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 <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/zon_1972.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </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
~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

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

.. code-block:: text

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

.. code-block:: text

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