Contains reports on three research projects

Adams, N. I., III

Bitter, F.

Brossel, J.

Dickinson, W. C.

Eshbach, J. R.

Hillger, R. E.

Johnson, H. R.

Koster, C.

Loomis, C. C.

Sagalyn, P. L.

Wimett, T. F.

DSpace@MIT

V. RADIO-FREQUENCY SPECTROSCOPYA. MOLECULAR-BEAM RESEARCHProf. J. R. Zacharias V. JaccarinoProf. B. T. Feld J. G. KingDr. J. Levinson C. KosterJ. T. Eisinger W. B. PohlmanInvestigation of Quadrupole Interaction in HomonuclearDiatomic Molecules of Spin 3/2The perturbation of the energy levels due to the quadrupole interaction operator ofthe formHe Q q J 3i .)q= -ZJ(2J -l)i l (Zil - 1)J 3 (il " )2+ (i. J) - iJ 2 3(i 2  iz j) -where J = rotational quantum number of moleculeand i 1 = i2 = 3/2 spin of identical nucleiwas investigated. It was found that a given J-level was split into a number of levelscorresponding to different values of F, the total angular momentum quantum number ofthe molecule. In some cases there were two levels corresponding to a given J and Fvalue. Due to the difference in symmetry properties of the unperturbed J-levels cor-responding to odd and even values of J, different expressions for the energy levels arisein these two cases. The following results were obtained.AEJ=0; = 0e QqJ= 1EF 2e Qq211-51 + 5472 1340110-34-(V. RADIO-FREQUENCY SPECTROSCOPY)J >, 2 (J even)FJ-2J-1J+ 1J+2AEe2QqAEe Qq1 J(J+ 1)+ (2J - 1)(2J + 3)(J large)112J > 3 (J odd)AE----- (J large)e QqJ - 1+ 36(23 + 3)(2J - 1)-15(2J2 - J - 12) (6J2 - 75J - 216) 2 + 24(4J 2L12(2J2(2J + 3)(2J - 1)6+ j16(2J 2 +22J - 9)2 + (J -51)(J + 2)(2J - 1)(2J + 3)1 -z 2 - 5j + 92(2J + 3)(2J - 1) 2(2J + 29J - 45)2 + 8 J(2J - 1)(2J +102(2J + 3)J2(2J + 3)C. KosterReferences1. For the form of quadrupole operator in a symmetric top typePhys. Rev. 72, 715 (1947).2. For matrix elements necessary in calculation, H. M. Foley:molecule, J. M. Jauch:Phys. Rev. 71, 747 (1947).-35-J+ 12(2 - 1)AEe QqJ-22(2J -1)J+ 1J+ 21 133+ 1205)(J + 2)1-13-60- 9)(J 2 - 1)(V. RADIO-FREQUENCY SPECTROSCOPY)B. NUCLEAR MAGNETIC RESONANCEProf. F. Bitter J. BrosselDr. W. C. Dickinson P. SagalynN. I. Adams III T. Wimett1. The Double Resonance Method for the Investigation ofAtomic and Nuclear MomentsWork on the optical detection of r-f resonance has been continued, and it has beendecided to adopt the name above for the method, since the essential feature is thesimultaneous application of two resonant frequencies which have a common energy level.Experimentally the work has been confined to increasingthe sensitivity of the apparatus, and to the constructionof equipment for accurate field measurements. A de-tailed theoretical analysis of effects to be expected inmercury has been completed, and a report is beingprepared. An unexpected result is the complex struc-ture of the resonance lines predicted by the Rabi-Maiorana (1) formula for angular momenta greater thanone-half. For example, the average probability ofFig. V-l Resonance curvefor angular momentum quan- finding a particle having a resultant angular momentumtum member unity. quantum number unity, and known to be at some time ina state with m = 0, in a state m = + 1 at some much later time, is shown in Fig. V-1.The transitions are produced by an r-f rotating field of angular frequency w and amplitudeH1 perpendicular to a constant field Hz . The parameterH zyH1measures the approach to the resonance condition w = yHz, where y is the gyromagneticratio.Experimental verification of predicted results is being undertaken.F. Bitter, J. Brossel, P. SagalynReference1. I. I. Rabi: Phys. Rev. 51, 652 (1937).-36-T+IW-JIFig. V- 2 Two views of the new barrel-type electromagnet.Fig. V - 3 Cross section of the electromagnet.(V. RADIO-FREQUENCY SPECTROSCOPY)2. A New Barrel-Type ElectromagnetA magnet designed jointly by one of us and Everett Reed of Arthur D. Little Inc. hasbeen completed and installed. Two photographs of the instrument are shown in Fig. V-2,and a cross-section is shown in Fig. V-3. Preliminary tests have yielded the resultssummarized in Fig. V-4. The maximum temperature of the copper for full powerFig. V-4 Field in kilogaussPOWER IN KILOWATTSusing 11-inch diameter pure iron pole pieces.(20 kw) was about 70 0C, or 160°F. Field measurements were made with a new type ofgaussmeter constructed at our suggestion by the Rawson Instrument Company, and nowcommercially available. The gaussmeter consists of a coil rotated at constant fre-quency in the unknown field. The induced current is rectified and measured on a metercalibrated to read directly in gauss on scales of 0-500; 5, 000; or 50, 000. Preliminarydata on the uniformity of the field produced by 11-inch diameter pure iron pole-piecesmay be summarized by stating that for gaps up to almost one-half of the pole diameter,the field was uniform to better than 1 percent in a centrally located volume with a diam-eter about one-half that of the poles themselves. At points about three-fourths of theway out from the middle, the field in general differs by less than 5 percent from itsmaximum value. At small separations and low inductions the uniformity is considerablybetter than is indicated above.A complete report is being prepared.F. Bitter, N. I. Adams-38-(V. RADIO-FREQUENCY SPECTROSCOPY)3. Factors Influencing the Positions of Nuclear Magnetic ResonancesA doctoral thesis entitled "A Study of the Time Average Magnetic Field at the Nucleusin Nuclear Magnetic Resonance Experiments" has been written and submitted to thephysics department. W. C. Dickinson4. Deuteron-Proton Moment RatioOur major effort has been directed toward adjusting the Helmholtz coils for maximumfield homogeneity and obtaining reproducible narrow proton resonance lines. Line widthsof less than a hundredth of a gauss have been obtained (see Fig. V-5), and the remainingFig. V-5 (top) Very sharp nuclear magneticresonance absorption line obtained in a circuitwithout modulation. (bottom) Dispersion lineobtained under similar conditions.line broadening due to the field mightbe reduced by a factor of five or moreif a more sensitive probe arrangementwere used for measuring field varia-tions. Experience indicates that ade-quate adjustments may very probablybe made with the position screws andrelative current control on the two fieldcoils to produce a field uniform to onepart in a million over a volume ofabout a cubic centimeter.The main difficulty encountered inhomogenizing the field has been in dis-playing and examining the field varia-tions while making the adjustments.The method used has been to observeon an oscilloscope the proton nuclearresonance from a small oil sample ina probe which is moved about in thesinusoidally modulated field. The pre-cision of this scheme is limited by thebroadness of the "wiggles" which areobserved and also by field fluctuationswith time.The problem of field instability resulting from rapid temperature fluctuations (as highas 0. 10 C in five minutes) in the cooling system for the coils has been solved by passingtap water through a 150-gallon mixing tank before running it through the cooling system.Still remaining is a slow drift of the order of a quarter of a degree per hour. The re-sulting field drift (one gauss per hour) is sufficient to make it impossible to maintain thefield at a resonance position long enough to make adjustments of the order of one part-39-(V. RADIO-FREQUENCY SPECTROSCOPY)in a million.In order to eliminate the possibility of line broadening due to both the amplitude andfrequency of the field modulation which is generally used in nuclear resonance experi-ments, a circuit has been developed which requires no modulation and makes possiblethe direct observation of a resonance line. The circuit consists of a bridged-T nullnetwork (mentioned in the Quarterly Progress Report, April 15, 1950) containing thesample coil and followed by an r-f amplifier, a rectifier and balanced d-c amplifier whichdrives a recording milliammeter directly. Stability of the unbalanced voltage from thenull circuit is very important in obtaining accurate line shapes, a requirement adequatelyfulfilled by the null-T circuit. Examples of resonance lines obtained with this recordingarrangement are shown in Fig. V-5. The resonances were obtained from protons in anoil sample about 4 mm in diameter and length at a thousand gauss.T. F. WimettC. MICROWAVE SPECTROSCOPYProf. M. W. P. Strandberg Dr. R. B. Lawrance H. R. JohnsonDr. R. E. Hillger J. R. Eshbach C. C. LoomisDr. G. W. King B. V. Gokhale M. T. WeissJ. G. Ingersoll1. Hydrogen Deuterium SulphideThe resonant molecular absorption between rotational energy levels was measuredfor hydrogen deuterium sulphide (HDS) in the microwave region. Twelve lines wereobserved in the frequency range 7000 Mc/sec to 76, 000 Mc/sec for HDS 3 , five lineswere observed for HDS 3 4 , and one line for HDS 3 3 . Stark-effect measurements on severalof these lines yield the permanent electric dipole moment of HDS32 to be 1.02 + 0. 01debye units. The calculated absorption coefficient is given for each line. The data issummarized in the tables on p. 41.A simple theory, correct to the first order, was developed to correct for the centri-fugal distortion of a molecule. Using the matrix elements derived by H. H. Nielsen (1)for the general polyatomic molecule, the true absorption frequency is obtained in termsof a rigid rotor frequency and five centrifugal distortion constants. The theory wasevolved for immediate application to the asymmetric HDS molecule, but the formulationis perfectly general and can be used for other types of molecules. The value of thistheory lies in the fact that these same distortion constants can be calculated with aknowledge of the vibrational spectra and structure of the molecule which allows one eitherto correct doubtful assignments in infrared and Raman spectra or to predict with greateraccuracy the existence of new rotational absorption lines. The experimental values ofthe centrifugal distortion constants were determined for HDS 3 2 by a least-squares fitting-40-Rotational Absorption Frequencies of HDS 3 2 in the Microwave RegionInitial State Final State Frequency (Mc/sec) Absorption-l(T = 195°K)(cm-1-41 1, 0 51, 073.27 2.9 x 10-522,1 22,0 11,283.83 2.3 x 10-432, 2 32, 1 53,200.93 3.0 X 1043,2 43,1 10,861.07 1.3 X 105-553, 3 53,2 40, 929.20 1.1 X 10-664, 3 64,2 7, 936. 74 3.2 X 1074,4 74, 3 27, 566.31 2. 1 X 10-584, 5 84,4 75, 551.73 7.6 x 10-95, 5 95,4 17,212.61 2.2 X 10-6-6105, 6 105, 5 47,905.36 8.0 x 10116,6 116,5 10,235.81 1.5 X 10-712, 126,6 28,842.84 4.8 X 10- 70 ,7 6, 6Compound34HDSHDS3 4HDS3 4HDS3 4HDS3 4HDS 3 3The HDS 3 3AbsorptionTransition1,22,32,43,74,22,line is+ 11 1,01 22,02 32, 12 43, 14 74, 31 + 22, 0the mosFrequencies of HDS 3 4 and HDS 3 3Frequency (Mc/sec)50, 912.2711,235.4552, 979.6710, 802.3627, 392.0011,258.21t intense of a group of lines.Absorption(T = 1950K)(cm --1-51.3 x 101.0 x 1061.4 x 10-55.9 x10- 71.1 x 10 - 69.1 x10-8-41-(V. RADIO-FREQUENCY SPECTROSCOPY)process and are compared with the calculated values from vibrational data.Distortion Coefficient Calculated Value Experimental Value(cm - I ) (cm-1 )R 5  + 2.21 X 10 + 8.02 X 10-5 -56 - 2.69 105 - 2. 531x 10-4 -4DK + 9.16 10 + 9.133X 10-4 -4DK - 1.64 X 10 - 1.403X 10R 6  - 1.90 X 10- 5  - 1.067x 10 - 5The inertia defect A, which exists for all planar molecules, was computed fromvibrational data and used with the data obtained from the rotational absorption spectrumto obtain the effective moments of inertia of HDS 3 2 . The known microwave spectrumdoes not provide sufficient information to make this calculation directly. The resultingvalues are 40 2A = - 0. 244 X 10 gm/cma = 9. 682 cm-1= 2.890 x 10 - 4 0 gm/cm2Ib = 4. 844 cm = 5. 777 x 104 0 gmcm2I c = 3.140 cm -= 8.910 x 10-40 gm/cm2The equilibrium values of the moments of inertia were not determined because of lackof knowledge of the anharmonic force constants of the molecule. R. E. HillgerReference 1. H. H. Nielsen: Phys. Rev. 60, 794 (1941).2. Nuclear Magnetic Moment of S33The nuclear magnetic moment of S3 3 has been measured by means of the Zeemaneffect on the molecule carbonyl sulphide (OCS). The observed line intensity of the largestline of the hyperfine pattern (the coincident F = 5/2-- 7/2 and 3/2 -- 5/2 line and nearby1/2-- 1/2 line) of the rotational absorption J = 1 to J = 2 is shown in Fig. V-6 plotted asa function of the magnetic field. Theoretical curves are also shown for several valuesof the parameter gN - gmol. From this plot we obtain 1gN - gmol = 0. 57 + 0. 04 nuclearunits. gmol is given by Jen (1) and by Coles (2) and from their measurements is foundto be about j0. 031 with the sign undetermined. Since the sign of gN - gmol is undeter-mined in our experiment, the correction for gmol cannot be applied at this time. The-42-(V. RADIO-FREQUENCY SPECTROSCOPY)MAGNETIC FIELD IN KILOGAUSSFig. V-6 Relative peak intensity vs. magnetic field for the coincident F = 3/2+ 5/2,F = 5/2 - 7/2 transitions of the J = 1 - 2 absorption of OCS 3 3 (including contributionsfrom the nearby F = 1/2 - 1/2 transition).spin of S 3 3 is known to be I = 3/2 (ref. 3) and the nuclear magnetic moment is given byrN = NI. Thus we find for S 3 3 that ILN = 0.85 + 0. 10 nuclear magnetons, where partof the inaccuracy is due to the undetermined signs. A similar measurement with whichwe are in agreement has been made by Jen (1).J. R. Eshbach, R. E. HillgerReferencesC. K. Jen: Harvard Univ., Cruft Lab. Progress Report No. 14, p. 41 (Jan. 1, 1950).D. K. Coles: Advances in Electronics 23, 313 (1950).C. H. Townes. S. Geschwind: Phys. Rev 74 62 h 194RY3. StibineThe search for the J = 0 + 1 transition in the molecule SbD 3 has been completed. Theprocess of this search was interrupted to find transitions in the impurity molecules,phosphine and arsine. With the finding of these transitions the spectroscope could beused to purify the sample positively and thus to ensure that the search was conducted withstibine in the absorption cell. The following dipole moments have been measured forthese three molecules.-43-(V. RADIO-FREQUENCY SPECTROSCOPY)Molecule Dipole Moment (debye units)phosphine 0.55 + 0.01arsine 0.22 + 0.02stibine 0. 116 + 0.003A report on the quadrupole coupling in these molecules, and their structure, is inprogress. C. C. Loomis4. Ketene1 12 16Twelve lines in the microwave spectrum of ketene, H C 0 have been observedand identified, and the frequencies of these lines have been measured to six figures.Nine of the lines are J = 0-1, 1-2, and 2--3 rotational transitions for the molecule inthe ground vibrational state (Table I). The corresponding undistorted reciprocal mo-ments are a = 280, 000 Mc/sec (assumed the same as that for formaldehyde, H C 120 16b = 10, 293. 28 Mc/sec; and c = 9, 915. 87 Mc/sec (from measured lines, corrected forcentrifugal distortion). Symmetric top centrifugal distortion theory, carried to firstorder, gives a good fit to the observed lines, except the 0-1 line, with D = 0. 0015Mc/sec, and DJK = 0. 478 Mc/sec. (There is a 0. 63-Mc discrepancy between measuredand calculated values of the 0-1 line frequency. ) Stark-effect measurement gives for thedipole moment in the ground vibrational state, for the 0-1 transition, the value 1. 35+ 0.05 debye units. This is thought to be in reasonable agreement with previous studiesusing the temperature dependence of the susceptibility, which yield 1.45 debye units (1).Three of the observed lines are 0-1 transitions with the molecule in an excited vibra-tional state (Table II). Relative intensity measurements on these lines at room tempera--1ture give the associated vibrational frequencies as 420, 460, and 570 cm-1 , within about-120 cm-1. Start-effect measurement gives for the dipole moments of these states 1. 31,1. 31, and 1. 37 debye units respectively, and line frequencies give for (b + c), extrapo-lated to zero centrifugal distortion, the values 20, 267. 18 Mc/sec, 20, 220. 65 Mc/sec,and 20, 232. 34 Mc/sec respectively. There is some correlation with infrared absorptionmeasurements on the same molecule, but more microwave line-intensity measurement,including temperature dependence studies, is definitely indicated.Predictions of approximate frequencies to be expected for heavy ketene (D2C 2 O 1 6 )have been made; measurement of the 0.,1 and 1-2 transitions of this isotopic moleculewill enable the average structure in the ground vibrational state to be completely deter-mined. (Two values of b and two values of c enable calculation of three bond distancesand one angle.) Measurement of the vibration satellites on the 1-2 transition of ordinaryketene will yield the average reciprocal moments for the excited vibrational states, andmeasurement of these satellites for heavy ketene will enable calculation of the completeaverage structure in each of the accessible vibrational states. Intensity calculations-44-Table ILines in the Ground Vibrational StateCalculated Measured CalculatedIntensity Frequency Frequencycm-1 Mc/sec* Mc/sec3.1425.152.955. 084. 7212.0220.039.339. 3-6x 10x o-6x10-6x 10-6xlOx 10-6x1010-6X10-6-6Xl - 6209.76417.90038.80793.62625.68057.92190.24615.88617.3020,209. 1340,417.8440, 038.9140,793.7360,625.7060, 058. 0361, 190.2760,615.7860, 617.34Literal Frequency4Dj0.75(b - c)6 - 32D(b - c) - 4DJK - 3 2DJ(b - c) - 4DJK - 32Dj3(b - c)6 - 108 D1.5(b - c) - 0.469(b - c) 6 - 6DJK - 108Dj1.5(b - c) - 0.469(b - c)6 - 6DJK - 108D24DJK - 108DJ3(b - c)6 - 24DJK - 108 DExperimental errors are + 0.05 Mc/sec at 20, 000 Mc/sec, + 0. 10 Mc/sec at 40, 000 Mc/sec, and + 0. 15 Mc/sec at60, 000 Mc/sec.Table IIThe Vibrational Satellites on the 000 * 101 TransitionMeasured Frequency Measured Measured CalculatedMc/sec Relative Dipole Moment Vibration LineIntensity (Debye units) Frequency (cm- 1 )20,209.76 1.00 1.35 ground state20,267. 17 0.41 1.31 420 + 2020,220. 64 0.30 1.31 460 + 2020,232.33 0.18 1.37 570 + 20Transition101202212211303313312322321101111110202212211221220(V. RADIO-FREQUENCY SPECTROSCOPY)indicate that these lines will be detectable in present systems. Measurements of theAJ = 0, AK = 0 lines, of which a large number occur in the microwave region, will givea measured value for a. These latter measurements, plus measurements of the 3-4and higher lines with AJ = 1, will yield data from which a more complete analysis of thecentrifugal distortion could be made.Intensity measurements quoted in this report were made by Dr. J. Goldstein atHarvard, who first found the lines of the 0 1 transition in Spring, 1949. Stark-effectmeasurements and frequency measurements of the 0-1 and 1-2 transitions were made byProf. M. W. P. Strandberg.Further investigation of the microwave spectrum of ketene is continuing.H. R. JohnsonReference1. N. B. Hannay, C. P. Smyth: J. Am. Chem. Soc. 68, 1357.-46-

Radio-Frequency Spectroscopy

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Radio-Frequency Spectroscopy

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