Contains reports on three research projects.United States Army Signal Corps (Contract DA36-039-sc-87376

Carr, P. H.

Lipsett, M. S.

Shane, J. R.

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III. MICROWAVE SPECTROSCOPY*Prof. M. W. P. Strandberg P. H. Carr M. S. LipsettProf. R. L. Kyhl P. Fowler J. J. O'GallagherProf. G. J. Wolga W. J. C. Grant D. W. OliverDr. R. A. McFarlane J. G. Ingersoll W. J. SchwabeDr. T. Ogawa F. Kacznarek J. R. ShaneS. B. Afshartous M. J. Keck N. TepleyJ. M. Andrews, Jr. P. F. Kellen J. F. WaldronH. C. Bowers J. D. Kierstead S. H. WempleA. SPIN-LATTICE RELAXATIONIn order to relate experimentally observed relaxation times to the spin-phonon tran-sition probabilities, it is necessary to solve the system of rate equations:dN.dN (W. .N.-W..N.)dt ji N ji iwith the constraint I N. 1. Here, N. is the fraction of particles in the i thlevel, and1W.. is the lattice -induced transition probability from state j to i.In matrix notation, this system of equations represents an eigenvalue problem:dN- WNdtwhere W.. = - W... The solution is N = DC, where C is a column matrix such that11 j ]1C i = exp(kiT), and D is a square matrix whose columns are the eigenstates(W-XkI) D. = 0The proper normalization of the eigenstates is given by the initial conditions. With thesolution written in this form, matrix techniques can be used to show the general proper-ties of the relaxation:(a) The eigenvalues are real and negative, hence the populations of the levels simplydecay to thermal equilibrium and do not oscillate.(b) The steady-state solution is a Boltzmann distribution.These properties will be shown for a four-level system with E 4 > E 3 > E 2 > E 1. LetS be a diagonal matrix with elementsE1 - E.Sij = exp 2kT 6If we use the fact that*This work was supported in part by U.S. Army Signal Corps ContractDA36-039-sc-87376.(III. MICROWAVE SPECTROSCOPY)E j - EiWij Wji exp(E kTthen W = S-lWS is a symmetric matrix, and so its eigenvalues are real. Since the secu-lar equation is invariant under a similarity transformation, the X's must also be real.The constraint Z N. = 1 requires that only three of the rate equations be independent.1Hence, lWI = 0 and X 0 is a root of IJW-II = 0. If we call this root X4 , the cor-responding eigenstate D4 is the steady-state solution WD 4 = 0.The system of equations for the elements of D4 is easily solved. The result is theBoltzmann distribution( E.D exp (- kT)i4 4 E;exp )i=1That the remaining eigenvalues are negative can be seen by writing the reduced secularequation in the form:X3 + PX 2 + q + r = 0whereP =-tr(W) = W ..ijq = > (WiiW..-Wi..Wi)i>j i i JS41 21 31Er = W4 2  W2 2  W32  exp kT)W4 3  W 2 3  W 3 3The quantities P, q, and r are positive, so by Descartes' rule of signs, Xi < 0 fori =l1, 2, 3.The results presented here can easily be extended to any multilevel problem forwhich the rate equations apply.J. R. ShaneB. MICROWAVE PHONONS AND THEIR ABSORPTION BY F-CENTERSMicrowave phonons have been produced, and their interaction with paramagneticimpurity centers in quartz has been studied. Phonon packets were produced by the(III. MICROWAVE SPECTROSCOPY)piezoelectric effect at the end surface of a quartz rod placed in the electric field of are-entrant cavity. These packets propagated down the rod, were reflected from theopposite end, and were detected at the generating surface by the inverse effect. Theamplitude envelope of the echoes consisted of a series of maxima and minima, or beats,caused by interference effects arising from a slight nonparallelism of the end surfacessuperposed on an exponential decay. From the decay, the average lifetime of the coher-ent phonons was found to be 10 - 5 sec. The t = 0 intercept of the envelope measured thesquare of the fraction of the microwave power converted into acoustic power, which wasfound to be a factor of 10 - 5 smaller than the computed value of 10 - 4  We attribute thisdiscrepancy to interference effects arising from roughness of the end surfaces, or tolattice damage at the generating surface which would decrease the piezoelectric effect.The absorption of phonons by spins produced in the natural quartz by gamma irradia-tion from a Co 6 0 source was detected as a partial saturation of the spin electron para-magnetic resonance. The partial saturation, S/S , was found to be 0.75 at 1. 7°K, 0. 75at 4. 2 0 K, and 0. 92 at 200K, the error in S/S falling between 2 per cent and 5 per cent.These values for S/Se were independent of the difference between the microwave andphonon frequencies within 20 mec. From microwave saturation measurements, theorder of magnitude of the spin-lattice relaxation time T 1 was found to be greater than-4 -63 sec at 1.7*K, and equal to 0.3 sec at 4. 2K, 3 X 10 sec at 20 0 K, and 3 X 10 secat 77°K. The spin-resonance absorption, which was measured as a function of micro-wave power, saturated in such a manner as to indicate partial inhomogeneous broadening,and cross relaxation took place between the closely spaced, narrow (approximately 1 gausswide) lines of the spectrum. These two effects prevented quantitative determination ofthe spin-phonon transition probability.P. H. CarrC. THE EVOLUTION OF BEAM-MASER APPARATUS IN THE MICROWAVESPECTROSCOPY LABORATORYSince the pioneering experiments by Johnson and Strandberg (1) and by Strandbergand Dreicer (2), interest in molecular-beam microwave spectroscopy has been acute inthis laboratory. The concurrent, now classic, experiments of Gordon, Zeiger, andTownes (3) lent further impetus to this interest which Peter and Strandberg (4) channeledinto maser spectrometry. Their work was directed toward beam spectroscopy of thealkali halides, yet gaps in experimental method and theoretical understanding compelledthem, at that time, to embrace widely divergent interests, such as information theoryapplied to microwave spectroscopy and mode control in microwave cavities of largevolume. From this earlier work, Venkates (5) was led to the studies on ammonia-maserspectroscopy which formed the basis of his doctoral thesis. When these studies were(III. MICROWAVE SPECTROSCOPY)completed our laboratory was left with apparatus that we decided to refine so that amaser spectrometer facility would be readily available. We are able to report that thisevolutionary process has been completed with the development and operation of a handysingle-beam maser and with the construction of a twin-beam maser. The functions ofboth of these instruments are quite flexible and conveniently arbitrary.This high-resolution equipment demonstrated its value when a need arose recentlyfor the frequencies of the hyperfine-split 1,1 inversion line of ammonia to be accuratelyspecified. Our single-beam maser was set up for this purpose, and the split line waseasily resolved within a few kilocycles at 23 kmc.Experience during the past few years has shown that within the bounds of cautiousinsight and good engineering, ammonia-beam masers are remarkably insensitive todetails of their construction. Once it is working, a maser works easily, and furthermodifications to the basic design are simply optimization procedures for extraction ofmaximum signal-to-noise with minimum effort.The apparatus described in this report is the result of evolution in the Laboratory.The basic design is simple, compact, inexpensive, and, in its way, foolproof. Basedon these attractive properties, a new twin-beam maser, more streamlined and sophisti-cated than its single-beam predecessor, has been constructed. It is intended that thefacility represented by this apparatus will lend itself to studies of oscillator noise, fre-quency standards, and stimulated-emission spectroscopy in general.The Single -Beam MaserVenkates' original maser (5) was modified and reworked until it took the presentform, which now permits disassembly, assembly, and operation within an hour and ahalf. The photograph shown in Fig, III-1 illustrates the single-beam maser assembly.From top to bottom the major components of the maser are arranged as follows: micro-wave cavity, state-selector and cold-trap, effuser, baffles, and diffusion pump. WithFig. III-1. The maser assembly.(III. MICROWAVE SPECTROSCOPY)this arrangement the beam source is nearest to the diffusion pump, and back-scatteredmolecules issuing from the effuser with trajectories outside of the entrance aperture ofthe state selector are quickly pumped away. Except for the diffusion pump and itsbaffles, all of these components are part and parcel of the top plate. In this way, thosecomponents that must be optically aligned are removable as a unit for servicing.Component alignment is ensured by a parallel tripod arrangement of three stainless -steel tubular supports that are fitted into the top plate, which is a sturdy piece of brassmachined to mate with an O-ring flange on the vacuum chamber. Two of the supportsare used, in effect, as an optical bench, and the third is actually a feed line to theeffuser. It extends through the top plate down to the effuser, and the ammonia is con-ducted through it. The first two supports, in addition to their function as an opticalbench, contain glass-insulated high-voltage leads that connect to the state selector.These high-voltage leads conduct coaxially through two legs of the tripod, and extendthrough the top plate, eventually encountering Kovar-to-glass vacuum seals.The vacuum system consists of a Megavac roughing pump, a 4 -inch diffusion pump,and an upright cylindrical tank that forms the vacuum chamber supporting the diffusionpump at the bottom and the maser proper at the top. The maser simply hangs down into-6the vacuum chamber, and the top plate and O-ring flange seal at least to 10 mm Hg.An ionization gauge and a thermocouple gauge connect to the side of the vacuum chamberto enable testing of the entire vacuum system that can be made independent of therelatively complex top-plate assembly.The cylindrical microwave cavity is mechanically tuned - an easily effected arrange-ment because the mode configuration is TM 0 1 0 . This mode is characterized by longi-tudinal surface currents and, consequently, a tuning vane inserted in a slot cut lengthwisein the cavity perturbs the frequency but not the Q. Thus tuning is accomplished by meansof a Sylphon bellows variably constrained to press from within the vacuum chamberagainst a tuning vane lever. The cavity has a single iris, and the maser signal isobserved in reflection.The state selector is a quadrupolar arrangement of four highly polished vanes withan aperture varying parabolically to match the smaller diameter of the effuser to thelarger diameter of the cavity. Teflon is used in judicious quantities to support andinsulate the vanes. Jacketed by a cylindrical cold trap, the Teflon-insulated stateselector can be called upon to support more than 32 kv before electrical breakdownoccurs.A stainless-steel dewar extends parallel to the tripod supports through the top plate.The cold trap clamps to this dewar and is cooled by conduction; the state selector iscooled, in turn, by radiation. During operation of the maser, the dewar is convenientlyand economically filled from the top of the entire assembly.A piece of Varian klystron grid stock is used as an effuser. Mounted on an adjustable(III. MICROWAVE SPECTROSCOPY)platform, it can be tilted and shifted around for correct alignment of the molecular beam.In order to facilitate the alignment procedure, a window is provided directly behind theeffuser, and when illumination is introduced through it along the beam axis, the effuser,the state selector, and the cavity can be brought visually into line from stem to stern.The Twin-Beam MaserThe twin-beam maser really consists of two independent masers mounted side by sideon a common top plate, sharing a common vacuum chamber. Each of them differs butlittle from the single-beam maser described above. The principal difference is that adewar of much larger capacity is located in such a way as to service both cold trapssymmetrically. This, together with new features of component clamping, and so on,makes it possible to remove any single component without disturbing its neighbors.Auxiliary EquipmentTo perform the function of reducing the pressure from a tank of compressed ammoniato a value near 1 mm Hg in an easily controlled way, an inlet manifold is required. Thepresent manifold admits ammonia through a pressure -reduction valve into a cylinder ofapproximately 2 inches diameter and 12 inches length. This cylinder is so arranged thatit can be bathed in liquid nitrogen and the noncondensed gas pumped off. The purifiedammonia can then be revaporized and conducted to a needle valve, beyond which athermocouple gauge meters gas flow that is then direct to the effuser inlet at the maser.The manifold is made entirely of metal and has small bellows-sealed valves throughout.Fig. 111-2. Block diagram of microwave circuit.(III. MICROWAVE SPECTROSCOPY)The detection scheme (Fig. 111-2) is balanced-mixer superheterodyne. The additionalstabilized klystron ("Signal Generator" in Fig. I1-2), with provision for frequency modu-lation, can be used to sweep over the spectral region that is of interest. If it is desired,the resulting beat frequencies can be displayed on an oscilloscope. In the case of simul-taneous operation of two or more of the masers the detection bandwidth can be narrowedfor better signal-to-noise ratio by the use of audio filters or other schemes. It is inter-esting to note that when we beat one of our ordinary dc-bridge-stabilized klystronsagainst the single-beam maser operated as an oscillator at the 3,3 transition of ammonia,a reasonably steady audio beat note is clearly visible against the background of klystronnoise.This brief report has been concerned with the summary of progress on the develop-ment of molecular-beam maser spectroscopy apparatus in this laboratory. Specificdevices have been discussed and, in this sense, it is a final report. But in the sense thatthis laboratory continues to be actively concerned with absorption and emission micro-wave spectroscopy, it is an interim report.M. S. LipsettReferences1. H. R. Johnson and M. W. P. Strandberg, Phys. Rev. 85, 503 (1952).2. M. W. P. Strandberg and H. Dreicer, Phys. Rev. 94, 1393 (1954).3. J. P. Gordon, J. J. Zeiger, and C. H. Townes, Phys. Rev. 95, 982 (1954).4. M. Peter and M. W. P. Strandberg, Theoretical and Experimental Study ofMolecular-Beam Microwave Spectroscopy, Technical Report 336, Research Laboratoryof Electronics, M.I.T., Aug. 26, 1957.5. H. G. Venkates, Ph. D. Thesis, Department of Physics, M. I. T., August 1958.

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