alpha_fs omega Im alpha = 0.211 a0^2 = 5.9e-18 cm^2 (derived in the record’s notes, not taken). A calculation; 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.