Contains research objectives, summary of research and reports on four research projects.Joint Services Electronics Programs (U. S. Army, U. S. Navy, and U. S. Air Force) under Contract DAAB07-71-C-0300National Science Foundation (Grant GP-28679)National Bureau of Standards (Grant NBS2-9011)U. S. Air Force - Office of Scientific Research (Contract F44620-72-C-0057

Apt, Jerome, III

Cooke, W. B.

Jacobson, A. G.

Kleppner, Daniel

Littman, Michael G.

Mattison, E. M.

Phillips, William D.

Pritchard, David E.

Wieman, C. E.

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III. ATOMIC RESONANCE AND SCATTERINGAcademic Research StaffProf. D. KleppnerProf. D. E. PritchardProf. P. ZimmermannGraduate StudentsJ. Apt III W. E. Cooke E. M. MattisonG. M. Carter M. G. Littman W. D. PhillipsRESEARCH OBJECTIVES AND SUMMARY OF RESEARCHOur interests center on the structure and interactions of atoms and simple mole-cules, and on their interactions with radiation at both optical and radio frequencies.Experimental methods involve colliding beam scattering, atomic and molecular beamresonance spectroscopy, high precision maser spectroscopy on stored atoms, and opti-cal fluorescence with tunable lasers.1. Van der Waals MoleculesVan der Waals molecules are held together by long-range interatomic forces, incontrast to the chemical forces which hold together normal molecules. Because theseforces are roughly 100 times weaker than chemical forces, van der Waals moleculesare frail and difficult to observe. We have produced a molecular beam of isolated, para-magnetic van der Waals molecules and are executing measurements on their optical andmagnetic properties.2. Atomic Scattering StudiesWe are continuing our studies of atomic scattering using polarized atomic beams.We have recently installed a new source which improves our ihtensity substantially, andpermits us to extend our studies to collisions that form complexes. Work is under waytoward the use of a tunable dye laser to produce a beam of excited-state atoms for usein our collision studies.3. High Precision Studies with the Hydrogen MaserWe are nearing completion of a program to measure the magnetic moments of hydro-gen and deuterium to very high precision. The results bear on the fundamental theoryof magnetic interaction in simple atoms, and are of use in evaluating fundamental con-stants. During the past year we have completed a measurement of the magnetic momentof the deuteron in terms of the Bohr magneton.4. Interactions in the Excited StateWe have initiated a program to measure atomic interactions in the excited state. Ourfirst efforts were directed toward creation of an optically excited diatomic complex. WeThis work is supported by the Joint Services Electronics Programs (U. S. Army,U.S. Navy, and U.S. Air Force) under Contract DAAB07-71-C-0300, the National ScienceFoundation (Grant GP-28679), the National Bureau of Standards (Grant NBS2-9011) andby the U. S. Air Force - Office of Scientific Research (Contract F44620-72-C-0057).QPR No. 108(III. ATOMIC RESONANCE AND SCATTERING)believe that we have evidence for the complexes. The results are of interest in thetheory of superradiance, and also because they demonstrate a previously unobservedreaction process - the formation of a molecule from the continuum at low pressurethrough absorption of a photon.D. Kleppner, D. E. PritchardA. VAN DER WAALS MOLECULESJoint Services Electronics Programs (Contract DAAB07-71-C-0300)NSF (Grant GP-28679)E. M. Mattison, J. Apt III, D. E. Pritchard, D. KleppnerA molecular-beam apparatus has been constructed for studying the magnetic-resonance spectrum of van der Waals molecules. The design philosophy of the machinewas described in a previous report. A diagram of the apparatus is shown in Fig. III-1.The source chamber is constructed from a stainless-steel cross of tubing of 12 in. diam-eter. It is pumped by an unbaffled 10-in. diffusion pump that has a speed of 4200 liters/second, which is adequate for handling noncondensable gases from the jet source.The entire source apparatus, including oven and skimmer, is suspended on a carriagethat rotates about a point in the first deflecting magnet. The spin state is selected bymoving the carriage. The oven's body, top and nozzle are equipped with independentheaters and thermocouples. The height and direction of the oven, the lateral position ofthe skimmer, and the distance between the skimmer and nozzle, can each be controlled.A collimating chamber, downstream from the source chamber, provides differentialpumping by means of a 600 liters/second diffusion pump.After leaving the collimating chamber, the beam passes through the magnet chamber.SOURCE COLLIMATION MAGNET DETECTORCHAMBER CHAMBER CHAMBER CHAMBERA C BMAGNET MAGNET MAGNETMMAGNETYOKE MAGNET 10COILS DIFFUSION4" PUMPDIFF1 ION DIFFUSION ARMCODIFFUSION PUMP IRONPPUMPSTAINLESS STEELFig. III-1. Molecular-beam apparatus for studyingvan der Waals molecules.QPR No. 108(III. ATOMIC RESONANCE AND SCATTERING)This chamber, which is fabricated from stainless-steel tubing, has a flat floor with mag-netic steel inserts to conduct the flux of the deflecting and homogeneous magnets. Thisarrangement allows the magnet coils to be external to the vacuum.The detector housing is attached to the exit of the magnet chamber, and is pumpedby a Vac-ion pump. The detector includes a hot-wire surface ionizer, a mass spectrom-eter, and an electron multiplier. The detector has a maximum count rate of 106 countsper second and a measured overall detection efficiency of approximately 0. 3.We have produced beams of potassium atoms, with the oven operated as an effusivesource, and have observed transitions between the Zeeman levels of the upper hyperfinestate. The width of this resonance, approximately 40 kHz, agrees with that calculatedfrom the resonance coil length and estimated beam velocity.Work is in progress to produce a potassium-argon beam.References1. Quarterly Progress Report No. 104, Research Laboratory of Electronics, M. I. T.,January 15, 1972, pp. 62-66.QPR No. 108(III. ATOMIC RESONANCE AND SCATTERING)B. MAGNETIC MOMENT OF THE DEUTERONJoint Services Electronics Programs (Contract DAAB07-71-C-0300)NBS (Grant NBS2-9011)W. D. Phillips, W. B. Cooke, D. KleppnerExisting high-precision measurements of the deuteron magnetic moment have beenperformed by means of nuclear magnetic resonance (NMR) with molecular samples.1-3The proton and deuteron NMR frequencies are compared in samples such as H20 andD20, H2 and D2, and HD. In all but HD the proton and deuteron are in different molec-ular environments, and therefore have different diamagnetic shieldings. Even in HD,the shielding for the two atoms in the molecules is not exactly the same. Since the dif-ferences in shielding are of theoretical interest, it is important to have a measurementof the deuteron moment that is independent of any molecular environment. We have madepreliminary measurements of the deuteron/electron magnetic-moment ratio in atomicdeuterium with a high-field deuterium maser. We expect the final precision of our mea-surement to be 1-2 X 10-8 compared with 5 X 10-8 for the best molecular measure-ments.2 We use a method similar to that of Winkler at al.4 for the measurement of theproton/electron moment ratio.1. TheoryThe energy levels of ground-state deuterium in a magnetic field are shown inFig. 111-2, where mj and m I refer to the projections of the electron and nuclear spinson the direction of the magnetic field.The energy level in Fig. III-2 given by the Breit-Rabi formula for deuterium isE (m, m.) 2 1/20 mvR ± (+R) 1 + 4m+ (1)h 6 J 2 3 v (1+R) V2 ((+R)where vo is the hyperfine separation, vj = -gyoH/h is the field-coupled electron spinflip energy, R = gi/g J , and ± refers to the sign of m .By means of microwave- and radio-frequency double resonance, the frequencies ofthe transition 2 -5 and one of the transitions a, b, c, and d are measured simultaneously.These two frequencies can be used with Eq. 1 to give the moment ratio R. Since cor-rections to free space of atomic moments are calculable for hydrogenic atoms,5 thisleads to the deuteron moment in Bohr magnetons.There are several systematic errors which can affect the measurement of themoment ratio: Collisions between deuterium atoms during the measurement processcause frequency shifts attributable to spin exchange. Collisions of the atoms with theQPR No. 108 a(III. ATOMIC RESONANCE AND SCATTERING)walls of the storage bulb cause a shift in the hyperfine frequency. Asymmetric distri-butions of magnetic-field inhomogeneities cause a shift in the observed frequency fromthat expected on the basis of the average magnetic field. If the microwave cavity intoELEVEL mj m1 +1/2 +12 +1/2 03 +1/2 -1-MASER TRANSITIONHc 4 -1/2 -d 5 -1/2 06 -1/2 +1Fig. III-2. Energy levels of deuterium in the ground state.which the deuterium atoms radiate when they undergo an electron spin flip is not tunedto the spin-flip frequency, there will be a cavity pulling of the frequency. Similarly, ifthe circuit that drives the nuclear spin flip is not tuned to the nuclear frequency, therewill be a shift.Fortunately, the error in the moment ratio produced by most of these effects changessign when a different nuclear transition is used. For example, when the cavity pullingcauses a positive shift for transitions a and c, it is negative for b and d. Because thefrequency of each nuclear transition is different, pulling caused by mistuning of the cir-cuit driving these transitions does not reverse sign in a simple way. This effect, how-ever, can be made quite small. For all the other effects, the theoretical expectationis that averaging the results for all four possible nuclear transitions should result in avalue for the moment ratio free of the systematic effects described, except for a smallfraction of the wall shift, which can be corrected for.2. ExperimentThe experimental procedure for this measurement is basically that used by Winkleret al.4 in their measurement of the proton moment. It was necessary, however, to makeQPR No. 108(III. ATOMIC RESONANCE AND SCATTERING)a substantial improvement over the absolute precision that they achieved in order toobtain the same relative precision. This is because the field-coupled part of the nucleartransition frequency is approximately 7 times smaller for deuterium than for hydrogen.The linewidth, however, is the same. Thus to achieve the same 1 X 10 - 8 precision inthe deuteron moment as was obtained for the proton moment, 7 times greater absoluteprecision in the transition frequency is required.The major limitation on the measurement of Winkler et al. was the inhomogeneityshift. By greatly reducing the magnitude of this shift and using different transitions tocancel the remaining shifts, we have been able to approach the desired precision.The inhomogeneity shift in the proton moment experiment was caused by a ratherlarge collimator on the neck of the maser storage bulb. The collimator was made ofTeflon tubes and constituted ~3% of the bulb volume. By using glass collimators thatoccupy only 0. io of the bulb volume, we have greatly reduced the inhomogeneity shift.3. ResultsThe result of measurements taken thus far isgl/g = 2. 332172696 X 10-4This result is uncorrected for systematic effects and represents simple averaging ofmeasurements on all four nuclear transitions. The statistical uncertainty is less than-81 X 10 The question of uncertainty attributable to systematic errors is under consid-eration. Tests with different sized collimators have shown no inhomogeneity shift.Results of spin-exchange measurements made by varying the density of atoms in thestorage bulb show no effect, in agreement with theory, but the tests are only accurate-8to 3 X 10 because of the poor signal-to-noise ratio obtained at the low density that theyrequire. We are currently studying the wall shift. Cavity pulling has been shown tobehave as expected theoretically and should cause no error when all transitions are aver-aged. The effects of mistuning the nuclear frequency circuits have been calculated to benegligible.References1. B. Smaller, Phys. Rev. 83, 812 (1951).2. T. F. Wimett, Phys. Rev. 91, 499A (1953).3. T. F. Wimett, Ph. D. Thesis, Department of Physics, M. I. T. , February 1953.4. P. F. Winkler, D. Kleppner, T. Myint, and F. G. Walther, Phys. Rev. A 5, 83(1972).5. H. Grotch and R. A. Hegstrom, Phys. Rev. A 4, 59 (1971).QPR No. 108(III. ATOMIC RESONANCE AND SCATTERING)C. DIAMAGNETIC SHIELDING OF H2Joint Services Electronics Programs (Contract DAAB07-71-C-0300)NBS (Grant NBS2-9011)A. G. Jacobson, W. D. Phillips, D. Kleppner1. Introduction and BackgroundThe diamagnetic shielding constant for the proton in molecular hydrogen, (H 2), hasreceived extensive theoretical study, and is the most likely candidate for ab initio cal-culation. As part of an effort to obtain a precise absolute experimental value for 0-(H2)we have compared the NMR frequency of protons in H2 and in tetramethylsilane,(CH 3 )4 S i, a popular NMR standard. A companion experiment to compare the protonfrequency in tetramethylsilane (TMS) and in atomic hydrogen is under way in our labora-tory. The diamagnetic corrections in hydrogen are known with great precision and thetwo experiments will be combined to yield an absolute value for a (H2).The shielding constant a is related to the observed NMR frequency v byv = (1 - ) (y/2 7) ( B , (1)where y is the gyromagnetic ratio of the free proton, and (B), the average magnetic fieldat the site of the proton, is related to the applied field Bo by(B) = Bo(l-g), (2)where X is the bulk susceptibility, and g is a geometrical factor. Under the assumptionthat the two samples have the same geometry, Eqs. 1 and 2 give, to a good approxima-tion,v(HZ)-(H 2) - a (TMS) = 1 -g[X(H2)-(TMS)]. (3)v(TMS)The average and applied fields differ because of the depolarizing effect of the sample,and the effect of nearby dipoles. Under the assumption that the nuclear motion is per-fectly random so that the molecule effectively "scoops out" a spherical Lorentz cavity,the nearby dipoles produce a local fieldBlo 4 7M = X(B).The bulk polarizability produces a demagnetizing fieldBdemag= -XBo,where x is a factor dependent on the sample geometry. If we use (B) = Bo + Bloc + Bdemag,QPR No. 108(III. ATOMIC RESONANCE AND SCATTERING)it follows thatg = x - 47T/3, (4)where we have assumed that gX << 1.For a spherical sample, x = 471/3 and g = 0. The samples used were cylindrical, how-ever, and in this case x = 27r and g = 27T/3.3. Methoda. Sample PreparationThe TMS and hydrogen samples were contained in identical heavy wall NMR tubes,5 mm OD, 2. 12 mm ID (Wilmad, Type 522-PP). Matheson research grade hydrogen wasused in a sealed sample at a pressure of 30 atm. The TMS, supplied by the Thompson-Packard Corporation, was outgassed by repeated cycles of freezing and evacuation.b. SpectrometerThe measurements were made with a 60-MHz Hitachi-Perkin-Elmer R20B NMRspectrometer. The TMS sample, but not the hydrogen sample, was spun. Under optimalconditions the TMS linewidth was 0. 6 Hz and the H 2 linewidth was 100 Hz. The magneticfield was stabilized by an independent NMR field-locking system.c. ProcedureIn the experiment we successively observed the TMS and the hydrogen resonance sig-nals. The TMS frequency was determined by displaying the resonance on a recorder, andcalibrating the frequency at several points on the curve. Because of the high signal-to-noise ratio and narrow linewidth, the TMS resonance frequency could be identified essen-tially to 0. 1 HIz by inspection.The hydrogen resonance frequency was determined by slowly sweeping the spectrom-eter frequency and digitally recording the resonance signal and spectrometer frequency.Typically, 40 points were taken during a frequency sweep of 300 Hz. A single sweep took400 s, and the system time constant was 5 s. The line was swept successively in oppo-site directions to eliminate distortion from the finite sweep speed. The data were fittedto a five-parameter Lorentzian absorption-dispersion curve.d. Verification of Shielding CorrectionWe made an effort to verify the value of the product gX(TMS), where g is the geomet-rical factor, which we took to be exactly 271/3, (the value for an infinite cylinder) in ourdata reduction. By using this value with the Frei and Bernstein1 result for Y(TMS), wepredicted a difference of 68. 2 Hz between the NMR frequencies of cylindrical andQPR No. 108(III. ATOMIC RESONANCE AND SCATTERING)spherical samples of TMS at 60 MHz. Our spherical samples were 4-mm spheres fittedwith thin cylindrical filling stems. The spheres were held by their stems in an ordinarythin-walled 5-mm NMR tube by Teflon chucks. They were compared with a variety ofcylindrical TMS samples, including the one used in the H 2 measurements.The results were inconclusive, because of unpredictable broadening, asymmetry,and spikes in the resonance line shape from the spheres. The difficulty may have beencaused by paramagnetic impurities or magnetic field inhomogeneity. In a few measure-ments in which the resonance lines were narrow and symmetrical, we obtained theresults 57. 5, 62. 0, and 63. 2 Hz, in comparison with the predicted value of 68. 2 Hz. Thus,although these results were consistent with the predicted result, they are not definitive.3. ResultsFinal results were based on a series of 19 independent determinations taken over aperiod of 10 weeks. The raw data are shown in Fig. 111-3. They represent the absoluteI 0-80 .413 .825 1.238 1.650 2.063 2.475 2.888 3.300 3.713S(H2 )- V(TMS)- 188.26 HzFig. 111-3. Experimental results for comparison of theNMR frequencies of the proton in H2 and TMS.difference between the H 2 and TMS samples. For v(TMS) = 60. 000 MHz, we find, forcylindrical samples,v(H 2 ) - v(TMS) = 190. 32(83) Hz,where the uncertainty represents one standard deviation. To obtain o0(H2) - cr(TMS), weuse Eq. 3 with g = 27r/3 and the following values for susceptibility:x(TMS) = -0. 543(5) X 10-6X(H2) = -4. 89(49) X 10-9QPR No. 108(III. ATOMIC RESONANCE AND SCATTERING)X(TMS) is from Frei and Bernstein, 1 and X(H 2 ) is based on a molar susceptibility of-6 2-3. 98(4) X 10 /gram formula weight. The final result is-6o(H 2 ) -- (TMS)= -4. 299(14) x 10References1. K. Frei and H. J. Bernstein, J. Chem. Phys. 37, 1891 (1962).2. Constantes Selectionn6es, G. Foex, "Diamagn6tisme et Paramagn6tisme,"C.-J. Gorter and L.-J. Smits, "Relaxation Paramagndtique" (D6positaires:ieMasson et C ' Paris, 1957).D. INTERACTIONS IN THE EXCITED STATEUSAF-OSR (Contract F44620-72-C-0057)C. Wieman, M. G. Littman, D. KleppnerWe are studying the process Na + Na + hv - (NaNa)*. The complex (NaNa) existsin a coherent superposition of the ground and excited states. The complex is bound by asmall first-order dipole interaction energy. The system represents a pure Dickesuperradiant state, and for the electronically symmetric state it should have a radiativelifetime exactly one-half that of an isolated excited atom. In our experiment the (NaNa)complex is observed indirectly by measuring its fluorescent lifetime.The superradiant complexes are formed by bombarding sodium in a vapor cell withphotons from a pulsed (5-ns) dye laser. The incident photons are at 5950 A, well to thered of the D-line transitions (5890 A, 5896 A). The fluorescent lifetime is measured bystandard timing methods. The decay photons are observed through a monochromatorwith a 5955-5995 A bandwith. The binding energy for the complex is approximately0. 02 eV. Fluorescence was observed with a lifetime of 8 ns. The free atom lifetime is16 ns (we verified this as a calibration check), so that the observed fluorescence is con-sistent with the formation of the superradiant complexes. We are repeating the experi-ment to obtain better precision, and to measure the fluorescence spectrum, as well asto study the dependence of the formation rate on the energy of the incident photons.Work is under way toward refining the measurement and determining both theemission and absorption spectra of the complexes.QPR No. 108

Atomic Resonance and Scattering

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Atomic Resonance and Scattering

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