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A microwave spectroscope at one centimetre wavelength Thomas, Blodwen 1948

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A MICROWAVE SPECTROSCOPE AT ONE CENTIMETRE WAVELENGTH. by Blodwen Thomas JSp '9*-* & sr A thesis submitted i n pa r t i a l fulfilment of the requirements for -the degree of MASTER OF ARTS i n the Department of PHYSICS The University of B r i t i s h Columbia ABSTRACT The object of this research was the construction of a microwave spectroscope at 1.25 cm. wavelength. The double modulation method, which was used here, i s discussed. The system was tested with ammonia, and the inversion spectrum identified. The effect of using various harmonies of detection i s shown. AC KNCWLE DGMENT. I am pleased to express my thanks to Dr. A . Van der Ziel, under whose direction this research was carried on. I would also like to acknowledge the help of Mr. D. Scovil, who built part of the equipment. This project has been conducted by myself with the aid of a National Research Council Bursary and a Defence Research Board grant. In addition, the Defence Research Board provided a grant for buying the microwave equipment. TABLE OF CONTENTS. 1. INTRODUCTION. A. Application of molecular spectroscopy to the study of molecular structure .... 1 B. Present state of microwave research .... 2 C. Object of the research at U.B.C. .... 3 11. THEORY. A. Types of molecular symmetry B. Linear molecules C. Symmetric top molecules D. Spherical top molecules E. Asymmetrical top molecules F. Isotope effect G. Hyperfine structure H. Ammonia: inversion doubling and hyperfine structure I. Stark & Zeeman effects J. Intensity and shape of lines 7 10 11 11 14 15 111. APPARATUS. A. Electronic apparatus i ) Klystron and power supply . . . . 18 i i ) Low frequency sawtooth modulation . . . . 2 0 i i i ) Radio frequency oscillator . . . . 2 0 iv) Attenuation . . . . 2 1 v) Waveguide absorption c e l l . . . . 2 1 vi) Crystal detection . . . . 22 v i i ) ladio frequency amplifier . . . . 23 v i i i ) Frequency measurements . . . . 23 B. Vacuum technique . . . . 24 IV) EXPERIMENTAL PROCEDURE A. Single and double modulation methods . . . . 26 V) RESULTS A. Ammonia inversion lines . . . . 3 0 B. Effect of harmonic detection on line shape . . . . 3 0 C. Effect of radio frequency modulation voltage on line shape . . . . 3 2 VI) CONCLUSIONS .... 35 V i i ) BIBLIOGRAPHY . . . . ' 36 ILLUSTRATIONS 1. Klystron power supply circuit following page 18 2. Block diagram of vacuum system " " 2k 3. Block diagram of double modulation spectroscope " " 27 k. Picture of equipment " " 28 5. Close-up picture of klystron, attenuators, and controls " " 28 6 . Ammonia inversion lines " " JO A MICROWAVE SPECTROSCOPE AT ONE CENTIMETRE WAVELENGTH 1. INTRODUCTION A. Application of molecular spectroscopy to the study of molecular structure. Molecular spectroscopy i s the determination of energy levels i n molecules for the purpose of investigating their molecular structure. These levels may be divided conveniently into three types: electronic, vibrational and rotational levels. Trans-itions between electronic levels form absorption or emission lines and bands i n the visible region; vibrational lines and vibration-rotation bands appear in the infra-red; rotational lines are i n the millimetre and centimetre (microwave) region. The high frequency oscillators necessary as sources for the microwave region are recent developments i n electronics, and are helping to remove the limitation of optical methods at the low energy levels. If a molecule has an electric dipole moment, transitions are possible between rotational energy levels, and a series of rotational absorption lines appears i n the microwave region. The line frequencies determine the moments of inertia and internuclear spacings of the simple molecules. Rotational line series also indicate the presence of isotopes, owing to the slightly differing moments of inertia. A rotational line may have hyperfine structure i f one of the nuclei in the molecule has an electric quadrupole moment. The quadrupole coupling coefficient iri the molecule can be calculated from the spacing of the hyperfine components, and the nuclear spin from the number of these components. Thus rotational lines are a measure of moment of in e r t i a , bond spacing, nuclear quadrupole moment, nuclear spin and isotopic mass ratios. B. Present state of microwave research. Since 19^ -6 molecules with electric dipole moments have been investigated mainly in the cm. region. Linear and symmetric top molecules have simpler line structures than the more common asymmetric top because of the higher symmetries of the former. The bond distances of such molecules as OCS have been measured by Dakin, Good, and Cole (9) and Townes, Holder and Merritt (26). The spectrum of NH^  i s an example of inversion doubling and i t s lines are measured by Good and Coles (13), Strandberg et al (220>, Simmons and Gordy (21). The interaction energy for quadrupole coupling is given by FJeld (11), and Bardeen and Townes ( 2 ) . The nuclear spin and quadrupole moment of CI, N, Br, and I are measured by Townes et al ( 2 5 ) , Gordy et al (15). A transition has been found in Cv, due to i t s magnetic dipole moment by Beringer ( 3 ) . Water absorption has a peak at 1.3^ 4- cm. - Autler et al ( 1 ) , Townes and Merritt (23). Townes et al (26) have found lines for several suitable linear molecules, Dailey and Wilson (8) for polyatomic asymmetric molecules by Stark effect. Rotating molecules which have an electric dipole moment show Stark and Zeeman effects in applied f i e l d s . Both have been boserved: i n NH^  by Coles and Good (6), methyl alcohol and S0 2 by Dailey and Wilson (7) and ( 8 ) , Jen ( 1 9 ) . The earliest microwave absorption measurements were made by Cleeton and Williams (5) i n 193^-. They found a broad absorption line in HH, at 1.25 cm. with a Hertzian oscillator. Recently several methods with balanced circuit detection for comparing absorption i n a wave guide were used by Beringer ( 3 ) , Good ( 1 2 ) , and Townes ( 2 i | . ) . Later improvements are those of Gordy and Kessler (lij.), Watts and Williams (27) Hughes and Wilson ( 1 8 ) . Gordy and Kessler f i r s t used a method of single frequency modulation of a reflex klystron, and demonstrated a graph of absorption versus frequency on a cathode ray oscilloscope. Since then, they and several others have used double modulation of the klystron. The additional modulation i s at radio frequency i n order to increase the sensitivity of the spectrograph by increasing the signal to noise ratio at the crystal detector. Hughes and Wilson measure the Stark effect with an equally sensitive method employing radio modulation of the line frequencies. Jen has adapted the method of Gordy and Kessler to high temperature by replacing the waveguide absorption c e l l with a resonant cavity for convenience of application of the magnetic f i e l d i n the Zeeman effect. The cavity i s also suitable for heating molecules to the desired energy levels. The accuracy of microwave frequency measurements i s very good: 10 kc. at 25,000 Mc. or better than 1 i n 10^ . The high accuracy frequency standards are bu i l t by multiplying a standard quartz crystal. High resolution is also obtained: separations of 200 kc. C. Object of this research. When this project was. started last f a l l , i t was decided to build a microwave spectograph at 1 . 2 5 cm. From this wave-length the project can be extended into the millimetre region i n the future. The double modulation method was chosen for good sensitivity and for the simplicity of the system. Microwave plumbing and klystron tubes were obtained from de Mornay Budd and Raytheon. The electronic equipment and vacuum system have been constructed and assembled here. k The vacuum system is b u i l t to allow investigation of absqption at pressures down to 1 0 mm. of mercury, The spectrograph i s now completed with signal detection at the second harmonic frequency. The klystron frequency may be swept from 2 2 , 0 0 0 to 2 5 , 0 0 0 Mc. or further, depending on the tubes. The frequency i s measured to four figures with a transmission type wavemeter. A frequency standard, being completed here, w i l l be accurate to six figures. With the spectrograph i t was planned to measure the inversion spectrum of ammonia, and this has been done. By comparing our results with those of Strandberg et al ( 2 2 ) , and Good and Coles ( 1 5 ) , the accuracy and sensitivity of this spectrograph could be tested. The effect of double modulation on line shape has also been studied with detection at several harmonic frequencies. From the results with ammonia, i t is seen that some improvements can be made to the system in order to increase the signal to noise ratio. In addition, familiarity with the techniques at this frequency w i l l lead to work at higher fre-quencies where many interesting molecules may be investigated. 11. THEORY A. Types of molecular symmetry. Molecules may be classed according to their degrees of symmetry into the types: linear, symmetrical top or rotator, spherical top, and asymmetrical top. Linear molecules, including a l l diatomic ones, have a zero moment of in e r t i a about their internuclear axis, and non zero but equal moments of in e r t i a about any two other mutually perpendicular axes. A l l other molecules have non zero moments of inertia about the three principal axes. If a l l three moments of 5 inertia are equal, the molecule i s a spherical tops i f two are equal - a symmetric top, i f a l l unequal - an asymmetric top. The rotational spectra are typical of the various types of symmetries, and may be interpreted to give information about the molecular structure by the following theoretical development. The main reference i s Hefczberg ( 1 7 ) B. Linear molecules. If the angular momentum of the electrons about the internuclear axis i s zero (as i s the case for the unexcited ground state of the molecules), and i f the molecule i s i n the zero vibrational state, then a linear molecule may be considered as a simple vibrator with zero moment of inertia about the figure axis. The angular momentum of the rotating molecule i s quantised: p = h / J (J •+ 1) From this the energy of the various levels i s given as s E J " JL " J (J + 1) h 2 21 8 -7T2 I or E s BJ (J + 1) B - =Vr where I • mfr? i s the total moment of inertia of the molecule about an axis perpendicular to the internuclear axis for this particular case of the simple linear rotator. The mass of the electrons can be taken into account sufficiently accurately by using the mass of the neutral atom rather than the nucleas as V . The molecule, however, is not completely r i g i d . The influence of centrifugal force results i n a slight increase in the internuclear distances when the molecule is rotating. The following correction can.be made to the energy of the levels: _E_ = BJ (J + 1 ) - DJ 2 ( J + 1 ) 2 he where D^ .B. This extra factor i s negligible for linear molecules. The total eigenf unction of linear molecules i s IfJs 1^ 2}/v i(l rthe product of electronic, vibrational, and rotational eigenfunctions. The rotational level of a molecule i s called positive or negative depending on whether ihe total eigenfunction remains the same or changes sign by reflection of a l l particles at the centre of mass. /* If and Jfl v are unchanged by this symmetry operation, the symmetry character depends only on i ^ . : even J rotational levels are positive, odd J are negative. If the linear molecule has a centre of symmetry, i t also has the property symmetric or antisymmetric re exchange of identical nuclei. The total eigenfunction remains the same or changes sign when a l l nuclei on one side of the centre of mass are simultaneously exchanged with corresponding ones on the other side. In linear molecules alternate levels are symmetric and antisymmetric. If the linear molecule has no centre of symmetry, the s t a t i s t i c a l weight of a rotational level in a symmetric electronic state Cf) i s gj B 2 J - f 1 , the number of orientations of J i n a magnetic f i e l d (which i s developed by the rotational motion). If the molecule has a centre of symmetry, then ihe nuclear spin of the identical pairs of nuclei has an influence on the s t a t i s t i c a l weight. The even and odd levels each have a different weight factor which depends on the spins and must be multiplied to the term 2 J+ - 1 . If a l l pairs of identical nuclei have zero spin, alternate levels w i l l be entirely missing. If non zero spin, the ratio of intensities i s determined by their spin. However, a linear molecule with a centre of symmetry cannot have an electric dipole moment, so i s of no interest i n the microwave region since i t cannot have rotational transitions. One case has been observed 7 of a homohuclear diatomic molecule which shows transitions due to magnetic dipole moment - Cvj. The thermal distribution of these levels combines the Boltzmann factor and the s t a t i s t i c a l weight of each level. The population of a rotational level is N, <~*> g, e - §<J . For the linear kT molecule with no centre of symmetry, gj r 2J +1 as above. The graph of Nj versus J increases at f i r s t due to gj then decreases due to the exponential factor. The solution of the matrix elements shows that for electric dipole radiation a molecule must have a dipole moment i n order for the transition probability to be observable. The selection rule i s 4 J B 0, 11. The symmetry selection rules are: transitions can occur only from a positive (even j) level to a negative (odd J) level, and only between states with the same symmetry (a jump cannot occur between a symmetric and antisymmetric level). These two rules show why a linear molecule with a centre of symmetry cannot have rotational lines, since they automatically eliminate the transitions - +1, However, a linear molecule with no centre of symmetry (i.e. one with a permanent electric dipole moment) can have lines. Considering - -M, the absorption wave number i s : y (cm"') » 2B (J-H) - Ifi) (J-M) 5 where J refers to lower level. This is an almost equidistant line series, and characterizes linear molecules. Examples of such molecules are OCS, C1CN. C. Symmetric top molecules. The symmetric top molecule has a non zero moment of inertia about i t s figure axis i n addition to equal moments of i n t e r t i a about two other perpendicular axes. The two equal moments w i l l be called Ig, the third 1 ^ . The total angular momentum represented by the quantum number J miist be perpendicular to the figure axis i n a linear molecule, but a symmetric top can have a constant component of angular momentum along the figure axis. Examples are NH , the methyl halides. The figure axis natates about the constant J direction, and at the same time the molecule rotates about the figure axis. The component of J along the figure axis is called K, and K may take the values X , J - 1 , ... - J. Again assuming no electronic angular momentum, the energy of the levels i s E. JK he where B = h A BJ ( J + 1 ) (A - B) 8 T T 2cI B 8 i r 2 ( j I A It i s evident that a l l states with KfO are doubly degenerate. If - I, 4 L, the molecule i s a prolate symmetric top, i f I > I i t i s oblate. ° A B Taking into account the effect of centrifugal force on a non r i g i d rotator, the energy levels are corrected! EJK « BJ (J+ 1) -f (A-B) K 2 - Dj J 2 ( J - M ) 2 - D J RJ ( J f l ) K 2 - DgK^ he where C^B or A. The number of molecules i n a given J, K level i s - E ^JK^JK 6 idP^  where the factors of g have been discussed. There kx . JK is a series of graphs of N J K versus J for each value of K. Since J^K, the total number of molecules i n a given J level i s not a smooth function, compared with the distribution i n linear molecules. The symmetric top molecule must have a permanent dipole moment to allow dipole radiation, as for the linear molecule. Due to the symmetry i n this case, the moment w i l l l i e along the figure axis. The selection rules are ^ J - 0 i 1, <a K = 0. The latter ruie i s necessary because rotation about the figure axis does not change any component of the dipole moment along a given fixed direction. Again the symmetry selection rules are: transitions are allowed only between a positive and negative level, and between levels which have the same sta t i s t i c a l weight factor due to nuclear spin. The f i r s t restriction always permits transitions in prolate symmetric tops, but only i n oblate tops which have double levels (for each K value) due to inversion doubling. The absorption frequencies are: V (cm"') a 2B (j+1) - 2i> K 2 (J + 1) - /^>. ( J ^ 1 ) 5 JK J This i s a series of approximately equidistant bands -which may be resolved into very small fine structure splitting (for example, 20 cm"' i n HH^ ) due to the term containing K, when the effect of centrifugal force on a non r i g i d rotator i s considered. Each J level has J+1 components, not 2J+1, because of K degeneracy. In NH^  each fine structure line i s double due to the separation of inversion levels ( .8 cm-'). As for linear molecules, the rotational levels of the symmetric top are either positive or negative as the total eigenfunction i s unchanged or changes sign on reflection of a l l particles at -the centre of mass. The s t a t i s t i c a l weight g i s a more complicated factor since i t JK must account for inversion doubling, two fold K degeneracy, and effect of nuclear spin. A non planar symmetric top has a " l e f t " and "right" form of the molecule. If the potential energy h i l l separating the two positions i s not i n f i n i t e l y high, a slight splitting occurs into two almost coinciding energy levels - inversion doubling, which is discussed more f u l l y i n later section. One level is positive, the oiher negative. In addition to this s p l i t t i n g , each level with KfOis doubly degenerate as seen from the formula for E J K. In addition, a true symmetric top has an axis of symmetry, and the nuclear spin of the identical nuclei causes differences i n the s t a t i s t i c a l weights of the levels. For a molecule with a three fold axis of symmetric i n a to t a l l y symmetric electronic and vibrational state, the levels with K r 0,3,6. . have greater statis-t i c a l weight than with K - 1,2,k,5,..• If the spin of the like nuclei is zero, the levels with K = 1,2,4.. are missing entirely. The spin of H i n NH i s h. and the ratio of intensities for this molecule is 3 2 : 1 . The weight factor includes 2 J + 1 i f K = 0 or 2 (2J + 1 ) , K^O, the nuclear spin factor, and the inversion doubling i f i t s separation i s negligible. D. Spherical top molecules. The moment of inertia about any axis through the centre of mass of a spherical top molecule is the same. Since this type has an i n f i n i t e number of non coinciding axes of symmetry, the dipole moment must always be zero. Therefore no rotational dipole radiation i s possible for such molecules. They have the same energy level formulas as linear molecules. Examples are: CH^, CCi^, SF^. E. Asymmetric top molecules. As usual the total angular momentum J i s constant for a given level. A l l three principal moments of inertia are different, and the double degeneracy due to K i s removed to give 2J -f-1 levels for each J value. The energy of the levels: E - f ( I A , I B , I c , J) i s more d i f f i c u l t to represent by quantitative rules. As for symmetric tops, levels are positive or negative. However, the possibility of inversion doubles each level into two of opposite symmetry. If there 1 1 are also identical muclei i n the molecule, the eifs are symmetric or antisymmetric on exchange of pairs, and the s t a t i s t i c a l weights depend on the spins. As before, the molecule must have a permanent moment to have rotational lines. The selection rule is 4J - 0t±l . The motion of "the asymmetric rotator no longer requires the restriction on the axial component: of momentum of the symmetric top. A complicated sprectrum i s allowed, because of the removal of degeneracy i n the fine structure, and the symmetry selection rules seldom restrict. Examples of asymmetric top molecules with a permanent dipole moment ares H 2 0 , D2 0 , E 2 CO. P. Isotope effect. If one of the nuclei in a molecule has isotopes, there w i l l be separate series of lines due to the different moments of inertia. The position and spacing of the lines differ slightly. The mass ratios of -the isotopes can be calculated very accurately from rotational spectre. If the masses of isotopes are already known, the isotope effect can be used to calculate the distance of the isotopic nucleas from the centre of mass of the molecule. Since this distance is not appreciably affected by the different masses, ihe line shift gives the difference in moments of inertia and hence the distance measurement: A. I = 4 on . f - X G. Hyperfine structure. If one of the nuclei has an electric quadrupole moment, (in addition to the molecular dipole moment) there i s an electrostatic interaction energy between the quadrapole moment and the gradient of the molecular electric f i e l d at the nucleus. This causes a small splitting of the energy levels due to I J coupling into 21 + 1 (if I < J) or 2J+• 1 12 (J<^l) levels - the so called hyperfine structure. For a linear or symmetric top, the interaction energy i s t 1 - 3K 2 J (J +1) 3/L1P ( C t l ) - I (1*1) J (J+1) 21 (21 - 1) (2J - 1) 2J + 3) where C = F (F •+1) - I (I +1) - (J +1) F r |j-f-11 , |j+I - l | , •• • [J - 11 and where Q i s the quadrupole moment of the nucleus, V i s the electrostatic potential at the nucleus due to the other charges i n the molecule, K. i s the component of J on the figure axis (called z here), I i s the spin of the nucleus which has the quadrupole moment, F a J +-I. The interaction i s calculated from the quantized angle between I and J -Feld (tl), Bardeen and Townes ("2>). The new quantum number F i s the resultant of the nuclear spin momentum and the molecular rotational momentum. The selection rules for transitions are <3F » o ,±7, d j - o, ^1, &K a 0. Thus the number of components in a transition determines the nuclear spin. Since F» (J+l) . . jj-l| the number of lines observed at a single transition is the minimum of ^ 1 - t i , ^ J - t l . The separation of the hyperfine structure determines the quadrupole coupling coefficient Q —i . A rotational line with this hyperfine structure i s characterized 0 2 by a strong central line with weak satellites symmetrically placed on either side. In order to have this quadrupole s p l i t t i n g , i t is necessary that I ^  1, J >1. H. Ammonia inversion doubling and hyperfine structure. A l l non planar molecules have two identical potential minima corresponding to the two equilibrium positions of the nuclei resulting from inversion at the centre of mass. I f the potential h i l l between the two minima i s i n f i n i t e l y high, there can be no transition 1 3 from one configuration to the other, and the energy levels of each form are identical. However, i f the potential h i l l i s not i n f i n i t e l y high, by quantum mechanics the molecule w i l l transfer from one equilibrium position to the other after a certain time, and the energy levels are spl i t into close doublets. In the case of ammonia the N nucleus has two positions with identical potential minima along the figure axis. There i s an equal probability of the N nucleus being on either side of the plane of the hydrogen nuclei. Because the two potential wells are symmetrical about the o Distance orN zero plane the eigenf unctions can ft~o»Yt zero pl£U\c be the same or opposite i n sign when the N isreflected at the origin. Therefore there i s a possible symmetric and antisymmetric combination of the separate oscillator functions of each minimum, which correspond to the two slightly s p l i t levels. Since the probability of finding the nucleus in either minimum i s equal, the population of the two levels is according to the Boltzmann distribution for thermal equilibrium} the two levels have slightly different energy and therefore different population. Inversion doubling is described by Herzberg ( 1 7 ) and Dennison ( 1 0 ) . Transition from the lower to upper level can be observed i n ammonia. The jump & J = 0 , 4 K B 0 now emits a quantum because of inversion doubling. If the gas i s i n the zero vibrational state, tJie splitting i s small, about ,8cm. for a l l J, K values. The energy difference depends slightly on J and K since the small 14 rotational energy has an effect on the shape of the molecule and hence on the height of the potential h i l l . The dependence is given empirically l i i by many of the references mentioned f o r ammonia. Since N H has a quad-rupole moment and a spin of 1, these transitions are not single lines, but have the hyperfine structure previously described. The diagram indicates the jump due to the selection F = 7+l J J - l F = 7 + I 7 T-l rule 4P » 0 , £1 The separation J + 1 —» J i s not equal to J -* J - 1 so there i s a strong central |^  line with 2 longer and 2 — shorter wavelength satellites. 1 Actual photographs of these lines are found i n the results. I. Stark and Zeeman effects.. "When an electric f i e l d i s applied to a molecule, a dipole moment i s induced which can take up various directions with respect to the f i e l d . The interaction energy depends on the orientation of the orbitalangular momentus vector re the applied f i e l d . Thus tiie Stark effect i s a splitting of the rotational levels into multiplets, and can be used for measuring the strength of the electric dipole and i t s orientation re the figure axis of the molecule. Most molecules have an even number of electrons, and therefore a zero magnetic moment. But, i f a molecule i s rotating, a weak magnetic f i e l d i s generated by the orbital motion of the atoms and i s proportional to the speed of rotation. Therefore the Zeeman effect 15 may be observed. The applied magnetic f i e l d interacts with the rotational magnetic f i e l d , and the rotational levels are s p l i t into multiplets, depending on the orientation of the applied f i e l d re the orbital angular momentum vector. Refer (6), (7), (19) f° r experimental results i n microwave spectroscopy. J. Intensity and shape of lines. The intensity of absorption at a given frequency depends on the number of molecules i n the i n i t i a l and f i n a l states, and the probability of transition from the i n i t i a l to f i n a l state. The - E_ population N of the various rotational levels i s KTTr ^  gT„ e 1?.K-JK JK &JK kT for linear and symmetric top molecules, where g i s tlge s t a t i s t i c a l J K . weight of the level with energy E . The absorption coeffient at any frequency i s given by Van Vleck and Weisskopf (27), They calculate oC (absorption coefficient per cm.) classically from the Hamiltonian and electromagnetic theory, then generalize to a quantum mechanical system. They assume adiabatic collisions as the means of restoring thermal equilibrium, i.e. the time interval of c o l l i s i o n i s much less than tiie interval between collisions for a molecule. They apply a correction to the theory of Lorentz since certain app roximations usually made are no longer valid i n the microwave region, inhere the coll i s i o n frequency i s of the order of magnitude of the absorption frequency. They obtain: 06- 8j£ji ^_ 2f.£ ; \ * i / v t j - f ( v c j , v ) e V l ^ k 1 ' 6hc kT — r f -- J C where y=incident frequency, y.. =frequ3ncy of the absorption li n e , and •f(Vijy)±s the structure factor which, gives the shape of the line This formula holds i n the microwave region where rotational energy i s much less -than thermal energy. The structure factor determines the shape of the line i n terms of the half width . The main limitation on the shepe of the line or the half width i s the length of the wave train absorbed by the molecule between collisions: Dennison (10). It i s seen that the half width is the reciprocal of the time interval between collisions: = ^  . Therefore, from kinetic theory, the half width of a line i s directly proportional to pressure i n the region from about 10 microns to 10 cm , as measured experimentally by Bleaney and Penrose The absorption at the centre of the line i s : V* 3KT A V Since a^and N are each directly proportional to pressure under the conditions usually holding i n microwave measurements, i t follows that the height of the absorption line is independent of pressure, though the line width decreases with decreasing pressure. For good resolution in absorption measurements i t i s necessary to work at .01 - .001 mm Hg pressure. At low pressures or at high intensity of radiation the height of the absorption line does decrease at low pressure. This i s explained as saturation broadening. When the co l l i s i o n frequency i s so low that i t becomes comparable with the rate of transitions per molecule to the upper level by absorption of energy, then the distribution of molecules between ground and excited states is disturbed by the excess 1 7 power. The rate of return of molecules to the lower level by c o l l i s i o n i s comparatively slow, so that the distribution of molecules becomes that corresponding to a higher temperature, and the absorption coefficient f a l l s . This effect i s greater at the centre of the line than at the sides and therefore the line appears to be broadened. 1 8 111. APPARATUS A. Electronic apparatus. i ) 2K33 fclystron and power supply. The 2K33 reflex klystron ocsillates at 1.25 cm. and has a power output of ij.0 milliwatts. Its frequency of oscillation can be altered by electrical and mechanical tuning over a range of at least 3000 megacycles. This tube has a wave guide output at one side and a tunable plunger at the other. The power supply must be voltage controlled: i t requires about - 1800 volts for the cathode which accelerates the electron beam, the grids of the resonator or tuned cavity are at ground, the focussing grid controls the current flow and i s at -1800 - -2000 volts variable, (the klystron operating current i s made variable since tube, characteristics vary sl i g h t l y ) , the reflector i s at -1800 - -2300 volts variable. This latter range usually covers the most efficient modes of oscillation. The c i r c u i t diagram i s shown on the following page. The modulation voltages are applied to the klystron reflector directly at the supply. The output power i s more than sufficient for absorption measurements. The theory of operation of reflex klystrons i s well developed by Pierce and Shepherd (20). A direct current beam i s accelerated from the cathode, controlled by -the focussing grid, and i t passes through the resonator grids into the d r i f t space containing the reflector electrode. If there is a radio frequency voltage on the resonator the elctrons w i l l become velocity modulated when passing through i t . The length of time spent by the electrons i n the d r i f t space i s KLYSTRON POWER SUPPLY KLYSTRON CONNECTIONS 1. CATHODE MODULATION 2. GRID S. HEATER 3 R E F L E C T O R fe. H E A T E R 19 controlled by the reflector, which reverses their direction. By the time -that -the beam has returned to the resonator i t has become density modulated. The slow electrons catch up to the faster ones i n the d r i f t space since the latter travel a longer distance before turning back. If the phase relations are right, the beam w i l l give up energy to the resonator and build up oscillations i n i t . The natural frequency of oscillation of the klystron i s obviously determined by this resonant ci r c u i t . Its equivalent capacity i s formed mainly by the two close parallel grids, and i t s induetince by the surrounding loop. These factors indicate a method of tuning the klystron. If the grid separation i s made mechanically variable, as in the 2K33 tube, then the klystron frequency can be altered over a f a i r l y large range - several thousand megacycles. A decrease i n spacing causes an increase i n capacity and, therefore, an increase i n frequency of oscillation. Solution of the transconductance of the reflex klystron shows that the tube w i l l oscillate most easily when f . t e n+x, where f i s the klystron frequency, i t is the time spent in the d r i f t space, and n is the number (integral) of the mode, t i s inversely proportional to the reflection voltage VR. Then, i f the reflection voltage i s , for example, increased s l i g h t l y , t w i l l decrease, and the conductance w i l l contain a small capacitive term - in this case negative. This term has the effect of decreasing the tuning capacity of the oscillator c i r c u i t , and therefore increasing the frequency. This means that, over a small range of variation of V , the tube w i l l try to maintain the maximum conductance possible i.e. f.t = n + f-. This range of oscillation i s called a mode and may be 10 - 50 megacycles wide. The maximum power i s developed at the centre of the mode. If the reflector 20 voltage i s varied over a wide range, many modes of oscillation appear. The mode with smallest (n r 1) gives most power output, but the oscillation i s most stable at higher modes since the real part of the conductance increases with n. This property of klystron tubes makes them ideally suited for frequency modulation by sweep voltages. A low frequency linear sawtooth voltage i s applied to the reflection to sweep the klystron frequency through the whole or part of a mode so that part of a spectrum can be traced out on a scope. In the double modulation method, a much smaller radio frequency sine voltage i s also applied to the reflector to modulate the absorption over a small range while the sawtooth gradually sweeps the position over the whole range, i i ) Low frequency sawtooth modulation. The low frequency sawtooth oscillator is a gas triode as usual, and was bu i l t with, a cathode follower circuit to increase linearity. Its frequency is easily varied from 1 - 100 cps. The amplitude required to cover a complete mode of oscillation is from 20 - 80 volts, but i s reduced to about 5 volts for studying absorption i n order to decrease the required band width of the amplifier and thus reduce crystal detection noise. The sawtooth voltage i s also used as the horizontal sweep on the oscillope which i s used to observe the absorption. The frequency has been kept at L\.0 - 60 cps for easy viewing on the scope screen, but better results can be obtained at much lower frequencies with a persistent screen scope, as explained under crystal detection (vi) i i i ) Radio frequency oscillator. A standard tuned plate tuned grid oscillator was 2 1 b u i l t to operate at 8 6 kc. The output coupling gives a variable voltage up to 1 volt since a fraction of a volt i s necessary for radio frequency modulation of the klystron for accurate reproduction of the absorption lines. The double modulation method i s described i n the experimental procedure. iv) Attenuation. Two attenuators were bought from de Mornay Budd. One is a standard 11 decibel, tlie other is a variable calibrated attenuator to 3 5 db. It has been found preferable to attenuate the oscillator signal rather strongly, and then use high amplification after detection. If the input power i s too high, saturation broadening occurs. In addition, the signal to noise ratio of the crystal has an optimum value at a certain low power level. The crystal noise seems to increase more than the detected signal at high power levels, whereas the signal becomes smaller than the noise at too low power levels. v) Waveguide absorption c e l l . * The absorption ce l l consists of two five feet sections of 1 . 2 5 cm waveguide ( 2 3 , 0 0 0 - 2 7 , 0 0 0 mc) with cross section. It is gold plated to prevent corrosion. For convenience a U bend i s placed halfway along the guide to bring the tunable crystal mount up to the other controls. The guide is closed at both ends with thin mica windows, as described i n section B, and a short s l i t cut along one side for evacuation and f i l l i n g . There is an optimum length of waveguide to give maximum sensitivity (for measurement of small absorption coefficients) as calculated by Hershberger ( 1 6 ) . If the c e l l i s too short, l i t t l e power w i l l be absorbed by the gas; i f too long, the losses i n the 22 waveguide become excessive. In order for the change in power reaching the crystal to be a maximum at an absorption l i n e , the optimum length for the c e l l may be shown to be that where the power reaching the crystal has fallen to l/e of the incident power at beginning due to waveguide losses. This occurs when / = i - where OL is the power absorption « « - C C coefficient which accounts for losses i n the guide walls or i n any dielectric material. For copper waveguide at 1.25 cm. the optimum length i s about 10 metres. However, the function which determines the point of ^Rv,^* has a broad maximum: the 10 feet used here does not cause an appreciable decrease in sensitivity. vi) Crystal detection. The crystal diode i s the silicon 1N26. We have bought tunable crystal mounts. The input power on the crystal i s held well below the burnout value by the attenuators. The crystal output goes to a radio frequency amplifier. Crystal noise during detection is high. It i s necessary to consider how this noise may be reduced since i t greatly decreases the sensitivity of the spectrograph. "When detecting a small repeated signal on top of a constant microwave power level, the crystal noise i s inversely proportional to frequency. For a small frequency interval A)/, the noise electromotive force developed effectively i n series with the crystal i s e f r k ^ . I n the method of single modulation (discussed later), the total noise is calculated by adding these emfs quadratically over the -whole frequency band between upper and lower limits determined by the audio amplifier band width. J u 17 23 Thus the noise i s independent of the frequency of the sweep voltage when only singly modulated, because both and w i l l be multiples of the sweep frequency. In double modulations e 2 - kB where B i s the band width of the radio frequency amplifier, since Po (rf modulation frequency) i s almost constant compared with the small band width centred at V0 . Therefore the crystal noise level can be made much smaller in the double modulation method by taking from the crystal only a small band of frequencies at.radio frequency. Since a l l frequencies occurring i n the radio frequency signal must be multiples of the low sawtooth frequency, the band width necessary to reproduce the signal w i l l be proportional to the sawtooth frequency which is therefore a means of reducing the noise level. Sweep frequencies of 1 cps have been used by some researchers to improve sensitivity in this way. v i i ) Radio frequency amplifier. The radio frequency amplifier contains three tuned stages of amplification with automatic volume control, and a diode detector. The gain i s 1 0 , and the band width 1 0 kc. It is tuned to 1 7 2 kc to receive the second harmonic of the oscillator frequency -the purpose of this i s simply to increase the signal to noise ratio at the crystal. Its input i s matched to the crystal, the output goes to a scope. v i i i ) Frequency measurement. A calibrated transmission type tunable cavity wavemeter from de Mornay Budd i s accurate to four figures at 2 5 , 0 0 0 Mc. Another project being completed i n this department i s the construction 2k of a microwave frequency standard. A 200 kc temperature controlled quartz crystal is multiplied and mixed with a variable accurate signal generator to give a continuously variable frequency standard at 25,000 mc. This standard w i l l be accurate to six figures. B. Vacuum technique. A block diagram of the vacuum system is shown on the following page. A mercury diffusion pump i s used to evacuate the wave-guide absorption c e l l . A Philips and Pirani guage give continuous pressure readings over the required range. The waveguide i s sealed at the two ends with thin mica windows. I t was found that beeswax and rosin i s most convenient for sealing these windows to the guide. The U bend halfway was completely sealed from the outside with low vapor pressure Apiezon sealing wax. A brass block was soldered onto the s#lit in the waveguide; the glass tubing from the pump i s sealed into a hole d r i l l e d i n the block, again with Apiezon wax. The gas f i l l i n g system consists of a 3 gallon reservoir bottle and a partially closed off stop cock which feeds into the waveguide at the same point at the pump. The bottle i s evacuated, then f i l l e d with several cms of gas. The stop cock inner bore i s blocked to halfway with a low vapor pressure wax. The open half i s turned toward the gas supply, then turned through 180° so that a very small volume of gas at several cms pressure i s released to the much larger volume of waveguide. The pressure i n the guide may thus be regmlated from .01 micron to 10 micron i n small steps. The pump i s closed off to make a static system i n the guide at constant pressure for any length of time during which absorption measurements may be made. The minute amounts of gas thus used are not sufficient to injure the gaages or forepump. So far the i n i t i a l gas supply has been anhydrous BLOCK DIAGRAM OP VACUUM SYSTEM MICA WINDOW -TP— 3<Z TWO 5 ' S E C T I O N S OF W A V E G U I D E M I C A WINDOW X 3C B R A S S B L O C K =0 P H I L I P S G A U G E P I R A N I G A U G E Z E MERCURY TRAP MERCURY DIFFUSION PUi.;P =0 S T O P C O C K . S E A L E D E N D » J 1 1) 1 wen HAKOi U R Y : E T E R 3 G A L L O N B O T T L E -GAS R E S E R V O I R ! GAS S U P P L Y POREPU:. ' .P ammonia only. The system w i l l , however, be satisfactory for most other gases. 26 IY* EXPERIMENTAL PROCEDURE A. Single and double modulation methods. Although the double modulation method i s used here, i t i s an added improvement to the single modulation method, so the latter w i l l be described f i r s t . The klystron i s frequency modulated by applying the low frequency sawtooth voltage to the reflector electrode. The modulated microwave power passes through the attenuator and waveguide absorption c e l l to the crystal diode detector. The crystal output passes through an audio amplifier to the vertical plates of a scope to be used for viewing absorption. The horizontal deflection of the scope i s obtained directly from the sawtooth voltage. Since the klystron frequency is proportional to the sweep voltage, the scope shows a graph of absorption versus frequency. The absorption lines are much sharper than the gradual change of the contour of the mode of oscillation, so that the mode may be cut out by a high pass f i l t e r before the amplifier, or, instead of a f i l t e r , two differentiating circuits at the amplifier w i l l pass only the highest frequency components. Two are necessary to give a symmetrical pattern almost indentical to the original line shape. Reflections i n the guide are also broad, low frequency signals and are eliminated by the above devices. The limitation i n sensitivity of this method i s due to the relatively high crystal detection noise at the low frequency. The single modulation method was tried here f i r s t with a three stage audio amplifier and a high pass f i l t e r with cutoff at 100 cps. It was not successful because the high gain amplifier distorted the signals, and the f i l t e r introduced further distortion. In addition, more careful design is necessary to eliminate blocking of the amplifier tubes. A better system appears to be a three stage audio amplifier with a differentiating c i r c u i t between each tube. The circuit constants must again be chosen carefully to prevent distortion. In addition to the low frequency sweep used i n the single modulation method, a small radio frequency sine voltage is also applied to the reflector for double modulation. This system is now being used here, and a block diagram i s found on tine following page. The radio voltage sweeps over a small frequency range which is gradually moved acros s the mode by the low frequency sawtooth. Thus the power received at the detector becomes modulated by the radio frequency, so that, after detection, a radio frequency amplifier is used i n place of an audio amplifier. After amplification the radio frequency signal is detected and placed on the scope to give a trace of absorption versus frequency as before. Since the effect of the radio frequency modulation and detection on the absorption i s similar to differentiation, the low frequency mode contour and reflections do not appear very large at the output. However, the beginning and end of the mode are usually sharp enough to give strong signals: these are useful as markers of the position of the mode. The greatly increased detection frequency over the siggle modulation method increases the signal to noise ratio at the crystal diode considerably. In this experiment the oscillator i s at 86 kc and the radio frequency amplifier i s tuned to the second harmonic, 172 kc. Oscillators at 172 kc, 57 kc and 1+3 kc were also tested to observe the effect of the f i r s t , third and fourth harmonic detection on the line shape, but the best results so far have been obtained at the second harmonic. BLOCK DIAGRAM OF MICROWAVE SPECTROGRAPH R.E. OSCILLATOR POWER SUPPLY PUMP KLYSTRON ATTENUATOR - WAVE GUIDE J CRYSTAL DETECTOR SAW TOOTH OSCILLATOR R .F. AMPLIFIER OSCILLOSCOPE. The low frequency voltage i s variable, but usually held at 5 - 1 0 volts since a small klystron frequency sweep permits a small band width for the amplifier and hence less noise. The radio frequency voltage i s variable up to several volts. I t must be sufficiently small that i t sweeps across only a fraction of the absorption line in one cycle, because the r f output shape depends on the size of this voltage as well as the original shape of the line. The effect of various voltages on line shape i s shown i n the results. To sweep over a spectrum, the klystron is tuned mechanically from i t s lower to upper limit of oscillation. As the klystron i s tuned i n small steps (the intervening frequencies are covered by the width of the mode), the total length of the waveguide system must be adjusted each step for maximum output by the tuning plungers at each end. The 2K33 :klystron w i l l oscillate from 2 2 , 0 0 0 to 2 5 , 0 0 0 Mc or further ,in this way. A brass block and screw with dial was constructed to f i t on the tube for tuning by hand, and i s shown in the pictures of the apparatus on the following pages. The f i r s t plate shows a l l the electronic and vacuum equipment. The microwave plumbing i s seen better i n the close-up following. At the front are the klystron and attenuators leading to the waveguide! the crystal detector mount is directly behind at the other end of the waveguide. The anplifier (rf) and high voltage control panel are also shown. The connection from the waveguide to the glass evacuating and f i l l i n g system is. seen i n one corner. .The contour of the mode is not completely cut out by the double modulation system. In addition to the expected sharp signals at the beginning and end of the mode, the shape of the whole 29 mode i s not entirely flattened out. When absorption lines appear on a slope, they become distorted. The double modulation method does, however, completely cut out reflections, because these are very broad signals and therefore have no high frequency components. A wave reflected from the end of the crystal mount, the mica windows, or U bend w i l l pass back and forth i n the waveguide. This path length w i l l cause the incident and reflected waves to add i n phase at some frequencies to form standing waves, but to cancel at other frequencies. Thus a standing wave pattern should appear as background on the absorption versus frequency graph on the scope. However the pattern i s very wide except for very long absorption paths so that the signal can not pass through the rf amplifier. In our waveguide of 1 0 feet, a complete cycle of reflections from one maximum to the next would cover about 5 0 Mc variation of the klystron frequency. The effects of pressure and saturation broadening have been discussed in the theory. Both were observed here. It was found necessary to measure absorption below . 0 1 mm pressure in order to resolve "the ammonia lines. The gas pressure i s easily regulated as previously explained. At higher pressures the double modulation method i s not so useful since the lines are too broad. At low pressures, saturation broadening i s observed unless the input power i s sufficiently low. The input variable attenuation of k5 db i s high enough so far to prevent this effect. i 30 V. RESULTS. A. Ammonia inversion lines. A l l the ammonia lines i n the region 23,000 -2lj.,700 Mc have been found and identified. Their frequencies have been measured by Good and Coles (13) and Strawdberg et al (22) more accurately than is yet possible here. A typical line with satellites due to nuclear quadrupole coupling is photographed from the oscilloscope and shown i n figure 1 on the following page. This is -the general appearance of the lines at second harmonic detection. At large J,K values the hyperfine structure becomes too small to observe; the satellites were seen here up to 5 ,5. They could not be observed on the weakest lines, although of low J,K values, partly because insufficient radio frequency amplifi-cation before the diode detector causes small signals to be detected quadratically, and partly because the noise level has not been reduced to the absolute minimum. B. Effect of harmonic detection on line shape. The radio frequency modulated signal may be amplified and detected at the fundamental or at the harmonic* frequencies. 'When the radio frequency modulation voltage sweeps across fen absorption l i n e , the size of the fundamental signal is proportional to the rate of change of absorption (i.e. the slope of the line). Therefore the output at this frequency should have the shape of the line differentiated once. The envelope of this signal, after detection, is that seen on the scope -there i s a dip at the central frequency of the line. If detection is at twice the fundamental frequency (second harmonic), the signal expected i s the absorption line differentiated twice; at the third harmonifi i t appears differentiated three times, etc. These expected line shapes may-be calculated from an analysis of the effect of double modulation on the absorption. If the detection i s linear, the odd harmonics have a zero amplitude at the centre of the line with a sharp discontinuity of slope. The even harmonics have a maximum at the centre. If the signal reaching the detector i s small, the detection w i l l be quadratic. In the case of odd harmonics, the consequent mixing then causes a small signal at the centre.of the line so that there i s a smooth dip with positive amplitude instead of a sharp cusp at zero level. Figure 2 represents detection at the fundamental (odd harmonics) and may be compared with figure 1 , detection at second harmonic. The even harmonics s t i l l have maxima at the centre but -the small hyperfine structure i s decreased. Figures 3 and k represent the same line but 1 2 db attenuation at the input has been added for figure 1+. Thus reduction of the power level has placed the satellites at ihe quadratic detection level and they are much more reduced than the main line. The sidebands on the second harmonic picture were suppressed in figure 1 , by using a small radio frequency voltage, but may be seen i n figure 5 . The line shapes at third, fourth, f i f t h , and sixth harmonics were also investigated on the scope with a variable oscillator. As expected, the number of side bands continually increased, while a l l odd harmonics had a dip, and even harmonics a maximum at the centre of the structure. However, the amplitude of the signal decreases as the number of the harmonic increases, so there i s no advantage in working at higher harmonics. The f i r s t harmonic i s the largest, and therefore should have relatively laarger satellites since the signals could be kept more easily above, the quadratic detection level of the diode. However, one 3 2 problem arising at fundamental detection is that the dip at the centre of the main line does not always show up. When the line occurred along a slope of the mode contour, one of the' sidebands was suppressed and the line appeared single. For frequency measurements the central frequency must be sharply defined and i t would be wrong to use the top of the single line. To overcome this d i f f i c u l t y , a double differentiating circuit may be added to the radio frequency amplifier. Then a sharp signal should appear at the position of ine slope discontinuity at the centre of the line regardless of the distortion of the sidebands due to the mode contour. If the sharp point has been smoothed out by quadratic detection, then the doubly differentiated signal w i l l be smaller. However, i t s position w i l l s t i l l be independent of the slope of mode, so that frequency measurements may be made accurately. This method of detection w i l l be tried here i n the future. C. Effect of radio frequency modulation voltage on the line shape. If the radio frequency modulation voltage is so small that i t sweeps over only a fraction of the line width per cycle, then the line shape i s reproduced without distortion. I f , however, the frequency sweep i s of the same order of magnitude as the line width, then the structure is broadened and distorted. The dependence of the width of the observed signal structure on radio frequency amplitude may be easily shown. Let the absorption line f a l l to zero amplitude at f i n i t e frequencies f 1 and f , so that the difference gives the line width a = f 2 - f-j. If a linear sweep only i s applied to the klystron, then absorption appears only during the time interval required to sweep from f^ to f^. If a small radio frequency voltage i s added, the klystron frequency w i l l reach f^ at an earlier time represented by the frequency sweep of one half cycle 33 of the radio frequency, and the klystron frequency will s t i l l be at f^ at a later time when radio frequency is furthest negative. Therefore the absorption signal appears to be of width a -f»2b where b is the amplitude of the radio frequency (in terms of frequency sweep). The pictures taken at second harmonic detection show this broadening effect due to increasing radio frequency sweep voltage, and also the distortion effects which occur in this case. Figures 3 ~ 6 were all taken at sufficiently low pressure to eliminate collision broadening. Figure 3 has a small radio frequency sweep, and the input power is high enough to show the satellites. Since the radio frequency sweep is low, i t does not broaden the line appreciably, but, in this case, the line is broadened by the high power level - saturation. In figure h the input power has been reduced by 12 db, so that the satellites, quadratically detected, are too small to observe. The radio frequency sweep is not changed in figure U» Very small sidebands are distortion introduced by the radio frequency sweep as mentioned in section B. In figure 5 the radio frequency voltage has been increased, and the 12 db retained. The width of the structure is observed to increase over figure k as discussed above. In addition, further distortion occurs: the two sidebands, formerly very small, have increased. As the radio frequency sweep is increased further in figure 6, the width increases, and the two sidebands become larger than the central band. Figures 3 and U demonstrate saturation broadening. When the microwave power used for the line of figure 3 is reduced by 12 db, the line becomes narrower as in figure 1+. The amplification of the scope after detection was increased. This narrow line was maintained as a reference for figures 5 and 6, when the radio frequency sweep was increased to show i t s effect on the width of the structure. It may be noted that the lines are well above noise level in general. VI. CONCLUSIONS. The 1 .25 cm spectroscope has been tested with ammonia and found satisfactory i n most respects. A l l of the ammonia lines i n the frequency sweep of our klystron were detected and identified. The second harmonic detection i s more accurate at present than the f i r s t harmonic, but the sensitivity of the system would be increased by changing to the f i r s t harmonic and using differentiating circuits as discussed i n the results. The limitations on the magnitudes of pressure, input power, and radio frequency voltage have been indicated. At present the accuracy of frequency measurements i s only to four figures, but further work i s being done here on a microwave frequency standard. In order to increase the size of the hyperfine structure more radio frequency amplification i s necessary to make the detection linear. 36 BIBLIOGRAPHY. 1. S.H. Autler, G.E. Becker, J.M.B. Kellogg ... Phys Rev 69, 69k, I9I+6. 2. J. Barden, CH. Townes ... Phys Rev 73, 97, 19(48. 3. R. Beringer ... Phys Rev 69, 693, I9J4.6. 70, 213, 1946. 1+. B. Bleaney, R.P. Penrose ... Proc Phys Soc 5 9 , 1+18, 1947. 60, 83, 19I+8. 5. CE. Clecton, W.H. Williams ... Phys Rev 1+5, 23!+, I93I+. 6. D.K. Coles, W.E. Good ... Phys Rev 70 , 979, I9I+6. 7. B.P. Dailey ... Phys Rev 72, 8l+, 191+7. 8. B.P. Dailey, E.B. Wilson ... Phys Rev 72, 522, I9I+7. 9/ T.W. Dakin, W.E. Good, D.K. Coles ... Phys Rev 71, 61+0, I9I+7. 10. D.M. Dennison ... Rev Mod Phys 3, 280, 1931. 12, 175, 191+0 Phys Rev 31, 503, 1928. 11. B.T. Feld ... Phys Rev 72, 1116, I9I+7. 12. W.E. Good ... Phys Rev 6 9 , 539, 19U6. 70, 213, 191+6. 13. W.E. Good, D.K. Coles ... Phys Rev 71, 383, 191+7. 11+. W. Goody, M. Kessler ... Phys Rev 71, 61+0, 191+7. 72, 61+1+, 191+7. 15. W. Gordy, J.W. Simmons, A.G. Smith ... Phys Rev 72, J>hk> 191+7. 16. W.D. Hershberger ... J l Appl Phys 19, 1+11, I9I+8. 17. G. Herzberg ... "Molecular Spectra and Molecular Structure" Vol. 1 and 2, Chapter 1 Van Nostrand. 18. R.H. Hughes, E.B. Wilson ... Phys Rev 71, 562, I9I+7. 19. C.K. Jen ... Phys Rev 72, 986, I9I+7. Bibliography .. continued. 2 0 . J.R. Pierce, W.G. Shepherd ... Bell Sys Tech J l 2 6 , 4 6 0 , 1947. 21. J.W. Simmons, W. Gordy ... Phys Rev 7 3 , 713, I9J48. 2 2 . M.W.P. Strandb'erg, R. Kyhl, T. Wentink, R.E. Hillger ... Phys Rev 71 , 326, 19^ 4-7. 2 3 . C.H. Townes,S.R. Merritt ... Phys Rev 7 0 , 558, 1946. 2l+. C.H. Townes ... Phys Rev 7 0 , 6 6 5 , 1946. 2 5 . C.H. Townes, A.N. Holder, J. Bardeen, F-.R. Merritt ... Phys Rev 71, 6i)4, 1947. 2 6 . C.H. Townes, A.N. Holder, F.R. Merritt ... Phys Rev 72, 513 , 1 27. J.H. Van Vleck, V.F. Weisskopf ... Rev Mod Phys 17 , 227, 1945. 28. R.J. Watts, D. Williams ... Phys Rev 7 2 , 263 , 1947. 72, 1122, 1947. 

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