University:
Widener University
Course:
PHYS-121 | Fundamentals of Physics I
Academic year:

2023
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223

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2
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byersvolatilise

Lecture # 21 Supplement Contents A. Appendix III: Coeﬃcients 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 See Microwave Spectroscopy by C. H. Townes and A. L. Schawlow, Dover Publications, New York (1975) for complete text of these Appendices. A. Appendix III: Coeﬃcients for Energy Levels of a Slightly Asym metric Top, pp. 522-526 SUMMARY Rotational energy is given by w = K 2 + C1 b + C2 b2 + C3 b3 + C4 b4 + C5 b5 + . . . � B + C� B+C J(J + 1) + A − w 2 2 C−B b = bp = 2A − B − C � A+B A + B� For an oblate top, energy = W = J(J + 1) + C − w 2 2 A−B b = b0 = 2C − B − A For a prolate top, energy = W = Where the ﬁrst few constants K, C1 , C2 . . . are identical for pairs of degenerate levels, they are usually listed for only the ﬁrst of the two levels. (C1 , C2 , and C3 were computed by J. F. Lotspeich; C4 and C5 by J. Kraitchman and N. Solimene.) 1 Lecture #21 Supplement B. Page 2 Appendix IV: Energy Levels of a Rigid Rotor, pp. 527-555 SUMMARY Energy (in cycles/sec) = W/h = + C)J(J + 1) + 12 (A − C)Eτ . Eτ is tabulated as a function of the rotational level JK−1 K1 (or Jτ ) and of the asymmetry parameter κ = 2BA−−AC−C . 1 (A 2 Values for positive κ only are tabulated, since those for negative κ can be obtained from the relation Eτ (κ) = −E−τ (−κ). For further explanation see Chapter 4. This table was reproduced with the permission of the Ballistics Research Laboratories, Aberdeen, MD, from Ballistics Research Laboratories Report No. 878 (September, 1953), by T. E. Turner, B. L. Hicks, and G. Reitwiesner. It was prepared for reproduction by S. Poley with the aid of an IBM card-controlled typewriter at the Watson Scientiﬁc Computing Laboratory. Tables of Eτ for J up to 40 and values of κ = 0, 0.1, 0.2, 0.3, . . . 1.0 are given by G. Erlandsson, Arkiv för Fysik, to be published. C. Appendix V: Transition Strengths for Rotational Transitions, pp. 557-559 SUMMARY � Intensity of a transition between rotational levels Jkl and Jmn is proportional to ��2 �� (κ) = (2J + 1) �(µ x ) J J � � (µ x )2 x S Jkl Jmn kl mn Here µ x is the dipole moment along one of the principal axes of inertia (x = a, b or c), and S is the quantity tabulated here as a function of initial and ﬁnal state and of the asymmetry parameter κ. However, each value has been multiplied by 104 to eliminate decimal points. The upper sign for values of K applies to transition subbranches listed in the two left-hand columns, and the lower sign to those in the right-hand columns. The axis along which a dipole moment is required to produce a given transition is indicated by a superscript to the left of the subbranch designation. Thus c Q10 indicates a Q branch (ΔJ = 0) with a change in K−1 of 1, a change in K1 of 0, and that a dipole moment µc along the c axis is required for the transition. For further discussion see Chapter 4. [Tables in this appendix are taken from P. C. Cross, R. M. Hainer, and G. W. King, J. Chem. Phys. 12, 210 (1944).]