Contains reports on two research projects

Tinkham, M.

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V. MICROWAVE SPECTROSCOPYProf. M. W. P. Strandberg J. G. Ingersoll I. H. Solt, Jr.B. F. Burke J. D. Kierstead P. A. TateC. F. Davis, Jr. M. Peter M. TinkhamA. PARAMAGNETIC RESONANCE IN OXYGEN GASStarting with the improved theory of the field-free energy levels and state functionsof the oxygen molecule reported earlier (1), precise Zeeman effect calculations havebeen made to locate individual lines of the spectrum. About 40 X-band and 40 S-bandtransitions have been studied. For each of these, the constant term and slope of theenergy level separation at the appropriate value of the external field Ho (obtained pre-viously by graphical interpolation (2) have been calculated. From these quantities, mag-netic fields for the experimental resonance frequencies 9396 Mc/sec and 2987 Mc/sechave been calculated to within a few gauss. These calculated fields have been comparedwith the experimental X-band results reported previously (1) and with the S-band spec-trum obtained subsequently. In this S-band spectrum, 78 lines were resolved in theregion between 1980 gauss and 9300 gauss. In essentially all cases, the theoretical fieldchecked with the experimental field to within 8 gauss; most were much closer. A smallsystematic deviation is being investigated. With this number of lines calculated exactly,it should be possible to identify most of the remaining lines by combining the graphicallyestimated positions with the temperature dependence of the intensity (which gives anestimate of K) and with the results of the circular polarization experiments (which willdiscriminate between AM = + 1 transitions).With the line identification program well under way, a start has been made on line-width studies. The widths of 6 lines of the X-band spectrum have been carefully meas-ured at 800 K and at pressures of 1 to 4 mm Hg. Although there is a small extrapolatedwidth at zero pressure because of inhomogeneity of the magnetic field over the cavity,fitting the slope of the pressure dependence by least squares should give the correct linebreadth parameter in gauss/mm Hg. This is then converted to the more meaningful fre-quency width by use of the slope of the energy level separation mentioned above. (Thefact that Beringer and Castle (3) incorrectly made this conversion with Vo/Ho ratherthan dvo/dHo largely accounts for their anomalous linewidth results.) The result,Av = 6.05 +.10 Mc/mm Hg, for the lines K = 1, J = 2, M = -1-0, 0- 1, and 1- 2 indi-cates, as might be expected, no appreciable M dependence of the collision-broadeningcross section. This result, and the results Av = 5.5 + .1 Mc/mm for K = 3, J = 4,M = -1-0; Av = 5.1 + .1 Mc/mm for K = 5, J = 6, M = -1- 0; and Av = 5.1 + .1 Mc/mmfor K = 9, J = 10, M = 0-1 indicate a small K dependence which roughly fits the form1av = C + C2 K1 2-15-(V. MICROWAVE SPECTROSCOPY)predicted by some theoretical considerations. Further linewidth studies to check thisdependence, the J dependence, and the temperature dependence are planned.M. TinkhamReferences1. Quarterly Progress Report, Research Laboratory of Electronics, M.I.T., July 15,1953, pp. 28-292. Quarterly Progress Report, Research Laboratory of Electronics, M.I.T., April 15,1953, p. 193. R. Beringer, J. G. Castle, Jr. : Phys. Rev. 81, 82, 1951B. CIRCULAR POLARIZATION IN CAVITIESIn certain magnetic resonance experiments it is desirable to excite a single, circu-larly polarized mode in the cavity containing the sample under study. In this case, theinstantaneous H vector at the sample rotates in a plane with constant magnitude ratherthan oscillating along a line, as in the usual linear polarization. Since the perturbativeHamiltonian can quite generally be writtenf = gpH J= gp H J + - (H J + H )z z 2 + _ +it is clear that such circularly polarized radiation (being either H+ or H_, dependingon the sense of the rotation) will only induce transitions between states connected bymatrix elements of J_ or J+, respectively, but not both. Thus we obtain a sharpexperimental distinction between AM = -1 and AM = + 1 transitions. This techniqueallows a determination of the sign of the gyromagnetic ratio of the absorber.An immediate application in this laboratory will be in the experimental analysis ofthe complex spectrum of oxygen gas. In this molecule one can have absorptive transi-tions of either AM = + 1 or - 1, depending on the way the electronic spin and the rota-tional angular momentum are coupled in the particular states involved. Thus the use ofcircular polarization will divide the spectrum into two groups, giving considerable aidin the analysis of the spectrum. Another prospective application is in refining measure-ments of the selection rules governing transitions in paramagnetic salts in which thecrystalline electric field partially breaks down the angular momentum quantization.The experimental method of providing such a polarized field is to excite the twodegenerate orthogonal TEll1 modes in a cylindrical cavity 90 *out of phase. These modesare excited through a hole precisely centered in one end to maintain the degeneracy ofthe cylindrical symmetry. This hole couples into the center of the side wall of a piece-16-(V. MICROWAVE SPECTROSCOPY)of square waveguide in which the two orthogonal TE 0 1 modes are equally excited. Onecavity mode is excited by the transverse H of one guide mode; the other is excited bythe longitudinal H of the other guide mode. The phase and amplitude of the two standingwave modes at the hole are independently adjusted by orthogonal shorting vanes in theend of the guide. One can readily show that the two incident waves must be phased togive linear polarization along one diagonal of the guide, whereas the reflected wavebearing the information from the cavity is linear along the other diagonal. A piece ofmicrowave plumbing has been built to couple properly into these modes. With this appa-ratus, a klystron has been stabilized to the cavity with a modified Pound-Zaffaranoscheme, and some preliminary tests have been made. The relative signal strengths onreversing the sense of the circular polarization indicate that a 20-db enhancement of onemode over the other is easily obtainable. A vacuum-tight model for the oxygen experi-ment is under construction.M. Tinkham-17-

Microwave Spectroscopy

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Microwave Spectroscopy

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