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22s_580ln_fa08

22s_580ln_fa08 - MIT OpenCourseWare http/ocw.mit.edu 5.80...

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MIT OpenCourseWare http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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Lecture # 22 Supplement See Microwave Spectroscopy by C. H. Townes and A. L. Schawlow, Dover Publications, New York (1975) for complete text of these Appendices. Contents A. Appendix III: Coe cients for Energy Levels of a Slightly Asymmetric Top, pp. 522- 526 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 B. Appendix IV: Energy Levels of a Rigid Rotor, pp. 527-555 . . . . . . . . . . . . . . . 2 C. Appendix V: Transition Strengths for Rotational Transitions, pp. 557-559 . . . . . . 2 A. Appendix III: Coe cients for Energy Levels of a Slightly Asym- metric Top, pp. 522-526 SUMMARY Rotational energy is given by w = K 2 + C 1 b + C 2 b 2 + C 3 b 3 + C 4 b 4 + C 5 b 5 + . . . B + C B + C For a prolate top, energy = W = J ( J + 1) + A w 2 2 C B b = b p = 2 A A + B B C A + B For an oblate top, energy = W = J ( J + 1) + C w 2 2 A B b = b 0 = 2 C B A Where the first few constants K , C 1 , C 2 . . . are identical for pairs of degenerate levels, they are usually listed for only the first of the two levels. (
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