Electron Paramagnetic Resonance of Nitrogen Afterglow Condensed at 4.2°K Citation Harding, John Thomas (1958) Electron Paramagnetic Resonance of Nitrogen Afterglow Condensed at 4.2°K. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/63PX-2V80. https://resolver.caltech.edu/CaltechETD:etd-11012004-141238 Abstract NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. The electron paramagnetic resonance (EPR) spectrum of nitrogen afterglow condensed on the walls of a microwave cavity at 4.2[degrees]K indicates the presence of considerable quantities of ground state nitrogen atoms. The hyperfine coupling constant for the [...] state is estimated at [...]. Frozen dissociation products of ammonia produced the same nitrogen resonance line and, in addition, the resonance spectrum for atomic hydrogen. Item Type: Thesis (Dissertation (Ph.D.)) Subject Keywords: (Physics and Mathematics) Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Minor Option: Mathematics Thesis Availability: Public (worldwide access) Research Advisor(s): Pellam, John R. Thesis Committee: Unknown, Unknown Defense Date: 1 January 1958 Record Number: CaltechETD:etd-11012004-141238 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-11012004-141238 DOI: 10.7907/63PX-2V80 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 4352 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 01 Nov 2004 Last Modified: 16 Oct 2023 21:08 Thesis Files Preview PDF (Harding_jt_1958.pdf) - Final Version See Usage Policy. 6MB Repository Staff Only: item control page

ELECTRON PARAMAGNETIC RESONANCE OF NITROGEN AFTERGLOW CONDENSED AT 2° Thesis by John T. Harding In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1958 = ACKNOWLEDGMENTS The author expresses appreciation to his thesis supervisor, Dr. John R, Pellam, for his encouragement and advice. The research reported in this thesis was performed in a joint undertaking with Mr. Terry Cole of the Gates Laboratory of Chemistry. Both his advisor, Dr. Don M. Yost, and Dr. Harden McConnell of the Chemistry Department have taken a keen interest in this project. Their guidance is gratefully acknowledged. The Sloan Foundation, the National Science Foundation, the Newmont Fund and a Standard Oil Co. of California fellowship all aided in the undertaking of this research. ~ij= TABLE OF CONTENTS. Acknowledgments Table of Contents Abstract I. IT. III. Ve VI. Introduction A. Historical Summary B. Purpose of Present Investigation Experimental Design Experimental Procedure Results A. Nitrogen Be Ammonia Speculative Comments A. Nitrogen B. Ammonia Conclusions Figures Appendices I. II. References LO 13 18 25 26 31 ABSTRACT The electron paramagnetic resonance (EPR) spectrum of nitrogen afterglow condensed on the walls of a microwave cavity at ).2°% indicates the presence of considerable quantities of ground state nitrogen atoms. The hyperfine coupling constant for the 7S state is estimated at ah /h = 11.2 Mc/sec. Frozen dissociation products of ammonia produced the same nitrogen resonance line and, in addition, the resonance spectrum for atomic hydrogen. ~lL~ I. INTRODUCTION. A. Historical Summary Active Nitrogen Gas When nitrogen gas at a few hundred microns pressure is conducted through a region of electric discharge, a modification is produced known as active nitrogen. Its prominent feature is a yellowish glow which persists up to several hours, Initial investigation, quite naturally, was of a spectroscopic nature. Lewis (1), using a low dispersion instrument, obtained spectra containing the most prominent features of active nitrogen in 190. It remained for John Strutt, Lord Rayleigh, to demonstrate the extreme chemical activity of the products of the discharge. In a series of definitive experiments, Rayleigh (2) discovered a number of unusual properties of active nitrogen. Intensive investigation and analysis followed these dis- coveries. What emerged from the results is a fairly complete and consistent description of room temperature nitrogen afterglow which can be summarized as follows: 1. Nitrogen molecules in a variety of excited states exist in the afterglow. Their presence is revealed by characteristic emission bands (3). The yellow glow itself is due to transi- tions from excited vibrational states of the °/7 level to an intermediate metastable level, = . ~2- 2e Although there is no optical spectroscopic evidence for atomic nitrogen in the gaseous afterglow, the spectrum for ground state N is found from paramagnetic resonance (). Diffusion experi- ments (5) indicate considerable quantities of particles lighter than molecular nitrogen, and specifically Mass 1) has been observed in mass spectroscopy (6). 3. The glowing material reacts violently with a number of non- metals, including phosphorus (to form red phosphorus), sulfur, and iodine; in the process it becomes absorbed and the yellow glow is extinguished. An interesting feature is that the reaction with phosphorus proceeds most rapidly after the yellow glow has diminished in intensity. It has no effect on cool metal but an intense flame spectrum is obtained when the glow is passed over metals heated to only 250°C. Similarly, the flame spectra of many compounds are developed when they are vaporized in active nitrogen. In many cases these substances are too unstable to be seen at the temperature of a Bunsen flame. Unsuccessful attempts to condense the glow at liquid air temperature indicate the absence of complex molecules. The chemical activity cannot be ascribed to ions as their removal by electric fields does not alter any of the above properties. It is of interest to note that originally controversy centered on whether the activity of the afterglow was due to nitrogen itself or to impurities. Very pure nitrogen seemed to give little afterglow, whereas the addition of small amounts of oxygen stimlated the glow considerably. However, it was later discovered that traces of numerous ~3- foreign gases added to nitrogen aided the glow. Since these foreign gases by themselves fail to exhibit the properties of the nitrogen afterglow, it is concluded that impurities are catalytic for a good yield of active nitrogen in the discharge but that they play no role in the properties of the afterglow. Excited Solid Nitrogen In 192), Vegard (7), in an attempt to reproduce the 5577A green Line found in the Auroral spectrum, bombarded solid nitrogen with cathode rays. A layer of luminescent solid nitrogen was thus formed, The same green glow persisted over five minutes after the cathode rays were cut off. A set of three emission spectra was found. The strong yellow-green line of the Aurora appeared in a group of diffuse lines, while a conspicuous line emitted during intense Aurora display was included in a group of sharp blue-green lines clustered about 5230A. Also, in both cases the spectra were dominated by negative band heads from 708A to 391A. The slow fading away of the light after an Aurora display corresponded to phenomena observed in solid nitrogen. Broida and Pellam (8) in 195), observed the spectrum of nitrogen which they had excited by a microwave electrodeless discharge and then condensed on the walls of a dewar maintained at ).2°K. The improved technique in the preparation and deposition of the discharge products of nitrogen greatly enhanced the spectrum as obtained by Vegard, Sub- sequent analysis of the spectrum by Broida and Herzfeld (9), and Broida and Bass (10) produced compelling evidence of the existence of meta- stable molecules and of considerable quantities of atoms in both the -l- ground and first excited states. The sharp blue-green lines (cx lines; 4 life, 15 sec) are caused by transitions between the first excited state (7D) and the ground state (“S) of the atom, These consist of five lines spaced by 20/em; their center of gravity is shifted 10h/cm from the single line observed in the free atom, This *D to *S transi- tion is highly forbidden in the free atom, which explains its absence in the gaseous glow. The large crystal fields which produce splitting in the solid can stimlate transitions so that the atoms are de-excited by radiation to the ground state rather than by recombination to excited molecular states. The diffuse yellow-green lines (lines; % life, el sec) are observable only while active products are being deposited. They are produced by transitions among atomic states with n = 3, and S. The remaining spectroscopic feature of the condensed glow is the A bands, the first positive bands of molecular nitrogen. These persist faintly for several minutes at he2 Ky although a blue glow can be restored after periods greater than an hour by heating. Inasmuch as excited states in atoms and molecules have lifetimes mich shorter than this, the excited molecular states must arise from recombination of ground state atoms. This then is indirect evidence of the presence of considerable concentration of ground state atoms in the discharge products for appreciable lengths of time. B. Purpose of Present Investigation A definitive test for the existence of long-lived atomic species in condensed nitrogen afterglow would clearly be extremely useful in understanding its unusual and spectacular properties. Since the ground an ‘state of atomic nitrogen (*S) has a net spin, it should exhibit paramagnetic resonance in the vicinity of the resonance expected for a free S electron. Accordingly, we proposed to condense dissociated nitrogen in a microwave cavity and investigate its resonance proper- ties. If the presence of atomic nitrogen were thus revealed through its ground state, it was proposed to search for the EPR spectra of the excited 7D and ’P states and also to discover the temperature and time stability of the observable atomic species. =n II. EXPERIMENTAL DESIGN. The experimental problem is essentially this: to produce excita- tion of molecular gas by electric discharge, to condense the products rapidly before recombination can occur, to introduce the solid sample into a favorable field region of a microwave cavity, and to observe absorption of r-f power by the sample as a function of magnetic field. The sample must be maintained below its condensation temperature while its spectrum is taken. A Raytheon diathermy (Microtherm) unit operating at 250 Mc/sec provides the excitation energy to the gas (see figures 1 and 2 for the dissociation apparatus), The diffusing head supplied with the machine for medical purposes is replaced by a tapered resonant cavity with a transverse slot provided for the glass tube which ‘conducts the gas through the dissociating electric fields within the cavity. The gas flows from a tank of commercial compressed gas through a valve system and into the discharge region. A floor pump is used to draw a contin- uous stream of fresh nitrogen through the discharge and to maintain the pressure of the gas at a few hundred microns. Preliminary investiga~ tion showed that the yellow material formed in the discharge (active nitrogen) can be conveyed through glass tubing of greater than a few millimeter bore for distances more than a meter, Smaller bores or the use of metal tubing extinguished the glow in shorter distances. The method employed in this investigation for collecting a con- densed sample in a cavity represents a considerable advance over that previously developed by Jen and co-workers (11). They condensed active ~T- hydrogen on a sapphire rod placed in a stream of yellow glowing gas. The rod was maintained at 42° by contact with a reservoir of liquid helium, The coated rod was then inserted into a cavity. The dis- advantages of this approach are the difficulty of manipulating the sample under liquid helium and the necessity of placing the sample in the volume of the cavity rather than on the walls where dielectric losses are zero and magnetic fields strongest. Our method consists of conducting the glow directly into the sample cavity where it is deposited on the walls at ).2°K (fig. 1). A length of waveguide (fig. 4-A) enters the cap of a liquid heliun dewar (fig. \-B) and extends down into the constricted portion of the dewar between the pole faces of a magnet. It is terminated by a reflection cavity. The gas is conducted from the discharge through a 9 mm I.D. glass tube entering the length of waveguide a few inches above the dewar cap and traversing within to the cavity. The gas emerges at the bottom of the waveguide through the ) mm diameter cavity coupling hole or iris, whence it condenses instantly onto the cavity walls. A teflon gasket at the ‘upper end of the section of waveguide permits evacuation of the cavity when a vacuum is drawn on the glass tube. A double dewar system, the outer dewar (fig. h-C) filled with liquid nitrogen and the inner filled with liquid helium, surrounds the system, Rising vapors from the helium absorb the greatest part of the heat conducted down the waveguide. The loss of helium is less than 200 cc/hour. A d-c magnetic field plus a radio frequency magnetic field are required for paramagnetic resonance. We employ an Arthur D,. Little aBuw electromagnet (fige 5) powered with three storage batteries in series. Sufficient field homogeneity is obtained through the use of 11" Armco iron pole faces with a gap of 24!. & proton resonance field controller provides time stability plus a means for varying and measuring the field by varying and measuring the proton resonance frequency. See Appendix 1 for details of field calibration. Two 11" coils (fig, 5-D and 5-E) are wound to adapt the ADL magnet to magnetic resonance, One, of 608 turns, provides 0O cps modulation necessary for phase sensitive detection of both the electron and proton signal. The field correction current was fed into a 2000 turn coil. Consideration of a good signal-to-noise ratio leads to the selec-~ tion of an r-f field at 9500 Mc/sec; iwe., the 3 em or X microwave band. (See figure for the microwave system.) A TS 13/AP surplus test set at full output gives 25 milliwatts of microwave power at from 8500 to 9700 Mc/sec. A unidirectional coupler feeds power from the generator through a wavemeter (fig. 2-W) and a tuning stub section to the E arm of a Magic Tee microwave bridge (fig. 2-T) whence the energy divides into two symmetrical H arms of the Tee. Terminating one arm is the sample cavity as described above; a precision attenuator and phase shifter in the other serve to balance the bridge. Any unbalance of power reflected from the H arms is detected by a crystal diode in the fourth arm of the Tee. The d-c magnetic field is modulated sinusoidally at 00 cps by 1 to h x 10°* wfm? peak to peak. As the field traverses the resonance region, the crystal diode detects a signal whose component at 4,00 cps Ju has an amplitude proportional to the derivative of the resonance line. The signal plus noise is amplified before being fed into a phase sensi-~ tive detector which filters out all but the 00 cps components. An absorption spectrum is traced by a Brown chart recorder activated by the rectified output of the detector. An automatic frequency controller serves to lock the klystron to the sample cavity resonant frequency and, incidentally, suppresses the dispersion component of the paramagnetic resonances The Varian EPR spectrometer (v-l,500)* is a commercially available unit whose operation is sufficiently similar to ours that reference is to be made to it for specifications and circuit diagrams. % Available from Varian Associates, 611 Hansen Way, Palo Alto, Calif, =~1LO-= III. EXPERIMENTAL PROCEDURE. In the experiments described for nitrogen and ammonia, the following procedure is followed: 1) 2) 3) h) 5) 6) 7) Evacuate inner dewar, test for leaks, and fill with helium gas to 1 atm. Evacuate dissociation apparatus including tube to sample cavity. Fill outer dewar with liquid nitrogen. Precooling takes at least one and one-half hours. During precooling insure that the spectrometer is functioning. Greater stability is obtained by giving the electronics time to reach thermal equilibriun, Transfer liquid helium into inner dewar. Obtain the cavity resonance by varying the frequency of the klystron. This condition is most easily observed by modulating the repeller voltage of the klystron with the linear sweep from an oscilloscope and watching the output of the diode in arm four of the Magic Tee on the oscilloscope. Isolate the sample cavity from the dissociation circuit. With the diathermy power at about 50 watts (half power), adjust the flow and pressure of nitrogen gas until a spark coil triggers a continuous discharge. Adjust pressure further until a strong yellow afterglow appears in the gas issuing from the dissociation region. (Ammonia gives no afterglow; adjust for a bright discharge.) Now open valve leading to cavity and condense discharge products for two to five minutes. It is 8) 9) =1l1~ well to observe the cavity resonance during this time to prevent lowering its Q too greatly. Finally, isolate the cavity and stop discharge. Observe cavity resonance on scope and adjust attenuator and phase shifter on Tee until the resonance curve is completely suppressed. Then unbalance attenuator slightly to allow diode to operate in more linear region of its characteristics. Measure frequency of klystron with wavemeter and switch klystron to automatic frequency control. Sweep magnetic field through region where resonance is expected from knowledge of magnetogyric ratio of paramagnetic species. This is .3h w/m? for an S state. The Brown recorder side mark- ing pen is used to record the proton resonance frequency for field calibration. IV. RESULTS. A. Nitrogen Using condensed nitrogen afterglow as a sample, we observed the paramagnetic resonance spectrum illustrated in figure 7. Several such spectra were obtained, all showing the same features: three distinct lines whose center values are marked A, B, C, plus two weak satellites at points 1 and 2, The spectroscopic splitting factor, g,, for the central line is 2.0013 £ 0.0005 while for free spin resonance g, = 2.0023 (12). The splittings from the center line of the triplet are each 0.000 weber/meter? and of the satellites, 0.001) and 0.0016 w/m* for 1 and 2 respectively. A long lived species is indi- cated inasmuch as the resonance signal did not diminish noticeably in intensity in spectra taken several hours apart. The spectrum obtained is the one expected from ground state atomic nitrogen (see Appendix 2). The observed splittings for the triplet yield a value for the hyperfine coupling constant, A, of Afi*/h = 11.2 Mc/sec. This compares closely with 10.5 Mc/sec found by Heald and Beringer () in the EPR of nitrogen afterglow at room temperature. A can be calculated for a given configuration, and for a pure 1s? ,2s" ,2p° » a, State (very nearly the ground state of a nitrogen atom), the result is zero (13). A treatment involving configuration inter- action would be necessary to confirm the experimental A. The significant difference between these results for condensed afterglow and the data of Heald and Beringer on the EPR spectrum of -13- room temperature afterglow consists in linewidths of the members of the triplet. They report a linewidth of 0.00009 w/m? in the gas, whereas we observe almost 0.000) w/m? in the solid. On the assumption that this broadening was due to dipole-dipole interaction between atoms in the solid, we expected that dilution of the afterglow with inert gas would decrease the linewidths. Precisely the opposite result was obtained from a 10/1, argon/nitrogen mixture which was dissociated and condensed at 2°. The spectrum is shown in figure 8 and it is seen that, although the splitting is unchanged, the lines are about twice as wide as for pure nitrogen. The explanation may well be that the N atoms act as lattice defects in a closely packed molecular matrix. Argon may form a smaller crystal structure than N, with a greater overlap of molecular and atomic electron wavefunctions. Experiments are in progress to obtain additional information on the stability of the frozen active nitrogen. The equipment is being modified to permit operation at temperatures above ).2°%. No explanation is offered for the satellites 1 and 2 except that impurities are suspected since the intensity varies from one run to another. Be Ammonia The discharge products of ammonia were produced and condensed by the same method used for nitrogen. Figure 9 shows the EPR spectrum obtained for NH,. The components of a doublet lie 0.02729 weber/meter? below and 0.02355 w/m? above the position where a free S electron resonance would appear. In frequency units the separation of the ~1)- doublet is 1433 Mc/sec. A triplet spanning 0.0008 w/m? with its center line satisfying the free electron resonance condition appears between the doublet. There are two main facts that serve to identify the doublet: 1. The hyperfine splitting of the ground state of hydrogen amounts to 1420 Mc/sec. 2. Jen et al (11) have observed a similar EPR signal from pure hydrogen under the same experimental conditions and have identi- fied the source as atomic hydrogen (see Appendix 2 for analysis of EPR data on solid hydrogen). Likewise, the triplet is identical to the spectrum reported in the previous section for pure nitrogen. Accordingly, it must be concluded that both atomic nitrogen and atomic hydrogen are present in the frozen dissociation products of ammonia. -15~ V. SPECULATIVE COMMENTS. A. Nitrogen If the explanation of the « lines in the condensed afterglow is correct, one should expect to find measureable quantities of ®D atoms persisting for 15 seconds after the discharge has ceased. The fact that Heald and Beringer (h) were unsuccessful in their attempt to find the EPR of the ®D state does not necessarily mean that its magnetic resonance is actually unobservable, either because of extreme line broadening or large zero field splitting, particularly since both of these effects are usually of small magnitude in a gas. More likely, the number of ®D atoms available in a cavity full of gaseous afterglow is simply too small to produce a detectable signal. On the other hand, it may be possible to collect a sufficient number of ®D atoms in a condensed afterglow, but in this case there is evidence for consider- able zero field splitting, namely the 20/cm splitting of the *D - *S optical transitions. Thus, even in fields of 1 weber/meter® complete quenching of the orbital angular momentum occurs. The resulting paramagnetic resonance should differ from a pure spin resonance only to the extent determined by spin-orbit interaction and would thus serve to establish the spin-orbit interaction energy for the ®D levels. This is an experiment worth trying. -16- Be Ammonia In addition to N and H, there are other possible dissociation products from NH,: NH, NH,, N,H,. The configuration of NH is knowm (35 ground state) and a spin resonance should be expected. None, however, is observed. If an accurate ratio of N atoms to H atoms, Ny/Ngs in the discharge products were known, the presence of other species could be inferred, For example, if Ny/Ny = 1/3, it could be reasonably inferred that the dissociation process was exclusively NH, —> N + 3H, particularly since recombination into molecules is evidently slow for these species. Ny/Ny can be determined to the accuracy with which the relative integrated EPR absorption signals, Ay/Ays ave known. If the magnetogyric ratio, J, and the spin angular momentum, Jh, are known for each, the ratio of nitrogen to hydrogen is Avg Jy(Sq +2) / Ay dy Jy(dy +1). Zero drift and noise in the EPR detector makes an estimate from our data of N/Ny =F] uncertain within a 300% error. With care,mich greater accuracy could be obtained. The experiment will be performed again with more adequate equipment. -17~ VI. CONCLUSIONS. In conclusion, the results to be drawn from this research include: 1) Atomic nitrogen can be collected within a solid matrix of molecular nitrogen by freezing out the products of a nitrogen discharge at liquid helium temperature. 2) This atomic species may be detected by EPR methods. It is identified with a high degree of reliability from the char- acter of the absorption spectrum, 3) Permanance of the observed atomic nitrogen signal suggests a high degree of stability, at least in the concentrations obtained. Thus far no observable decrease in the signal has been observed over periods of several hours. h) Similar experiments with ammonia in place of nitrogen have shown the presence of both atomic nitrogen and atomic hydrogen. (The spectrum of the latter is known from other EPR work.) No direct evidence for other dissociation products is apparent. Two additional experiments are suggested. Stability of condensed nitrogen atoms should be investigated at temperatures between .2°K and the condensation point. In addition to indicating at what temperature recombination takes place, valuable information on the crystal structure may be obtained from line-width measurement. Another interesting possi- bility is to attempt to find the low field resonance of the quenched a) levels of atomic nitrogen. choke flange to vacuum pump epibonag sd- hesive seci — teflon L . / gasket { 4 \ f N 7 N to diathermy ———_ - \ ‘ SAAN ‘ ~~ QQawy flow adjust valves pyrex tubing f f gas inlet X- band “ waveguide | { | | | | —sample cavity Fig.l GAS DISSOCIATION AND CONDENSATION APPARATUS GENERAL VIEW OF EQUIPMENT =20- sapeicanennignseifenspionsinnsentanstieevmaaaihil a 4 Fige 3 CLOSEUP OF DISSOCIATION APPARATUS Rinsing Fig. hk LOW TEMPERATURE SYSTEM Fig. 5 DEWAR SYSTEM BETWEEN POLES OF ADL MAGNET Fig. 6 ELECTRONICS: PROTON CONTROLLER AND EPR SPECTROMETER y, =9555 Mc/sec -.0010 34146 +.0010 weber/meter2 Fig. 7 EPR SPECTRUM OF CONDENSED NITROGEN AFTERGLOW v =9539 Mc/sec — ! at -.0010 .33994 +.00I0 w/m? Fig. 8 EPR SPECTRUM OF NITROGEN DILUTED WITH ARGON == ) =9518 Mc/sec | | B—> l l i: -O273 33967 w/m? +.0235 Fig.9 EPR SPECTRUM OF CONDENSED DISSOCIATED AMMONIA APPENDIX I. Magnetic Field Calibration The use of a proton resonance field controller greatly facili- tates highly accurate measurements of magnetic fields. The proton reference sample used here was a 1% molar Fe(NO,),-6H,0 solution in water, Using the value for the magnetogyric ratio given by Thomas (lL), Yproton * 2+67530 * 0.00006 x 10°m? /weber-sec, one obtains the field in terms of the proton resonance frequency, B(weber/meter?) = 234.859 ) (Mc/sec). ~26—0 APPENDIX IT. Calculation of the EPR Spectra for Hydrogen and Nitrogen If it is desired to evaluate the effect of a magnetic field, B ; on the energy levels of an atom, it is necessary to know the quantum mechanical analog of the classical magnetic moment, Ki » inasmuch as the addition to the Hamiltonian is -M-B, The atomic magnetic moment operator can be written: JA = YJ ) Be = % Je, where J is the angular momentum operator and Xo is the magnetogyric ratio. For pure orbital angular momentun, J=L , d¢ =1Bohr Magneton/ 4, while for pure spin, J=3, Y¥,= 2 (actually 2.0023) Bohr Magneton/ 4. Intermediate cases depend on the specific configuration. Ina like manner, the nuclear magnetic moment depends on the spin operator: BA = Xi I > where iA = 2.6753 x 10 meter*/weber-sec (1) for protons. A given configuration possesses (2J + 1)(2I + 1) degenerate magnetic sublevels, Inasmuch as each of these levels is an eigenstate of the operators Jz and di, » the effect of a magnetic field is to remove the degeneracy by adding an energy AE = -(8 mp + kirms)h B to a state with J, and J, eigenvalues, m, andjm;. Selection rules for transitions stimulated by radiation permit only those of the form: Aymy= +1, Apmi=O or Ama=tl, Amm,= 0 The first corresponds to transitions responsible for paramagnetic -27= resonance absorption and the latter for nuclear resonance absorption. It is to be observed that transitions can occur for only two radiation frequencies, namely: Avepr = GAB or hUma= YAB. Consider the effect of hyperfine interaction between the nuclear and electronic magnetic moments. The interaction term which mst be added to the Hamiltonian for the system will be proportional to the cosine of the angle between I and J and may be written: V= ALS where A, the hyperfine coupling constant, depends on the configuration. The second order formila for the perturbed energies, AE; = Via + x, IVegl' A i-Ey), is utilized once the matrix elements, the V435'8 » of the perturbation energy in the unperturbed representation are calculated. It simplifies the calculation of Vaj to note that, IJ-L54+4207+1J), were, Js dx tid, , Je hk -t4d etc. These are the spin raising and lowering operators since, J lang) = VU - png) +g +!) UY (J, amyl) , J “i pny) = VG +g) (J m5 +I) LW, ml) . To illustrate the calculation, consider a ground state hydrogen atom (7S, I = 1) in a magnetic field. There are four degenerate substates: _ . ss -~ Lt le Meg = MM s=F, Mi Zz Qe Amrs= ~-Z, mF FZ Le __/ 30 rms = FE , mest 3 he puss ~-S,rmirrr. ~2B— Then Viz = -h (sms + Yum) B+mmAh* and Vas = AA Note that all elements between states of differing My tri mist be zero because internal forces cannot change the net vector angular momentum. The new energies are: 1 AE = Vi, =-¢h(K+ YB + $M, 2. AF, = Vaz + ZAR =-thl fs+pJB-4M+N, 36 AE, = Vox + AR) =-zk(f-K)B-2M—-N, be AEs = Vaq =-5 KE -Y)B +2M-~- M= Ah? ,N=M*V7i(K- (IB *=M/KYsB since L/h x 600, Paramagnetic transitions can occur between states 1 and 2, and between states 3 and ), with, hve-1 = kA&B- M+N, Most. EPR spectra are observed as a function of field with D held fixed. In terms of B; the resonance condition is: Bt = (hv 4tM-Ne@) ids: Thus, the hyperfine coupling serves to split the paramagnetic resonance line. To first order in A, this splitting, AB = 2M/hf, is symmetrical about the free electron value (A= 0), but to second order there is a displacement of the lines by an amount, ($\B)*/4(B.+B), toward lower fields, =29~ Jen et al (11) observed two lines in the EPR spectrum of condensed hydrogen dissociation products. One lay 0.0276 weber/meter? below the free electron spin resonance position, and the other 0.0231 w/m? above. The field averaged .32) w/m?. The theory predicts a displacement of the center of gravity of the doublet by, > (0.2342 + 0.02746)/.32h = -.0020 w/mn* The experimental value, (-0.027h6 + 0.02341)/2 = -.00202 w/m*, differs by 1%. The same technique used for hydrogen is readily applied to the ground state of nitrogen (1s?, 2s?, 2p’, *S, 1 = 1). There are twelve degenerate substates, which makes the calculations lengthy. The results give (2I + 1)(2J) = 9 paramagnetic transitions yielding five distinct lines, at, hY¥;B= (hv + Ak?-2D), (hv +Ab?), (hv -D) D= (AKD/K YB. If we assume that the natural EPR line-widths are mich greater than D/ h Mss the spectrum is a triplet. From the separation, A B ’ of its extremities, we can calculate the hyperfine coupling constant. The triplet spectrum described under results on nitrogen gives the value, 2 -4 AB = 2A = 8x10 W/m? @ 9500 Messec. With ¥e/aT = 2.80 x10* BERee , the hyperfine coupling constant is given by, Ah = 45 (2.9 x10%) = 11.2 Mec/sec, -30= and thus, nea 2 2 2 D/h Xs = AREAL) = (ARIA Vag = 5x10 W/m", far below our limit of resolution. l. 26 3e he De om Te 90 LO. =~31- REFERENCES. P. Lewis, Astrophysical Journal (1903) Vol. 17, 258-269 Astrophysical Journal (190) Vol. 20, 9-57 R, J. Strutt, Proceedings of the Royal Society Ser. A (1911) Vol. 85, 219-229, 377-388, 533-536. See also volumes 86, 87, 88, 91, 92, 93 Joseph Kaplan, Physical Review (1932) Vol. 2, 86-96. Mark A. Heald and Robert Beringer, Physical Review (195)) Vol. 96, 65~6),8 E. Wrede, Zeits. fur Physik (1929) Vol. 54 1-2, 53-73. D. S. 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