lambropoulos_1976 ================= P\. Lambropoulos, "Topics on multiphoton processes in atoms", Adv\. At\. Mol\. Phys\. 12, 87\-164 \(1976\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1016/S0065\-2199\(08\)60043\-3 `__ **Source kind:** compilation **Recorded technique:** Review of the perturbation theory of multiphoton processes in atoms \(resolvent operator, quantised field, dipole approximation\), of the methods of calculating generalised cross sections \(Bebb and Gold's average frequency, Morton's average matrix element, Zernik's and Gontier and Trahin's implicit summation, the Coulomb and quantum\-defect Green's functions of Karule and of Zon, Manakov and Rapoport, truncated summation\), of photon\-statistics \(field correlation\) effects, of resonances with intermediate states \(shift and width\), and of light\-polarisation, spin\-orbit, angular\-distribution and quadrupole effects, with the measurements to 1975\. The numbers it prints are other papers' \(tables' footnotes and text name them\)\. **Materials in structured entries:** None recorded. **Dataset quantities:** None recorded. **Contents:** 0 datasets; 0 formulas. Curation notes -------------- Journal pp\. 87\-164 = PDF pages 1\-78 \(journal page = PDF page \+ 86\)\. Identity checked on the first page \(PDF p\. 1 = p\. 87\: 'Topics on Multiphoton Processes in Atoms', P\. Lambropoulos, Physics Department, University of Southern California, with the contents list\) on 2026\-10\-09; the copy does not print the volume, 12, which is how the papers in the library cite it\. The PDF is a scan \(one page image, about 1820 x 2710 pixels, with an OCR text layer, per page\); all figures are raster\. Nothing is extracted\: no value of a noble gas fits a quantity and is the review's own \(below\)\. DEFINITIONS \(pp\. 94\-95, image checked\)\. Eq\. \(19\)\: W\_fg^\(N\) = sigma\_N I^N, 'sigma\_N is the total generalized cross section', Eq\. \(20\)\: sigma\_N = \(2 pi alpha\)^N / \(4 pi^2\) \(m K / hbar\) omega^N int \|M\_fg^\(N\)\|^2 dOmega\_K, with M\_fg^\(N\) the \(N\-1\)\-fold sum of Eq\. \(21\) over r\.e\_lambda \(the polarisation enters only through e\_lambda\); 'I is the total photon flux measured in \# photons/cm^2 sec at the interaction region\. The units of sigma\_N are cm^2N sec^\(N\-1\)'\. This is bebb\_1966's rate \(its Eqs\. 17\-18\) written as a cross section\. Bound\-bound N\-photon transitions, Eq\. \(23\)\: W\_fg^\(N\) = 2 pi \(2 pi alpha\)^N I^\(N\-1\) I\(omega\) omega^N \|sum \.\.\.\|^2, 'where I\(omega\) is the number of photons per cm^2 per sec per unit bandwidth' \(all energies are omegas in s^\-1, p\. 90\), without the fluorescence step; for N = 2 this is a frequency\-integrated cross section 2 pi \(2 pi alpha\)^2 omega^2 \|M\|^2 against I I\(omega\), the form of two\_photon\_excitation\_cross\_section \(TC\-872\) if I\(omega\) = I g\(omega\)\. PHOTON STATISTICS \(Sec\. III, pp\. 109\-115, image checked\)\. The N\-photon rate depends on the N\-th moment G\_N = sum\_n P\_nn n^N of the field \(Eq\. 44\)\: G\_N ~ \^N for a coherent \(Glauber\) state \(Eq\. 46\), G\_N ~ N\! \^N for a chaotic \(Gaussian, thermal\) one \(Eq\. 48\), and in general W\_N = sigma\_N G\_N \(Eq\. 49\), 'from which Eq\. \(19\) is obtained as a special case when G\_N = \^N = I^N'\: sigma\_N is defined for coherent light, and chaotic light gives N\! times the rate\. Fields with fluctuations larger than Gaussian give more \(p\. 112\)\. 'a pulsed laser operating in a large number of modes, say 50 or so, is for all practical purposes equivalent to a chaotic state' \(p\. 112\)\. Measured\: two\-photon ratios chaotic over coherent of 1\.88 \(Shiga and Imamura, Cs3Sb\) and 1\.86 to 1\.52 \(Krasinski et al\., cw argon laser\); 11\-photon ionisation of Xe at 1\.06 um \(Lecompte et al\. 1974, 1975\), multimode over single mode 'about 10^\(6\.9 \+\- 0\.3\) \(~ 11\!\)' \(p\. 114\)\. Resonant two\-photon ionisation well above saturation of the intermediate level is proportional to the average intensity and so independent of photon statistics \(Armstrong et al\. 1975b, p\. 114\)\. This is OEP 8's convention \(TC\-984, Q5\: residues for coherent light\)\. RESONANCES \(Sec\. IV\.A\-B, pp\. 114\-120\)\. The shift\-width function of a resonant level, R\_MM = \(s\_m^\(0\) \+ s\_m^\(1\) I\) \- i \(gamma\_m^\(0\) \+ gamma\_m^\(1\) I\), to lowest order \(p\. 119\)\: on an exact resonance the rate's slope in I goes from N \(low intensity\) to N \- 2 once gamma\_m^\(1\) I dominates; a near resonance can be shifted into or out of resonance by s\_m^\(1\) I\. The two\-photon amplitude near a resonance, Eq\. \(58\), is the resonant term with R\_a0a0 plus the off\-resonant sum, whose interference gives a Fano\-like profile \(Armstrong et al\. 1975a, p\. 126\)\. POLARISATION \(Sec\. V\.B, pp\. 135\-137\)\. Circular light has fewer channels; 'for low order ionization \(say 2\- to 4\-photon\) circular polarization will in most cases give higher rates', linear for higher orders\. Klarsfeld and Maquet's rigorous but not least upper bound of the circular\-to\-linear ratio for an S hydrogenlike state, \(2N \- 1\)\!\!/N\! \(p\. 136; 1\.5 for N = 2\)\. Table III \(tbl\_1d36c88a3c44, p\. 137; image checked\) lists alkalis only\: experiment / theory Na 3\-photon at 2 omega\_N 0\.42 \+\- 20 % / 0\.33; Na 5 omega\_N 0\.5 \+\- 20 % / 0\.07; K 2 2 omega\_N 1\.2 \+\- 30 % / 1\.16; K 3 omega\_R 2\.34 \+\- 9\.5 % / 2\.45, 2\.18; K 4 omega\_N 1\.67 \+\- 30 % / 4\.0; Cs 2 2 omega\_R 1\.28 \+\- 16 % / 1\.08, 1\.14; Cs 3 omega\_R 2\.15 \+\- 19 % / 1\.42, 2\.22, 2\.45 \(the extracted table runs the theory cells together, '2\.452\.18'; the image has one per line\)\. NOT TAKEN\. \(a\) Table I \(tbl\_891f75dc43eb, p\. 104; image checked\)\: generalised cross sections of Cs, Rb, Li, K and Na for N = 2 to 5 at omega\_N, 2 omega\_N, omega\_R and 2 omega\_R, linear and circular, Manakov et al\. \(1974a\)'s quantum\-defect Green's function calculations, and the text's alkali values \(Lambropoulos and Teague's Cs two\-photon 5\.52e\-49 \(circular\) and 4\.84e\-49 cm4 s \(linear\) at 2 omega\_R, p\. 106; Flank and Rachman's Cs three\-photon; Arslanbekov et al\.'s, Cervenan and Isenor's\)\: no alkali is a material, and they are reproduced\. \(b\) Table II \(tbl\_1943bdb19b84, p\. 129; image checked\)\: Agostini et al\. \(1970b\)'s observed exponents of the ion yield against intensity at 1\.06 um, K0 / K\: He 21 / 18 \+\- 0\.3, Ne 19 / 13\.7 \+\- 0\.3, Ar 14 / 10\.3 \+\- 0\.3, Kr 12 / 9 \+\- 0\.3, Xe 11 / 8\.7 \+\- 0\.3, and the postscript's \(p\. 158\) newer Saclay exponents with 28 ps pulses at 1064\.35 nm, 'He, Ne, Ar, and Xe \.\.\. 22 \+\- 1, 19 \+\- 1, 14 \+\- 1 and 11 \+\- 1' against theoretical 22, 19, 14, 11\: reproduced, and no quantity holds an observed exponent \(the review attributes the low values to instrumental saturation, p\. 130\)\. \(c\) Figures\: Fig\. 3 \(Xe 11\-photon ion number against relative intensity for 10 to 100 modes, Lecompte et al\. 1975\), Fig\. 4 \(Ne 13\-photon log sigma against the ruby photon energy, Baravian et al\. 1971\), Fig\. 10 \(He, Ne, Ar, Kr and Xe ion numbers against intensity, Agostini 1970b\)\: raster and reproduced; the rest are H, alkali or He 2 3S\. \(d\) The ratio 10^\(6\.9 \+\- 0\.3\) for Xe \(reproduced; no quantity\)\. TWO\-PHOTON IONISATION OF THE NOBLE GASES \(OEP 6\)\: none\. The only noble\-gas two\-photon calculation mentioned is Pindzola and Kelly's for argon \(p\. 154; pindzola\_1975, curated\), cited for many\-electron effects without numbers\. KRYPTON\: no two\-photon value in any form; only Table II's exponent \(12\-photon at 1\.06 um\) and Fig\. 10's raster ion\-yield curve, both Agostini et al\.'s\. FINDINGS \(the review's own inconsistencies; nothing is taken from them\)\. \(1\) The 'about 10^\(6\.9 \+\- 0\.3\) \(~ 11\!\)' of p\. 114 is not 11\!\: 11\! = 3\.99e7 = 10^7\.60, 0\.7 decade \(2\.3 times the stated error\) above\. \(2\) Fig\. 10's caption says 'Nd\-glass laser, lambda = 0\.53 u'; the text introducing Table II \(p\. 128\) says 1\.06 um, which Table II's K0 \(Xe 11, He 21\) confirm\. \(3\) 'As seen in Table II, there are differences between results obtained by different authors' \(p\. 136\) means Table I; 'the previous experiments \(Fig\. 10 and Table III\)' \(p\. 158\) means Table II\. \(4\) Cs circular\-to\-linear ratios\: the text \(p\. 136\) gives 1\.28 and 2\.14 for two\- and three\-photon, citing Fox et al\. and Kogan et al\. 1971 together; Table III prints 2\.15 for three\-photon and footnotes two\-photon to Kogan et al\. \(d\) and three\-photon to Fox et al\. \(e\)\. The reference list has Fox, Kogan and Robinson, Phys\. Rev\. Lett\. 25, 1416 \(1971\); pindzola\_1975 cites the same paper as Phys\. Rev\. Lett\. 26, 1416 \(1971\)\. \(5\) Flank and Rachman's linear Cs three\-photon value '0\.957 x 10^\-77 cm6 sec2' \(p\. 105\) has the digits of Table I's 9\.57 \(76\) and is exactly 1/100 of it \('almost two orders of magnitude smaller'\); their circular 2\.35e\-77 is 1/58 of Table I's 1\.36e\-75\. Identical digits in two independent calculations suggest a transcription or exponent error in one of them\. \(6\) The text's Manakov et al\. Cs four\-photon value '10^\-107' \(p\. 109\) is Table I's 5\.16e\-107 \(linear\) and 8\.70e\-107 \(circular\) rounded down a factor of 5 to 9\. FURTHER SOURCES CITED \(not in the library\)\: C\. Lecompte, G\. Mainfray, C\. Manus and F\. Sanchez, Phys\. Rev\. Lett\. 32, 265 \(1974\) and Phys\. Rev\. A 11, 1009 \(1975\) \(Xe photon statistics\); P\. Agostini, G\. Barjot, G\. Mainfray, C\. Manus and J\. Thebault, IEEE J\. Quantum Electron\. 6, 782 \(1970\) \(noble\-gas exponents\); G\. Baravian et al\., Appl\. Phys\. Lett\. 18, 387 \(1971\) \(Ne 13\-photon resonance\); V\. M\. Morton, Proc\. Phys\. Soc\. London 92, 301 \(1967\) \(approximate rates for H, the noble gases and alkalis\); S\. Klarsfeld and A\. Maquet, Phys\. Rev\. Lett\. 29, 79 \(1972\) \(the polarisation bound\); L\. Armstrong, Jr\., B\. L\. Beers and S\. Feneuille, Phys\. Rev\. A 12, 1903 \(1975\) \(resonant two\-photon ionisation and photon statistics\); N\. L\. Manakov, M\. A\. Preobragensky and L\. P\. Rapoport, Proc\. 11th Int\. Conf\. Phenomena Ionized Gases, Prague \(1974\) \(Table I\)\. **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 -------- 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 ` for the checks and decisions.