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Ugo Fano, Enrico Fermi, and Spectral Line Shapes

Ugo Fano, Enrico Fermi, and Spectral Line Shapes. Charles W. Clark. National Institute of Standards and Technology Gaithersburg, MD 20899 USA. Historical insights on the derivation of the “Fano profile” for spectral line shapes:.  ( ε ) ~ ( q + ε) 2 /(1 + ε 2 ).

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Ugo Fano, Enrico Fermi, and Spectral Line Shapes

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  1. Ugo Fano, Enrico Fermi, and Spectral Line Shapes Charles W. Clark National Institute of Standards and Technology Gaithersburg, MD 20899 USA cond-mat/0502210

  2. Historical insights on the derivation of the “Fano profile” for spectral line shapes: (ε) ~ (q + ε)2/(1 + ε2) Photoabsorption by atomic He above the first ionization limit, as observed at the NBS Synchrotron (now SURF III) R. P. Madden and K. Codling, “Two-electron excitation states in helium,” The Astrophysical Journal 141, 364-375 (1965) http://physics.nist.gov/surf cond-mat/0502210

  3. Ugo Fano1912-2001 1934 – Sc.D., mathematics, University of Turin 1934 – assistant to Enrico Fermi 1936 – assistant to Werner Heisenberg 1939 – emigrates to USA 1946 – joins staff of National Bureau of Standards 1966 – joins faculty of University of Chicago cond-mat/0502210

  4. Fano’s most influential work U. Fano, “Effects of configuration interaction on intensities and phase shifts,” Physical Review124, 1866-1878 (1961) Cited some 4500 times Ranked third in “citation impact” of all papers published in the entire Physical Review series [S. Redner, “Citation Statistics From More Than a Century of Physical Review,” physics/0407137] cond-mat/0502210

  5. Most-cited papers by some AMO physicists S. Chu 596 citations C. W. Clark 230 citations C. L. Cocke 167 citations C. Cohen-Tannoudji 477 citations E. A. Cornell 2355 citations K. L. Corwin 245 citations B. D. Esry 121 citations U. Fano 4500 citations W. Ketterle 1884 citations D. Kleppner 404 citations C. D. Lin 245 citations W. D. Phillips 255 citations C. Wieman 2355 citations D. J. Wineland 580 citations Nobel laureates Kansas State Faculty Others cond-mat/0502210

  6. Subject of the 1961 paper: excitation of a discrete state imbedded in a continuum Amplitudes interfere! He** 2s2p 1Po Example: photoionization of helium He+ 1s + p He 1s21S cond-mat/0502210

  7. Why was Fano’s 1961 paper so influential? It was published at the beginning of a new age of resonance spectroscopy, made possible by synchrotron light sources and high-resolution electron scattering instruments. Its results are broadly applicable to many systems of interest in atomic and condensed matter physics. Fano’s model is isomorphic to the Anderson model of a localized impurity in a continuum, which was published in the same year. This model is often referred to as the Fano-Anderson model in condensed matter physics. cond-mat/0502210

  8. Why was Fano’s 1961 paper so influential? Its central result had long been known, in particular via a paper published by Fano in 1935: U. Fano, “Sullo spettro di assorbimento dei gas nobili presso il limite dello spettro d’arco,” Nuovo Cimento, N. S.,12, 154-161 (1935) English translation edited by Guido Pupillo, Alberto Zannoni, and Charles W. Clark, “On the absorption spectrum of noble gases at the arc spectrum limit, cond-mat/0502210 cond-mat/0502210

  9. from J. M. Blatt and V. F. Weisskopf, Theoretical Nuclear Physics (Wiley, New York 1952) p. 401 cond-mat/0502210

  10. Fano 1935vs. 1961 Comprehensiveness: 1961 Timeliness: 1961 Acessibility of journal: 1961 Clarity of presentation: 1935 The 1961 paper has 4500 citations, the 1935 paper has only 150 – and 100 of these cite a wrong initial page! cond-mat/0502210

  11. Fermi’s role in Fano’s 1935 paper cond-mat/0502210

  12. Fermi’s role in Fano’s 1935 paper cond-mat/0502210

  13. Fermi’s role in Fano’s 1935 paper cond-mat/0502210

  14. Characteristic style of Fermi’s theoretical work Commentary by Franco Rasetti (1901-2001), in Fermi’s collected papers, Note e memorie, Vol 1. (University of Chicago Press, 1962) p.178 English translation of no. 30 by Alberto Zannoni, cond-mat/9912229 cond-mat/0502210

  15. Conclusion Fermi played a significant role in the development of Fano’s theory of line shapes. The manner of Fermi’s contributions is consistent with other reports of how he did his theoretical work The 1935 paper is worth reading, in its own right as a contribution to science, as an example of elegant exposition, and as a glimpse into the nature of collaboration between two great men. cond-mat/0502210

  16. Acknowledgements Archives of the Royal Society of London, for access to Fano’s bibliographic file The Italian Physical Society, for permission to publish an English translation of the 1935 paper My NIST colleagues Bill Gadzuk, Guido Pupillo, and Alberto Zannoni, for assistance in understanding the context of this matter and in translation of the 1935 paper cond-mat/0502210

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