A Review of the Literature on the Compton Effect Citation Briggs, Thomas Henry (1929) A Review of the Literature on the Compton Effect. Master's thesis, California Institute of Technology. doi:10.7907/R1Z9-6G10. https://resolver.caltech.edu/CaltechETD:etd-03222005-091536 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: Physics Degree Grantor: California Institute of Technology Division: Physics, Mathematics and Astronomy Major Option: Physics Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Thesis Committee: Unknown, Unknown Defense Date: 1928 Record Number: CaltechETD:etd-03222005-091536 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-03222005-091536 DOI: 10.7907/R1Z9-6G10 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 1055 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 23 Mar 2005 Last Modified: 03 Oct 2019 23:04 Thesis Files Preview PDF (Briggs,Jr_th_1928.pdf) - Final Version See Usage Policy. 3MB Repository Staff Only: item control page

A REVIPY OF TU LIPSRATORP GN THE COMPTON EFRECT Thesis ov: Thoméa Henry Priges, Jr. a) In partial fulfillment of the recuirenents for the degres of Vaster of Science 3 CUA Ataat or PY Montane ptoa banat sien) OCA TET AT am CALIFORNTA INSTITUTE OF TSRCHNOLOGY r Pegadens, C&allfornia, I Introduction As esriy as 1912 it had been fownd that scattered X-rays were softer than the incident rays. Sadier and weahem =? tested a prediction of the Thouson theory in that year thet the scattered reys should heve the saue ebsorption coefficient as the primary reys, They found quite the opposite to be true; nemely, the s@attered reys were softer tesn the primary reyes, Fiorance (1) ned founda the seme effect in the cese of the gamma reys from radium ee eerly as 1910, Any theoretical work which wes done following these exceriments was along clsssical lines end in no way approached the final explmetim later put for-~ werd by Compton after more accurate wessureaents had been carried out in 1924, Debye in 1915 ettemoted to extend the classicel theory of scattering by taking into account the arrangement of the slectron in the etom, He stated that there would be interference effects between the rsys scattered from the various ¢lectrons in the s*me ring, Byt even this was not complete, for it essumed the electrons to be arr«nged in only one ring around the nucleus, 4.4¥,Compton 4.80 attacked the problem of scattering from this point of view. But none of the methods seemed setisfaustory. ia) In 1982 Compton first obteined experimentei evidence for &@ chenge in wevel length uoon scéttering, Since it secned asible to explain this on any save the quantum theory, re) Compton wes led to develop suck an exnlenstioc: Rerly in 1983 Compton published his extreme corpusculer theory in suppcert of his previcus quantitative experiments. Practically simultencously, but independently, Pebye appiled the quentum theory to the scattering of X-rays end arrived at the same result as had Compton. The corpuscular picture end explen®tion are csiven lster, _— 4 h . : : . Imnedisetely oter investigators started Work to confirm Comptonts cate, Ross, in Californis, was the first to be successful, He improved on previous work by obteining 8 phetogreachic record, wheress Compton hrd been using an foo @ ry Lfonizetion chsmber, Dusne and ssociates «t Harvard, 4 however, seemed to obté@in negative results. But after repested trials thev too confirmed Compton and the 1lést reel opposition was removed. Whet Duene reelly observed at first wes a so-called "Tertiary" effect, which will be bricfly mentioned later, A ct present the experiments end theory upon the amount of sift of the modified line, send its dependence upon the re) Fh angle scattering, °se so well knowvm the no further work needs to be dme woon it. But the intensity distrib-~ ution of the shifted line is still in nded of much invest-~ igation, Following the early period of experimentél activity re~ fue <Q there came a large amount of theoretical work, Th sulted in the expleanestion besed upon the quantum theory. Then refimements of measureménts and a f-w new evidences on intensity distribution were mads. #auncey's theory of the scattered intense i ity end the wave mechsnics!' theory have been the lstest importent steps, Now it remains for exverimentelists to vroduce more securete intensity date end such &s can be compsered cone with snother for different oe engles of scattering, So fer the veriebiiity of « experime ental conditions have nesde this st best a compdiceted end uncertain teak, In the experimental chepter et the enc of this p&per we Will brieflv mention two methods which mey sccomplish ¥ this end, c.7,R,wiaaodt+! an ices cptein-d photographs of re- coil electrons by means of his will-~known cloud-¢ xpension apraratus, Quentitetive wesasurements on these plates verify the corpuscular explenetion of Compton nd give added weight to the evidence in favor of the quentum theory as opposed to the wave theory. At first the experimental results differed from theory in thet en umucdified line was found &t the sane time as the modified one, Also the modified line hed 4& greater width then either the primery or the inmodified lines, Part of the width could be expleined vy slight varisticns sn the value of the scattering angle, but not sil, by sny means, The explénations of these two voints «re taken up later on. Inesimich *s the Compton effect cen seenmiagly be ex-~ pleined upon ths basis of the classicel wave theory, the nausntum theory , or the new weve mechanics, jt is natural to try to obtain some correlstbon ehong the three theories, a4 No one of these three methods suits everv problem in sciencs, The weve theory can not explain the photo~slectric effect, the quantum theory es yet frile to interpret opbiceali inter- Terence, the weve mechenics is too new and difficult to heave had complete success, But there these thrse basic theories overiep to explein one end the géne phenomenon then it would Several attemnts heve been made in this direction end the correspondence principles so determined are wentioned, as they occur, in tris paver. No one of them is generaily ohenomencn of Professcr Comptonts 4 valid, However, this gecems to give mn excellent base from which to work, As more work is done on the subject it is hoped that more conclusive methods cf bridging between them will be found, It is for this re@son, pertiy, that sc much importence is olacedupon = correct solutim of the intensity problem, The wave theory of light has stood more precise tests than almost any othrer theory on the histcry of science, With the addition of Maxwellte equations end electromagnet ic ideas there seemed to be nothing more to be desired in expleining the voropagation of radiatiom, But Plenck in studying black body radiatiom foimd discrepancies which seemed to indicete that the electrons covld not be thought of ae continuous radiatiors, This led him to postubte his corpuscular theory, or cuentum theory of redietion, In the field of spectral eng lysis the quentum theory was eg pec olally attractive, The Gompton effect derived much of ite bmportsance from the fect that it was the first. direct experimental evidence fevoring the then new quantum theory by disclosing encoumters between quanta of radiation end "free" slectrons, Thus the Compton effect, with all the evidence which it presents, strongly confirms the idea thet radiaton travels in ousentea of energy hv, snd with momentum hv/e "“whick never expend, or at sil events élwéys reméin suall enough to be swallowed up in oe gulp by en atom, cr to \ strike an electrm with one single cmcentrated vlow,"(C) However, it is not bo be understood that the wave theroy is by this entirely superceded, For, as is elsewhere pointed out, the thenomens of diffrattion sre best explsined by the weve theory. The -~vantum idea may reelly be thought of es meking accord between weve and corpusculer theories, Nor can it be forgotten thet the quéentum theory involves the wave theory in its most fundsmentel concept, for the "quentum of a given radistioi is defined in terms of the frequency of the rédietion, and the frequency is determined n(C) by spplying the wave theroy, The discussion of the Compton effect which follews is the basis upon which someo f the present evidence for the suantum theory stands, ‘!s the yet unsolved questions 2 ere answered it can onlv be hooped thet the discord of Wave i) end corpusculer theorics will be removed by some unifying zeneralization, Tt h&ég been impossible to find & definite test to ~O- indicates the mann er in which scsttering takes place. The two proposed mechaniams ere (a) delayed, (b) instantaneous, The deleyed type su “poses the stow to absorb the quantum, hodd it for = finite small intervel of time, end then emit it, after heving moved an appreciable distance, This is e complicated process end one which je difficult to justify. At best the delayed theory covld not explain wmmodificd acatterimg which has been showm to be "ocherent"--i.e, to pe definitely in ph*se reletionshop with the vrimary red- jetion, On the whole the instant&ecus recoil of the quent ead emission of the electr n eme used througho’t modern theory. It is on this letter assumption that Jauncey béses bis intensity formula, By plecing absorbing screens in the path of the pri- mery rays, and then in the path of the scattered rays it was originslly shown that the scattered rays were softer than the incident reys. This same wehhod has also been =) aged to show thet gemma rays from radium mdergo soften- o jing upon scattering, However, since the energy of the gamma rays is so grest, nodne of the electrons are too tightly pound-=or practically none--not to suffer ejection as recoil electrms from the perent atom, Henee the unmod- s;ficd line is entirely absent or too feint to be observed, However, meesurements on the ch-nge of absorption coeffic~ jent agree wery closely with theory. This shows that 4s. the limiting case of infinitelv stort waveslengths is ap- prosched the scattering of electrons obeys the seme rules, =_7— Duane's Tertiary radistion, so-called, was attributed to photo-electrons emitted when the primary X-rays struck the scatterer, It vas supposed thet some of these entered the scattering subst-ncé that some of these entered the scattering substence and struck other atoms m&éking them emit obher X-reys, Duene tried to show that these would heave a maximum at about the ssme scoint as thst at which the Compton maximum occurred. But this view had to be abandoned for it cculd not explein the dependence of the shift upon the angle of sesttering. Before going on the theory of the Compton effect it A, z <My* 2 mir mey be well to present a ver ~ Reerth flee schematic diagram, due to Richt- | Phentey ah ce tiinn meyer, which readily shcws the | relations existing between the ) Meuwther ~ As. a gtten A ) various phenomene accompanying Z.cuw” S aa a —- Re cvetadten S sedate Repructed the interaction of readistion md Ros metter. a K ‘ 1 AI,= Zh’, ee An imagintry horizontal fF errr legal erg eer ce ae A pl uf ye] : RA sn . ame OF The line mey be drawn through the ‘*~ Crrnpetin Mod picek Coca CK bane “pen midd muare to separete . middle of the square to separste Fy. the radiation (lower helf) from the non-rediation (upper- half). It will be noticed that each radiation arrow is directly associsted with e non-rediation errow, This rela tion is indiceted by disgonally opposite positions, Thus the shifted frequency whbch oc-wre in the Compton effect is directly crposite the kinetic energy of the recoil electron, (The directions of the arrows have nothing whatsoever to do =B. with the direction which these rays and corpuscles actuaily may assume in experiments, Arrows at the too represent respectively: the recoil of the atom (4uv*), the recoil of the electrons as in the Compton effect (hunv® ), end the energy of the vhoto-electron (luuF ), where u is the velocity of the photo-electren, In the bottom half we have the fluorscent rediation which is charecteristic of the mstter with the relation dmu® =< bw-—hvo, Where nvg= Zbve, for the fluorescent radiation may be emitted at a number of different frequencies, which employs f to distinguish particuler quantum transitions. Then folloWs hv', the modified energy of the quantum thrown off in the Compton effect. Finally, there is the unmodifiea scattered quantum hv which ceases the unmodified line. II, Theoretical Thomson Classical Theory: The classical theory of the scattering, developed by J.,J,Thomson and extended by Debye, accowmted for weny of the experimental properties, The successes of the theory led to the general belief that sdatterting could be pleced side by side with interferencg and refraction as positive proof for the cl*ssicsl ideas of electrons end electromag— netic waves, However, Thomson's theory could in no way zecount for the Compton effect. And this new phenomenon, being quite opposed to the laws of electrodynamics, forced people to consider ecattering to be direct evidence in favor of the quantum theory for readiemt energy. Tt is true that the observed energy leaving & free electron upon sesttering is in close sgreement with Thomson's tlassicai theory, but it does not agres When the metter of wevelength ise conderned, The Thomson theory says that no chamge in frequency is to be expected upon the Classical theory. Even if one thinks of the Doppler principle as being setive in causing the shifting phenogenon, the scattering _varticlesa would have to be moving in the direction of the primary beam at & speed comparrble with, bué considerably less than that of light. This is not possible on the clascical (Thomson )theory, which supposes thet all the electrms in the radistior ere effective in scattering. Thus the classical electrodynamic theory appears irrecon- cilable with. the view that the part of the secondary réya thet. are of greater wavelength than the primary are truly ee vse ~1O— scattered, This objection, though has lost its force since both the modified and the unmodified scattered radiétion heve been observed. It was advenced soon after the Compton effect was discovered, The reason for failure of the Thomson theory is that the magnetic fickd vector, and hence also the radistim pressure, is negiecteal?”) Doppler Effect: This method cf explaining the Compton effect is based upon the fact that the electra after impact by the incident quantum is supposed to move off in a directicn, depéenden upon the initial conditions, and simultaneoursly to amit energy. This will be in the form of spherical weves, If the electron were stationary when it received the incident it were possible to assume thetythe rédiation then there would be a change of wavelength for scattering streight. forwerd in the diredtion of the primary radietion, But té&e electron must be considered to be in motion, and hence a double Doppler effect occurs, The electron is in motion both for the radietion it receives (primary) end for the red~ sation it emits (secondsry) as well, Hence in the forwarc direction there is no change in wavelength. An observer on. the moving electron receives the incident waves at a lower frequency than thet at which @ stetionary observer would receive them~-essuming th:t the electron is travelling in the direction away from the incicent waves. And this decrease of frequency in the forwsrd direction just colp:n- oroduced by the forward crowd- kh. z aetes the shorter wavelength ing effect of successively emitted weve fronts. Let it be in the accompanying fig, II, re- present some particulier phese in ot Bb a nearly ~lme incident waves the ciréeles represent that perticular phase in the scattered a4 es Ou wave which is slways emitted from the electron when sai oarticuler phase of the incident wave Grrives at the electron, heses then the corresponding ct echere and plane sre tangent at the instant of emission, emd will remétn tangent forevermore, in the forward direc- tion, since ‘n that direction the phése velocities are peralled end equal to the speed of light. However, Compton h-s célculsted that the oscillator c _ ¢ must heave @ velocity equal to Agmc = NM. +1 in the y eaund to Aenea SOY gy diredtion of the primery rey to obtain the correct change of frequency. Where Ay is the incident wevelength, and the other terns heave the usual meanings. The methematical derivation is mimportant for the purposes of this review, and if desired mey readily be consulted in & number of serly papers (cf, bibliography pepers numbered 18, and 110), It ie suffici that the results obteined by the Poppler considerations ~-omiftting relstivistic worrections-—nere the ene, to the first order, as those obtained by Compton's extreme corp= usculer view, Using the relativity consideraticns th reswits sre snelagous up to second degree terns. The end formule ia! ), AA 4 Ul- 24, where ic the incident freguency, 2 servetion is mth ct oO of frequency is ©, #s Fs . ’ } | ; fee by Comptonfs theory, end tor G=1e0?s AAs Zh Ie F447, f poseible of explsnation uvon the basis of stendatd ideas, rether then heaving to think of an entirely new set of concepts, even though. these new concerts ere more probebly correct, and (2) to give @ method upon which to base a possible correspondence priné¢tple between wave end quentum theories, With regerd to this last point, P.S.Epstein hes pointed out such & correscondente principle, He assumes a vistual oscillator redisting according to classical laws during the intervel of bmpact., This has a velocity which is the vectorial mean of the initbal Gnd final velocities, This gives the correct shifted values from the Doppler effect, The msin objection to the Doppler effect as sn explan~ ation of the Compton effect is that it requirss & uniform he velocity ah” for the electron, The radiation pressure, however, would give sn acceteration, aid while the é@ectron wes getting up to the required speed the Deppler effect ‘ 128 $ “ pe agg oh , would give the wrone. frequency. But since the Compton lins is diffuse and not sharp this East objection is not very strong, ~13~ Extreme Corpuscubar View: The extreme corpusculsr tteory in explsnation of the Compton scsttering was edvenced almost sinultancous ly by (17) Compton end Debye, To American writers it is knom as the Comoton theory end to Europesns as the Compton~Debye theory. We will snter into the expkenétion of this theory for the waveisigth chnge of sesttered ¥-reys sore fully then for the other theories for séverél reasons, In the first place it is the mo t generally accepted explenaticn and gives a picture most easily unaderstcai. Second, the Compton effect is taken ss being the first most important evidence. for the light quentum theory, and this Compton- “Debye axplenation is besed on thet hypothesis. And finally the resuits of sll the other theories may be shewn to be analagous to those obteined by this method, tefly the picture mey be given as follevs, For ~ Simplicity we assume the sectteringe electron to be at rest et the instent of impset of the incident light quantun avg. Where his, as uausl, Plenek’s constent, end vo the frequency of the incident beam-~"nadelatrahling"-in the notation of Cermen writers, The 3 ple st method bf der- ivetion is to amit reletivity corredtions for the eleectron after impveé, Ye shell here eomsider such teras, 4s the difference is not very great, end it adds to the completeness considerstions of the lew of iar te- in: h- Ad'eme? (aes ~ Ua conservetion of energy we ob. q ~14. Then, considering the X and Y components respectively of the moments, we have from the conservation of momentum Av. Av'. IA 3o gg 14h] law: Gos Re wo FG + Goo or ( / C= Ae wt A Po + MFC Ue Clay From squétions (14,1) and (14,2) we obtein, by elimination Cc : L of the angle @: (ty TUS Cet (aS which could have been obt ined directiy from the figure oy the law of cosines, The engle of scattering (>) is determined by the point et which the observation is made, and is, conzequently, 4 know cvantity. The thre> vnknowas to be determined by + hr 2: at . ' reg 2637 if at these three equations «re v' (changed frequency), ? © 6nd he angle of the recoil electron, Valude of m (mass of the = electron at rest), v (frequency of the incident radistion), end c (the velocity of light) are all numérieally kno, (A) Compton's deriveticn we write A te Pertiaiiv followin: OQ Yoke, f A = 7u for more convenient actation of the result. The solution, readily obdtained is: { a f i . 1 ¢ A FAS inc to ce Bi M44, a“ - A= Ke b/g (4 »G) OOK OG Brg sla 3 hs, Considerstions of cquation (14,4) show that the shifted wavelength must be larger then thet of the incident besem, Also, from (14,5) it is sapperent that for en angie of scat- + tering @:oWe have no ch=nge of wévelength, and for @=is0° 2 2 +, . . A é - 2 ure Aa the shift is & maximum, which i@ ecutl: 2 Mme 7 Oo. 045A The relation between the engle of scattering and the -~15- anglé at which the recofl electron is ejected B&s bes: ~—, £ a3 ent found sporoximsteiv to be” Syn ot & | It holds 3 ~N e where v' is nesrly eousl to v, because ti ry en the momentum triangle is nesrly isosocles, This mems thet if the scattering angle ¢ increases from 0 to 7 , then@ decreases = fron "/2 te oO. 7 Q se] fee his is directly evident, siso, fewm fig, II. xy NOW Fle f the initial motion of the scattering particle be taken into accowmt-~say witha velocity Vo which mskes the incident ray, then the y “ = / vi} — est y > el EL (f4, i ¥ Go 1 +h A 4, 7 Me Lv 2 7 o avd ro d & / 1408 dey . , ) a ae wv ‘fis fF a 3 g e 18 a = ? ¢ ros ° v7 rt - o . 74 wou y ! or,» y & 2 r , ~ * on _ 7 on f r a ¥ 7 a ar elie o a wo — a sua sg fb CN eg ew Yee sg Laney , en a ae & y é ¢ Where the capital Creek letters denote a new set of angles, corresponding in position but differing in magaituds from those of the first set of exuations. Lb, deBrogiis has Solved these equations and arrives at an answer 6¢ the same form as (14,5), but wore complicated, = ~~ y . : “@ ! 1 pI ONO ha ® Ne eo ? Yo vi . ~ farg, Pr Po? vo / = ra a ® aot & fie Zan rt oe eo Po oon Ors ¥ é Tf vo=O0 is substituted in (15,4) it then reverts to the form of (14,5). Farther, if the initial velocity is suff- ioienatly ere at (By 2) then the Gompton effect entirely 4igappears sad (15.4) gives the custouary Doppler effect oy . 97 for scattering by 4 moving electron | ), If,in setting up the energv equation for this type ct of scattering, sccount Were taken of o ce?) 1i posbible sources 5 : Lyset £V, we snould have to add a term ev to 3 of loss of ene Y cr r equation (14,3), sey. Where Mis the mass of the ‘atom éod V ita recoil velosity, But inasmuch as V is so mmall this term may readily be neglected in all cases, A further correctio: should, according to Compton in his boox, be 5 added--hvg-~~to denotes the energy required to remove the @ cattering electron from the atom, But according to Jaun-~ g re) te 's theory the process of scettering is conesived of as occurring in so skort a spsce of time that the electron moves only a negligible amount through the atomic force ficld of the nucleus, During the process the light quent in its interaction with the electro does no workof ion- Lgzatio. upon it, In this theory the electron obtains all its moamentuma and energy from the light quant in 4& sudden impulsive blow md sudsenuently, after the quant has trav- elled off with lost energy snd changed frequency, the electron "csobata up-"i11", so to spe'k, out of the Atom wpon the momentum gained from the collision... Tut the equation of conserve tion governing the collision sxpress only the ecuality of energy and momentum gust before impsct to the corresponding quantities just sfter impscot, fnd since in this Susll time interval the electron head not moved apprecisbly with respect to the atom these ejusatioas 2 on So Ga fa So be o ct e) mietin.a term expressing the work of ion-~ igation, Half-—Classi QO fo | ood 3 ry a oO ¥ This scltelesste 1+ theory of the Compton « effect wes inly advenced by Forsteri ing '® 0) built upon the fect that thet the dependence of the seve sleagth change upon the angle of sesttsering is in agresment with that found by the Deppler principle for the scattering of a moving electron in the direction of the primeryv ray. fu other words, it starts vith ideas from the corpuscuia theory and tries to skolain them by the wave theory, Its velocity whien 1% @ chief work is en attem it to justify the is neceas*ry for an electron to heve in order to yield the Doppler effect of the proper magnitude to expiain the observed BHift, Another way of expressing this is that it is desired to quentize the classical velocity equatiom hea Boees--*®— end thus obtain the quantum theorv for Ao), nt, rane o velocity, By substituting one limit in the end equations (for which see the above noted articles} the Compton effect sing the @ from & corpuscular View wolnt is obtainea, anadu other limit the clascicel Doppler effect is found This yields & correppondence between the two explanations of the Compton. phenomenon, QM the whole this theory is a complicated mixturs of syoeded ray) 4 tD or r supe weve and quentum idees which is now ltogeth w 2 by more coherent, if not simpicr treatment: Compton (4) points out thst the velocity #c which the exponents of this idea desired to quantize “is just that which an electro would acquire by the absorption of the energy quantum hv or by seattering svch @ quantum." They thought thet the electron ecattered its energy in ell direc- tions after it hed acquired @ velocity @c. But to do this all the recoil electrons should move forward with .a velocity 3¢C.. However, Compton points out that his experiaent q with S a Vv mon found these felocities to be ectualiv twice 4s great as this theory predicts, "This @C peprese its merely en teffective* velocity, mot a real velocity, of n the recoil eiectrm a Steatistichl Theory of the Compton Effect: Bohr suggested that inasmuch es the light quantum theory is meeningless without some of the notions of the wave theory (i.e. frequency) that there must be some duslistic theory to combine the best qualities of each, A (44) Bohr, Kramers, and Sleter “sought to unite these two heterogeneous views by the etertling assumption that the legwa of conservetion of momentum end energy were valid atetistically, rether then sctuelly for every individual progess, While experiments by Compton snd by Bothe and Geiger later proved beyond 9 reasonabke doubt thet this new theory was untenable, nevertheless we shall briefly desoribve it a8 of historicsl interest, and also shall show the method by Which it was disproved, They assumed thet "spherical clectrowagnetic Waves “21 Ou Oo are scattered by virtual oscillators, one such osctllator corresponding to each electron in the scattering medium, These virtual oscill&tors scatter the radiation ia spherical weves in @ manner similar to that demanded by the classical theory} but to accowmt for the change of wavelength they are suprosed to scatter es if moving with such a velocity that the Doppler effect will give the sasme effect as that predicted by the quentum theory 16") Further in their proof they find the rediétion pressure to be due only to the momentum of « few recoil electrons, Alsc the difference between the energy spent on the virtual oscillators and that reappearing as scattered rays does not appesr uniformly distributed among all the electrons, but rather ss the kinétic energy of a small number of recoil electrons, Thus it is found that the conservation of momentum is only statistically valid. Bothe end Geiger experimentally refuted this view in 2, atriking nenner (©?) The test of the theory is possible if one is able to detect indifidual recoil electrons end individual guenta of scattered X-rays, . Following Bohr, Yramers, and Slater's stathatica& view the probability 7 that a Beta-ray from the scattered X=rgpx should appear at the seme time as the recoil electron is estimated to be less thm 107”, Rothe end Geiger arrang:d two chambers with adjacent openings into which the scattered rays passed, One chamber contained en "hv-counter", the other an "encounter", On the view of Bohr and his associates there shoudd have been practically no e-count snd a very ~FA0- larce hv~count, But the German experimenters found very mweny more coincidences-~a ratio of one to eleven-~énd their apparetus could not detect every possible coincidence, (78 ) Comptoh and Simon performed a second type of ex- periment which also fefuted the statistical idea, "They passed very hard X-rays into * Wilson cloud chamber and ex~ amined the Beta ray tracks so produced, They measured the initial direction of the reco£l electron treck and so measured YW. Occasionally the quantum scattered in the direction @ is either scattsred again or ejects a photo~ electron 28 @ point outside the orimary beam of X-ray. Joining the origin of the first Beta ray tra&k to that of the second Beta-ray track, the angle between thém line sad the forwerd direction of the primary X-rays track is ~p , while the engle at which the first Beta-ray track sterts from its origin measures yn (134) These cloud exp *nsion experiments show tha the number of scattered quanta and recohl electrons sre, on the average, identical, These results are quite opposite from the ideas of Bohr and his collsborstors, md hence may be taken as mullifying their theory. Furthermore the experimental resvlts apeek fevorewly for the extreme light quentum theory. The Weve Mechanics System: Fundamentslly the wave mechanics starts out with the consideration of this equation: UV “Wt 4 OM (EU) = where Eis the total energy, U is the potential energy of the electron, Mu is the mess of the electron, This equation -21]~ considers, for our purposes, the action of only one electron, More terms would have tobe added to this equation for more 3 D complerw forms, As it is we 3 . Lt ie a a erence ee have reduced the problem toa 35 & w hydrogen~like one, i.e. one gE 4 ne ee slectron and the rest of the t ce ee mee ce eee eee eo ee ee nee eS system considered as wore or less of s nuciear entity, The equation has two particular cases, when F is poss itive and when it is negative. Certe@in restrictions are placed on yf ---the "“eigenfunktion"-~-nemely: it uust be finite when integrated over all space, it must be finite at all points in space, and finally it mst venish at infin- ity. In order for yf to satisfy these conditions FE mst heave discrete velues when it is negative. On the other hand, if FE is positive, then it (*) may as eume any one of @ continuum of values. The negatyve discrete values of Ez correspond to the old energy levels, The positive con- tinuous velues of F correspond to the energy of Gn electron in so-called hyperbolic orbits; i.e, an ionized electron, o In Wentzel's theory of the Compton effect a quantum @f radiant energy hv (syy the binding energy of an electron) ia givem to an electron which is initislly in one of the negaive energy levels, The slectron, instead of sbsorbing this energy completely, tnd thus gaining kinetic energy {as a shoto -electroa), radiates part or all of the enérgy it has received, its final state being cither the same as ~ia~ its initisl stete or env one of the states discrete or continuous higher than the initial state, The sbsorption and radistion of energy together with the transition of radistion of the @lectron from the initial to the final atete is here emceived as a single process, The radiation thus sesttered will be unchanged in Wevelength if the initial a and finel stetes of the electron are identicai, These singls fy processes (Since first writing D iv] axa KB te Q ey] a] b iO on) 5 D Q wv ay - Cute can 2B . this a paper by Bergen Davis has avpeared in the Physicel Review for September, 1988, It presents good evidence for Veis Ke cb the 8mecksl jumps where the initisl and finel electron are discrete energy levels.) The energy gained by the electron, if its finel state is higher then its initéal state, is ab. stracted from the radiation. The sesttered radiation should thus contain freouencies less then the incident radiation by suounts corresponding to all such possible transitions of energy that the electron can make, Corresponding to jumpa to discrete energy levels there should be shifted lines, differing from the incident radiation by amounts characteristic of the energy levels in the serttering atom, Sines the scettering atom is light these lines sre, in most ceases, very close to the umshifted line. The in~ tensity of such shifted lines is proportional to the prob- ability of such an electrm transition when the initial and final atates of the electron coincide. Finally, there is some probability corresponding to a trensition of the electrm from its initial disctete level to any region dB of the continuum of positive energy levels, Wentzells paper —2 3 purporss to show that these later probabilities have e maximum occurring st just the right continuuous energy Oo level to give the required shift: h/me(l-~cos6), In fact be t appears from his paper thet the enalytical condition fer the above mentioned megzimum is formeliy identicel with Compton's equation for the conserv«tion of momentum, Ac- cording to this the Compton shifted rediation should anu pear as & band whose méximum intensity occurs at the point observed énd calcualted by Compton for this shifted rad. tation, It is weli, st this scoint, to briefiy point out thet Jauncey's theorv will give exsctly the same result as to the position of the cut-offs and the Smeckal lines, anda qualitatively the same general shepe of continuous distrib. ution as does the Wave Mech@énice systsm, The principle difference between the two theories is in the assumption Oo of the naive Bohr atom with point electrons snd elliptical orbits by Jauncey; whiis Fentzel's theory is mors rigorous in taking the weave mweckanics atom in which the electrons are not points out sets of waves. "The weve mechanics stom aust be regarded es only « rsfinement on the Bohr atom, since in setting up the Hamilton-Jacobi equation for the weve mechanics atom the Hamilton fimetion is identical with the old-fashioned mechantésl fimction set up for the Bohr etom, Indeed, one sets up the HamiltonpJacobi eau- ation in identically the same wav @s though the Bohr atom model with point electrons in definite orbits were being ~B4— considered, Rut once having set | it up one substitutes for the ~ Hr 3 id n= generalized moments certein Mb, ¥ los Sy ; differential operators which a . ° then leaves the equation as om _ a weve-~squation insteéd of a al mechsnical e-ustion, ebout mass | : t - ooints, S UL 7 p [boo ON 1 - j The accompenying rough diasrens show ths sort of spectral distribution ons is to expect from the ty ea of jumpt clescified on the precesding page, The first part, showigg a rectangle gives the effect of the K electrons of the scattering stom, The secmd part is the separate effect of en elliptic orwit electrm, While the third part is a& combination of the first two curves, In the seeond paragrepn above it is stated that the Compton radiations should appesr as a bend whose meximum intensity should occur at the point crleuslted by Compton for his shifted radiation, Thbs predicted bend for the Somoton effect on the basis of the Cusntum mechanics has been observed by Sherper end slse by Dulfona of this Institute, Reeson for the Unshifted Line: It h@s previously been seen in the Compton corpuscular exolenation of the shifted line thet the absorption of aome of the original pv energy by the more looseiy bcuna yor L seers gs, . 3 4 2 7+ ~ + foliowe from this thet if the electron is morse closely coun Cas to the nucleus then there will be more energy absorbed in rdsr to throw it loose as 4 recohi electron, The heavy atoll, with closely bowmd electrons, will be harder to distort by cuan*um impacts, and hence the unmodified line Will have the greater intensity. In order for modified radistion to be found the change in hv, dhe to the scatter ing process, must *t least be e-ual to the critical ioniza- tion energy of the atom, One does not begin to get modified radiation wntil the frequency of the incident cuahtum not only excéeds, but even greatly exceeds, the critical ionization frequency, This is why there is no Compton effect for ordinary light, Allof this will b= seem to piay @ very important part in Jauncey's explanatid of the intensity of the modified line, In the limiting case thst the electron is 30 dosely bound in the atom that the single cuentum is uneble to release it then if fo llows that the original amount of ensrgy will be reradiatéd and no not- iceable change of frequency will teke place. The prob- ability of multiple collisions at the seme time is too small to be of value. What happens ifsthat the momentum of the entire e&tom is called into play for the case of hv impact on a closely bound electron, Thet is, the electron may be thought of as absorbing the entire auentum, receiving on this account a severe shock Which is not sufficient to knock it free, Then the entire atom must move~--if at all-~for the electron still remsins in its original orbit, Since the mass of 2 Bu the stom is several thousand times thet of the selectrm he equation (6) of the Compton Corpuscular theory h "me" must be repleced by "MN" in the dex e) nominator, so that delta lemboda becomes negligibly s a aad In every case for which we fing scatter: ing accofding cr o the Compton theory we will &lso encounter bound electrons ither in the inner K orbit or other more closely associeted tO) i sections of other orbits. Hence an wmmodified line may nearly alwéys be exoecte i, in the X-ray range, The unmod- a rh ces) ied line can be absent in the X-ray renge if the Xorays a ct he herd and the etom of low atomic number end mM rH e b engée of d e scattering larze, It @uffices that the recoil energy be suf. ficient te ionize the K elec trons. A theoretical method has been worked out for obtein! ng a sufficient concentrstion of e true "electron gast to resuit ‘n & shifted line alone, Tf en experimental proceedure to test this can bd obtained then an unmodified line would not be cxnected, When gamma 4 no a) @ ie) a used °s sn exciting energy sourceTe the modified line is very much more intense than the unmodified, showing thet voracticallv all of the eleetrons encomtered herve been Intensity Theories: More formulae for the intersitv and width of the wmodifiediline have been developed then theories of the. exolénation of the »sresence of the modified line. We cen here but mention each briefly end give their reistions to the other formulas, The two most satisfectory resuits =f 7 are obtained frow Jauncey's formuia and from the one devel- re) er oped on the basis of the wave mechanics. The physical picture behind Jauncey's reas Ming we shall &ttempt to oO give, For the weve mechanics ideas the reader is referred x. to geversl pepers listsd in the bibliography: 146, 128, 1eO. re It is well to name specif¥icslly eertsin definite prob- lems which exis a ct bee 3 ch ir a] | aed 3 ct t) fs] a pute cr <A iy ceed eld. Briefly they are ae follows. First, the question of totel shifted intensity as s function of the engle of seattering. Second, thet of the retio of the total shifted intensity to the unahifted inteasity as e& function of the scattering #ngle, Third, the atructure of the shifted line, Thet is, the intensity t tn sny region 4,. as 2 fimotion of the correspomding ehiit poe A -/A for eny given constant engle of scatterings Fourth, and finally, thepe is whet wight be called a problem, and o for which no satisfattory evlution has es yet been found, be etecte rs a wae Q anmely--~whet determines whether 4n Slectron wiii photo-electrically., The thecries of Jauncey end Wentzel 8 outlined below are the only satisfactory solutions for ity] the seemd 24 third intensitv problems listed ebove, In 5 % D> ra?) 3 ta) 4 ck Le) ct : 10>) Pty tse rat question Breit and Dirac heve Gevelopea fettly sstisfectory formule. < -eA et W Tiga t ™he shifted intensity es worked out oy Ere: 5 Lon, s s 2 a _ ro. L _/ +79 ag sented in Comoton's took is: Lge Fy i tye. cgi” where I, is the incident totensity, end A= -4l~ "Thig represents the simolesat possibis average cf the two aan : Ohi te benatty saadones by t} wrreaven’ limiting velues of the ‘ntensitv essigned by the correspe.t- ~p8~ i a oT Wentzel gives a very compect end cleer resume of the status of the clessicesl and corpuscular thecries upon the intensity problem, In the wave thecry the frequency end intensity problems receive equel cimsideration, awhile in the quentum theory the inteasity euestion is 4s problem the solution of woich is, in principle, very uncertain, end logicéily lese setisfaetory., In the ex. perimental section we mentioa two msthods which should in the near future go @ long wey towerda clesring up this uncertéinty. "The Rohr correspondence principle serves es one guide to the generally mentioned expression that qualttetively the classical caleu&etion of intensity for the quantum process is necess®ry; in the boundary case, where the frequencies from classical and quantum consider~ etions sre exactly the sane, then the computed intensities sre exactly right. In our csse, where the intensity ais- tribution of the different directions ef scattered rays are conderned, the statene f the correspondence principle js esveciélly meager and has sccordingly found freguéat sxplanation While in the frequency questicn the aifferent (97) thewuries lced to the same end formula." But it can be shown thet only two intensity formulas are in any wey compatible with exper‘ment—-namely those by Jauncey end Compton snd leter the one based upon the wave mechanics, Added importance is given to the need for ™m experiment— eslly deter ined intensity law by the fact that it would meke possible 2 mmowledge of the velocity distributia ef ' At first it was thought that the predicted width of the wodified line on theoretical grounds would give auch wider lines than actually ocenr, Put it is now found that ct ry Qs. a) ae liscrepancy is not *s grea st as at firct supposed, PuMond, in & paper soon to be oublished, hes found the agresment ron t i al to be €9.f006 ee can be exvected when the effect of ai the electrms in ths scattering atom is counted in. 4D points out that "those electrons which were thought to cive too wide a iine, as in the case of carbon K electrons, only centribute a part of the total modified intensity so that when the curve is addeS up for all electrons its general eppesrance is mot far different from the experimental curve, Obviously those electraas which cmtribute breedth to the curve caé mot contribute much intensity in any one epot sccording to Jauncey's theory~-which assumes thet ell electrons have equal a-priori probability of collision (modified or unmodified ecattering). For if the eres under the component pert cf the curve, for each electron, is to be the same the compone at curves Which are broad céanct be on," In the esrlier Jauncey theery the ciscrepancy in the width of the theoretical snd experimental curves was gttributed to one or all of several causes, Namely, some electrms are moving in elliptic orbits snd not in circular; there is an appreciable t ine of cemtact between electrons do not move C electron and quantum; or because th with as great a velocity as the current form of the atomic theory supposes, The ediacent figure V, shows the relation existing betwee experiment and the severél theories = upon the queaticn of total ahifted intensity es a function of the én fer experimentel velues, The othe curves are: (1) Classical, (8) Tebve (2) Compton's, (4) dJaunceyts, (5) the Weve Mechenica', Thev will now is ee 4 . 4 3 3 + y 7o° pot, be mentioned snd omeidered in the e:me order. DP Can Ag) , Si Clessicel Theory: J,J,Thomson developed the classical thecry of intensity which, #8 is seen from the accompanying figure, gives the same velucs for 180 degrees ae for zero degre-s, And except for ita initiel value is non-ccincident wit known exper- iments] date, The intensity I of the scattered line is Geveloped from cheericsl casideratios of elec trosmagnetic waves, und becomes more complicetec ae addit ional factors auch es wotion of the secondary rediator are considerec, Ch 4 rh tH (2) fe iB ct Dy ¢ primervy intensity, then the sorttere 4 f L e LT, i Jn fen @ | intensity for en angle 6 is: Lo-Res” 2 30,1 4 t ct re where Fis the distence from @ of cbservaticon. Quentun Pheory: ( Compton po ints out? A) en ot "e1l1 forms of the suentun st theorv of X-ray sesttsring ere based on the assumotion that for long wavelengths, where the motia impsrted to the as a scattering electrm is s small, the jntensity of the scattered CQ Ne -31- 2 pe ray ap oroée ches thet assiged by Thomson's classical theory," The correspondence principle of Bohr requires a Gi fferent Limiting intensity for @=O then Thcamson's theory. Breit shows this new limiting valwe to be: J = [,(t+a per Oj? 31.1 a From theoretical considerations and actuél experimenteé “ 5 ete the limits shovlda lie between those demanded by equeticn © Nebye in his originel paper (17). atetes tmt the intensity question (referred to es number 1, page 26) cen be solvec AY) only by sn assumption to the probebility of a single 9] process of scattering at a certein engle. Or, stseted in another way, the number of quanta scatters in any direction C may be assigmed by the classical theory, ys put vecause However, it is Iknewn thet thre tote] ebsorption of herd X-reys is less then @; hence Debye's formulee must o¢ excluded from fulfill ng the experinentel curv: coupleteiy. on end Too, from considerations of the TPeppler formmlé ead ite relstion to quentu:. theory, derived a form ats hased on these two ideas, Woo used * Lorentz trans formetion rn y 7, & - and cbdteined: To = Lepimce (tay) (31.2) ~32— hoo et tar where: & = smeA or: Ly ~ tor mc! acitanne? This approaches more nesrly the experimentsl form, but is 2 en to be quite differant even yet. It canaot be correct ran) 3¢ unless the form of corréspondence principle used in its determination be inapplicabis. Upon evaluation for sigma ” Woo fotind that he, too, had O=%3, which is enother arguement ageinst his formula, 4 Compton, bya different method, obtained: b+ 9 -¢. Fan (lea tan A? = ln 5 —.+4; ! doe | ae i ang Ton an (32.2) Thie last esvation indicetes a reduction of the scattering absorption cosfficient with feeauency, which is found to be trdcexperimentally, also, Jeuncey's formele gives results which sre in good agree~ ment with fect nd the theory behind which seems to *ecount for the physics for the serttering very completely, To obtsin the thecretiesl curve for anv practical cese is some~ what of © task for it involves many computetione. Briefly 4+ is as follows, For his intensitv formols Jauncey mekes the following six assumptions, He &ssumes,: (1) the Bohr-Sommerfeld etom~~-point electrons reé- volving in definite ellipticsl and circular orbits, (2) & priori probability of @ collisica between & light quéntun end m electrm equal fro #l1l siectrons, (3) impulsive action between light quanta end electrons ~~b,6, the time of intersection between ligktavanta end electron compared to the orbital pericd of the electrm is negligible. (4) s, conservstion of energy end momentum betwenn electron and light quentum when electrm is ionized by light quant end (bo) the seme between atom and light cuentum when electron is net ionized, The orcitsal momenuta of the slectrm is teken into accomt, (5) the electrm is ionized when recoil energy, as calculeted mder (48), exceeds the binding energy of the . : ; n 2 “a. lectron in question, and thet it is mot loizse in ail (G) unmodified scattered redistion is due to energy food sesttered under second part of (5). The process involves separste calculations for circular and ellipticel orbits of the electrons, We shall here ppo- :4 to outline the method followed for circuler orbits and then the variations preliminzsry to solving the elléptic~ el problem, The case considered is for 180 degret scatter~ ine, which is the simplest, snd at sHe same tine ives maximum displéecereants. Inaswuch es varietion of displéce- ment with scattering engle varies as (1-~cos@) it is readily seen that the curve will be appooximetely flat—-topped at 180 degrees--so thet this method will hold true for 176° scattering (which wes the experimentel engle used by DuMond, hg hy. ; 7 , j a “C Resides assuming electrons In « ee ~poe— : . #2 ™ P=lroe circular orbits, we wWili further gesume thet there ere an infinite ae anon mee Ven umber of them, The adjacent fig Vie — yy peu ma VI. is = vector picture of th ~b4— momenta for the case of electrms with initial velocity and scattering engle of Thi equals 180°, we will let 6 be the esngle between the incident quentum and the initial electron direction, v the incident frequency, v' the scat- tered frequency, B, 7 ee ; Bit ve » end the other quantities their usuel meanings. The esbove figure is necessitated by the law of conservation of linear momentum, From this «nd the law of the onnservetion of energy We are enebled to set u up two simultaneous 1 ec . ep. pa 7 in hal Aw’ | [aM _ eae Stee, PA ee | ; (34.1) ‘ : } : j } _ yt - = ot! H ay a ~~ Tpon so&ving for v' we obtain the relati ion: i: 3, fan a . CEE By oe Yeh ADA V IE ay or: 4 (+ 3 per Re ath 2A th (34.4) /\ = t- nm 2 Ae LO oa ay hence the change in Wavelength is: . , ae. 2 en tnus ~ \ / 7 cs ee a ! 34.5 A” ~ ‘s bors on Fr 4.t oa u . Sy las Sy & ( a ) * Mn examination of equation (5) shows thet « chenge in Weve- length is a nearly stetionary quantity of amount a(h/uc), with:a slight correction factor, and e@lso 4 variabie tern — the first term) whose importence diminishes with the in- nad which may be positive or negative ow cident we velengtny S depending uoon @, Tf all directions of electron velocity st the instant of collision sre equally provabie then thie latter term should occur negétively as often as pos itiveéy. This term accounts for the breadening of the line. The second term accounts for the wavelength shift, @ is slways ~35— & very smélli quantity, less than one tenth the speed of light, Yence 6, is less than one percent and mey, for our purposes, be neglected, Tf now we let A be the chenge in wavelength that is the shift of the redietion on either side of the shifted position for the case if initielly stetionary electrone (4.e, Bh/ac}) then the positive As are for shifts grester f : then eh/me, mad negative ones for lesser shifts, Then, from equaticn (5) after simplifving and unifying we obtein: A= 2 Gabe? (35.1) where: Aw = A+ ye end the subscript of PZis dropped, ind AA=27A% an Ag 48, (35.2) Tt is known that the probability that an electron will be hit by & quantum with an angle © between the two trejectcries. 1 3sin6 Ag . Hence, neglectimg /*agein: 6 and G+/6 is Pox ; Aa nr 3 “3 A® (35.3) In other worde, for eny A (shift from the position for rest~ ing electrons) the chance is independent of A and equal simply to the oroportional part of the totak spresd-~ 4 aA* _~-representad by dA. The area of the | rectengte (fig, VIII) is called unity , if the probebility of hitting the el- | ectron is taken as unity, Thus we ob- | ANE AK ol 2 tain the width of the shifted line on | either side of theA'-A position, The " NAM height involving the intensity is com- Fy, Wii. puted from more involved mathematical considerations, But it is readily seen that the area will be a total integrated , We intensity: “4BA Zax > Ze Now turning to the case of e]}iptical orbits, The curve ~~ 6~ of Fig. VIII holds true in this case, except that it becomes more and more of a tmie curve as the é@liipticity increases, This is because electron velocity varies in different portions of its orbit and accomt must be taken of this, So that it “is necessary to plot, first, e graph of the relation of speed of each electron against its position im the orbit, The area of the rectangle is proportional to the number of electrons in the type of orbit under consideration, or, it is proportim- al to the length of time sn electrm is in @ give speed intervel of the orbit, The total intensity must, of necessity, be Composed of components added together from the effects given vy each of the orbits of the electrons of the scatter. Above certain critical velocities the electron is so closely bound to the nucleus that a light quentum cannot knock it loose, This causes critical cut-off frequencies~- defined in @ later paragraph under "Limits dhe to the Cén- servation of Energy"~~, These cause irregularities in the intensity curve, Thet is, theoretically the width of the line will approach toc closely to the unmodified position A . But these cut-off frequencies govern where the cut~off for each particular electron orbit must occur, Hence pert of some of the comconent curves are made inoperative. The area whkch is thus cut off is added to the intensity of the unshifted line, The absissae are pletted equaily on either side of the aj: 240g position which is the shift for initially sta~ tionary electrons et the scattering angle of 180°. If there is more than one electron in the same type of orbit, then ~37~ the intensity for tatat tyre must be multiplied by the number cof electrons in the orbit, ™ rhe agreement between Jauncey's theoretical curve, the theory of other investigstors, and experimekt cannot def-~ initely be steted yet, for good experimental data is hard to obtain, But it has been shown that the maximum intensity dewmgended by Jameey is fer greater than thet show on the hotogréphic plates, The méximum shift end the width of the line are, however, in good agreement, as is also the general shape, Weve Mechanics: As is seen from ovrve (5) of the graph on page (30) the intensity curve as calculated from the new wave mech~ enics is in good azreement both with Compttm's tkeory elso with the sxvnerinentsl results, Dirac (120) evolves . act VS, the intensity formula Zg= = FH Kn We (t-e J where c s the velocity of light, v is ® Pi times the wave number fo th incident radiation, and ¥' is the seme for the acettered redietion, "a" is a small constaht ‘neglected in cond order effects, and is is e@ direction cosine, es This he shows to be just 4, tives as large as those formulae besed on the quantum theory. In particular this formulas agrees with the others at zero and 180 cegress. ‘Direc further p points out thet this is the first physical result obteinec from the new mechanics wi previcusly been mown. . W.Gordan'” ~’ showed thet the values of the intensity ~38— ef the Compton effect on the Basis of Schrodinger's wave mechanics is equal to the geometrical mean cf the correspond. ing quantities for the beginning and end conditions of the process based on the corpuscular theory, Thés suggests a & correspondence principle between quéentum ideas end th weve mechenics which mey, in the future, readilv be extended, Po@erizaticon of Shifted and "mshifted Lines: le marae § 20) atetcs thet "the atete of polarization of the scattered radiatio is the same es on the classical theory", ‘nd further, "the redirtion s€attered through SO degrees is thus pléne polarized for unpolarized incident rediation," This has been experimentally verified by Kali- : 122 a menn and Mark in cermany ) They investiget:c wether or not the primary intensitv actually approaches zere, and Di also whether the secondery ray is linesriy oolarized, To H or accomplish this the secondsry rays were analyz:c spectro ecopically at 9$O desrees, end then the enslyzing crystal J fen) o e wee turned with respect to the secondary réys, when it wee perpendicular to them, The Gnownt of this turning is mensured by an angle "A", The relation of fhe unmodified line is known, end elso it is knom that ite intensity in the case of linesr oolarizetion detracts from the customary sosttered redistim with the fimction cos*s, It was thus observed thet the ratio of the unmodified intensity to the modified intensity depended upm the angle 4, If this retho remains constant the n it proves that the Compton radiation be lineterly polarized--similariy to the normal scattering. ray, “he actuel results which they obtained proved th-t boty the ratio of the shift mo) gd end unshifted intensities was nd ‘o KR iy Q ct pro [3] ce fed | ae sof fe @ pendent of the pélarizstion mele, which mm Sy oO 3 @Q + Ch cb an ¥ & the intensity of the Compton radiation depends uoon the normsl westtered rey in the same manner thet the polarizstion depends vron it, with the extreme corouscular visdw several minor terms wust his cives, following Compton's book on page AdeAU' the tmetife gry FEMY™ (39.1) To determine the limitins conditions we omit Luv® as being négligibie, cad mea tas C for v' to dé 2 waximuy, Hence we have: Ad ay” Ad-hit (39,2) or: AA - A's A- limit to the frequency, the first equation being satisfied As" A), Since there is no finite lower when v' ig ©, then the wavelength of theseatbered ray may 2 heve eny value for which: = Ati o-aAy* This evwmation gives the lower Limit for the cut-off frequency. The only cther limit easily obtsinsble is from the knowledge that v wast be greeter than vg to threw an eléctron fram the stom and form a scattered rey. Hence it follows that when the electron ig firmly boind to the atem that no mod- ified line may be expected, The first cf thease limits tells why mo Compton line 4a Observed in the region of the visibie spectrum, —40. © Photo-electrbc Effcct vs, Compton Fffect: For a short time there appeered to be a conflict wetween the ides upon photoelectrms and the recoil electrons of the Compton effect. Millikan showed, in his experiments upon photo-slectricity, that the electron which is ejected must be free, Then Compton showed thet the momentum and hence the energy of the incident quantum becomes divid ed. This represented 4 definite dis@greement between the two theories; end sesmed to mem the complete abandonment of on or the other, Rut Klein and Rosslend (%,f,.P. IV,46,1921) fond en intermediate process, "Collisions of the second kind", which showed that the photo-~electrons and recoil electrons were upon two very distince bases. "Jollisime of the second kind" sdmit of enerey hv being transferred indirectly, without loss, from the light weve to the free electron, this obvisting the necessity of = direct transfer. > & Thet i8, energy cen be transferred from the light wave to the fres electron by being absorbed first by an aton, which iq thus thanged from the normal to an excited state, This excited atom cén return to its normal condition without rad- tetion by collisdéns of the seemd kind, which consis st in a treneferring its whole absorbed hv to & free @lectron, In the Compton effect the light quant collides directly with the free electron and can be changed in frequency if {t collides with a bomnd electron only if the bound ele on i rete of continucus, ia reised to # higher energy level, disc lision, Hence the shoto~electric affect cannot possibly represent the Airect intersection between & light th WEVE £ G “4 ry ct rth Go The experimentél errengement is rether fully set f f in Compton's book "Y-~ravs and Flectronan‘A) | so that there is no deed to describd that here, The apparatus used by Wlisen to obtain his “fishtreceks" »shotogrpens also needs ft ao description. HSowever, it mey be well to ssy 4 word his photogrephs,. ale cr Cc cr ty i @ Xs D bie 3 GG o ny By means of the pass*z¢ of the X-reys throwgh the gas one odtains two types of figures: &) electrons of long rengs, and b) slectrons of short raage, The log rangs prrticles ere photo-slectrons and ere eiscted most copiously by the longer Weve-length X-reys, The short renge Beta oerticles for recoil electrons) are found to be due to ahorter ‘vave Y-reys, These sre the "fish tracks" on the photographic plates, onof ct pete The range of these particles and their dirse emission furnish strong evidence for the corpuscular theory of the Compton effect. The light quantum ides demands a strong concentration of recoil electrms with paths in ths primary direction, which is in entire azyreement with exneriment, Pictures of these tracks have been taken which wield still more accursts measurement. The time of sxposurs requires to obtain a photograph is?) of the Compton effect is ebout one hyndred hours, It is obvious thet conditions will chemge tremendously during thet time go that inteasity conditions will vary within ord a a) agri fe rt 3 g mS ad rans ae ewe oat aa Gor ao > Q M4 ot ~ Sad ort Gea 7 yy Le > aya ty fa LA OV m fen our WwW ia hundred sf one £ i OO SUL Xt (Oo 2 c Sirs Re gh $ is A 4 a expos > ¥ ba from dr awa be 1 ree ve Th set isio mel Oe eee ae ~ aye eS ee ee o a, Eres q H ery wad ae) “2h og ya he et YER A. s & ~44. modified lins end its intensity aimultsneousiy from = Seeman oryatal spectrometer for practically a 270° ra ZS. c.d0.W.M.DuMond is et present carrying on work to obtain experimentél resulta with at least the first two of these devices, Tntil these or some similar exoeriventsl methods ora3ent tew data upon the intensity of the shifted line with regard to sesttering sngle and shift the theorist 14 or Work most uncertainly upon this suestion of the Compton effeet, Then the oroblem is finrlly solved much new light will be furnished science upon th ts we iat K rg a Cc p c i 4ng@e principles between the classicel wav $3 4 te os 4 . y-) * = ta ps . at of the structure of the “tom and the spesaa as we heve previovsiy out, the Compton effect has done mucn “so sete ote WA es = 3 a wad en a We. er a ee a sheorvy on « fimm basis “nd has répsaisa tne upon the lews of conservetion of snsrgy snd momen tua, Ta conclusion I take this opportudity of expressing wy very great indebtedness and sincerest thenks to Mr. d. 2 hag cided me with much valuable assistanee aX over ca and meny suggestions, end who hes most kindly reé the preliminary menuscnipt, Ivy, BIBLIOGRAPHY. The following bibliography of the Conpton effect covers as f G a Lly as possible all articles dazling with the subject hic 123 have axseared sine Professor Compton's original yeper at tne end of 1922. A fav dealing indirectly with thic type of scattering which apreered before then have been included g as being of fundamental interest. The firct arrangezent is by years end svb-grouped by periodicals--in chronelogical order. The second list is an alphavetical author list with unoers correspondifig to those appearing in the first index. The following abbreviations have bean resorted to: PR,--Physical Review. PNAS.-=Proceedings of the National Acadexy of Science. JFS,--Journal of tae Franklin Institute. JOGA,=-Journal of the Optical Sociaty of America. PM,-~-Philoscphical Magazine «f Lomion. PRE.j~~Procesdings of the Royal Society. 2UPz;--Teitschrift fur ~hysik. P7,--Physixalische ?eitschrift. NW.--Naturwissenscizft. CR.=-Corrtes Rendues. Cim.--TI1l Nuove Cimento, Rolomgna. A. Arranged Chronologically by Periodicals. 1910. i. Primary and Secondary Gama Rays. D.C,H,Florance. P.M. £0. S81-938. 15910 1912. @. Rontgen Radiation from Substances of Low Atomic Yeligit. P.M. 24. 138-148. 1912. Sadler and Vesher. 3 Seaendary Radiation Produced by X-Rays. AH. Compton. 2 Pul. Nat. Research Council. —$@. «1-58. 1922 1923, 4, Quantur Theory of Scattering of X-Rays by Light Tlewents. OR. 21. 485-502. liay 1923. AH, Compton. 5. The eotrum of Scattered X-Rays. A,H, Compton. 408-413, Sept. 1923. 1923 8. ‘cont'd, ) Scattering of X-Rays by Light Elements. C.E.M.Jauncey P.R, 28. 233-241. sept.1923. Changs in Wavelength by Scattering. P,A.Ross. PNAS. 9. 246-248. July 1923. 8. Wavelength of Secondary X-Rays. Clark and Duane. PNAS, &. 413-418. and 415-424. Dec. 1923. GS. X-Ray Seattering and J Radiations. Barkla and Sale Py, 468. 737-759. April 1923. ic Moe ‘on! ll. 17. 18. Absorption Measurerents of the Change in Wavelength Accompanying the Scattering of X-Rays. A.H.Compton PY a 46. 837-911 a Nov a 13 BS 2 Tavestigations of X-Rays and Beta Rays by the Cloud Method. C.T.R.Wilson I. PRS. 104. 1-84. Aug. 1923. II. PRg. I0d. 192-212. sept. 1923. Secondary X-Rays. J.A.Gray. Trans. Roy. Soc. Canada. 17. Sec.3. 165-166. 1923. A New «-Rey Secondary Radiation. .Bothe. ZFP, 16. 319-320. 1923. Uber das thermische Cleichvericht zwischen ¢trahlung und freien Rlektronen. Ww. Pauli. ZFP. 18. 272. 1923. Wavelength of Scattered X-Reys. H.tulenkamprf. ZFP. 19. 17+19. 1923. A New Secondary Radiation of X-Rays. W.Bothe. ZFP, 20. 3-4. pps. 237-255. 1923. Seatterine ef X-Rays and the Quantum Theory. P.Rebye. PZ. 84. 161-166. April 15, 1923. Change in Wavelength Accompanying the Diffusion of X-Rays. CR. (4177. 1031-1033. Nov.19,1923. ", Bauer. The Theory of the Diffusion of X-Rays. Bauer,Auger& Perrin. CR. $177. #%(1211-1218. hec.3,15923. The Scattering of X-Rays oy Hydgron. ¢.A,Scnott. PR, 83. 119-127. Feb.1924. Intensities of X=Rays Scattered from Rock Salt. Jauncey& May. P,R, £3. 128-138. 1924 no a a7. 33. 34. 4 (cont'd. } A Corpusculsr Quantum Theory of the Scattering of Polarized ; X-Rays. G.E.M.Jayuncey. PR 83. $13=+317. Har. 1924. The Recoil Elactrons From Scattered X-Rays. Compton & Hubbard. PR. 83. 439-449. April, 1924. The Corpusculer Theory of tie Distribution of the Recéil Electrons Produced by Polarized X-Rays. Jauncey. PR, 83. 5e&0-588, May 1924. Jauncey and Strauss. PR, 83. 762. 1924. A Generel Quantuy Theory of the Wavelengto of ccattered X-Rays. B,H, Compton. PR: 4168-176. Aug.1924. Theory of the Width of the Modified Lines in the Corpton Effect. G,E,M.Jauncey. P.R. 24 204. 1924 (abstract) wave Theory of the Compton Effect. C.Eckhart. PR. 24. 591-595. Dec.1934 Tertiary X-Fadiation. Clerk and Duane. PNras, 16. 41-47. Jan.1924. Secondary and Tartisry X-Radiations from Germanium. PNAS, 10. $2.96. ‘March 1924, Clark and Duans. Absorption Veasurements of the X-Rays Reflected froma A Calcite Crystal. YH, Woo. PNAS. 10. 145-148. Apr.1924. Secondary and Tertiary X-Rays fron Elements of Small Atomic Number. Clark, Duane, and Stiffler. Pyas, 10. 148-152. Apr.1924. Tertiary Line Srecéra in X-Rays. D.L.Wwebdster. PNAS. 10. 186-191. May 192 Theory of the Tertiary Radiaticn Produced by Impacts of Photo-electrons. Clark and Duane. PNAS, 10. 191-196. May 1924. Aosorption “easurerents of Certain Changes in the Aversge Wavelength of Tertiary X-Rays. Allison and Duane. PNAS. 16. 196-157. May 1924. Scattered X-Rays. P,4,Ress. PNAS. 10. 304-5096. July 15924. 1924 36a. 37, 46. 47, 43, 50. feont'd.} The Compton and Duane Effects. Becker. PNAS, 10. 342.346. 1924. Influence off Secondary X-Rays Spectra of Placing Tube and Radiator in a Box. Arestrong, Duane, and Stiffler. Same title as 37. Allé&égon, Clark and Duane. PNAS. 16, 3792384. Sept.1924, The Polarizing Angle of X-Rays Seattered by Parafin. PNAS. 10, 405.408. 1924. Jauncsy ond €treuss. Secondary Electrons Preduced ty Hard X-Rays. in Light Elements. H.Fricke, and ©.CGlaser. PRAC, 10, 441-447, Vov. 1524. The Seattering ef X-Rays. J.Maizlish. JFe. 178. 667-680. May, 1924. The Seattering of X-Rags. AH, Compton. JFs, 198, S7 a 78. July ,1924. Measurement of the Polarization of Secondsry X-Rays. JOGA, 8. 487-493. April,19s4compton end Hazenow. Theory of the Width of the Modified Spectrum Lines inthe Compton Erfect. CG. F.M.Jauncey PM. 47. 427-433. May 1924. The Quantum Theory of Kadiatbon. Bohr, Yravers, Slater. PY, 47. 7BB-L02, May 1924, as frem ae Metallic Filg ur Theory of X-Ray Scattering. L. Simons. The Emission of Beta and Gamma Ray and the Relation to the Quant PM, 48. 350-258. Aug.1924. Phenomenon ef High Frequency Radiation. M. deProglte Proc. Phys. Soc. 36. 423-428. Aug. 1924, X-Ray Emission frow Metal Filws. L.Simons. Proc, Phys. Soc. 37. 658-70. Dec. 1924. Avsorption of Hard Gamma Rays by Elements. N. Ahmad. PRS. A1O5. . 507-2515, 1924. On the Absorption and Scsttering of Gamma Raye. Ahwad& Stoner. PRS. AlO5. 8-19. 1924. An Investigation of the Absorption of Superposed X-Radiation, Prec. Roy. Soc. Edinburgh. 46. 48-58. 1924. W.H,Watson 1924 (cont'd.) 51. Scattering of X-Ray Quante and the J Phenomenon. Com ptan. Nature 113. 160-161. Feb.2,1924. 58. The Seattering of X-Rays. Compton and Duane. Nature. 114. 6287. Oct 25,1934. i. 53. Some Recent Researches on X-Rays: the J Phenomenon. Barkla Nature 114. 753-755. Nov.22,1924. — 54. A Necessary Consequence of the Compton Effect and its . Confirmation. L.Melitner. ZFP. 22. 334-348. 1924. 55. An Observation on a Correspondence Principle. Lenz. CFP, 25. 299-311. 1924. 56. An Experimental Method of Profing the Theory of Bohr, Kramers, and Slater; Bothe, and Geiger. Z2FP, 26. 44. 1924 57. Hardness Distribution of Scattered X-Rays. wessauer & Herz ZFP. 87. 56-64. 1924. 58. Concerning the Recoil Effect of Scattered Gamma Ray. ZFP, 28. 3878-286. 1924. D.Skobelzyn. 59. The Theory of X-Ray Scattering. 0O.Halpern. 60. Scattering of X-Rays by Free Electrons. kK. Forsterling. PZ. 85. 313-380. July 1924. 61. The Assymetry of the Electron Discharge Produced by X-Raya. PZ. 85. 546-550. Nov.1926. W. Leitz. 68. Assymetry of Electron Emission from Very Thin Meéal Lay ews. Ann. d. Phys. 73. 183-189. Uan. 1924. W.Leitz. 63. Diffusion of X-Rays. M. and L. deBroglie. CR. 178. 383-384. Jan.21,1924. 64. Change of Wavelength by Scattering in K Radiation af W. C.R, &#&. 908. Mar.10,1924. M. ‘deBroglie. 65. The Compton Effect. M. deBroglie and H. Dauvillier. CR. 178. 8076-2078. June 16,1924. 1925. 66. Measurements of Beta Rays Associated with Scattewed X-Rays. PR. 85. 306-313. Mar.1925. Compton and Simon. 68. 69. 70. 71. 78. 73. 74. 75. 76. 77. 78/ 79. 79a, 80. © 1825 (cont 'd.) Quantur Theory of the Unmodified Spectrum Line in the Compton Effect. G.E.M.Jauncey. PR. 85. 314-381. Mar.1925 The Intensity of the Scattering of X-Rays by Recoiling Electrons. Y.H.Woo. PR. 85. 444-451. April 1925. The Compton Effect: Quantum Theory of the Intensity of the Modified Bands. Gi7F.M.Jauncey. The Compton Effect: Dependence of the Intensity Upon Atomic Number. Bergen Davis. PR. 85. 737-740. June 1925. Ratio of Intensity of the Compton Lines. PA.Ross. PR. 26. 282. 1925. Directed Quanta of Scattered X-Rgys. Compton and Simon PR. 86. 289-300. Sept.1925. Wavelength of Scattered X-Rays. Alla&son and Duane. PR. 86. 300310. Sept.1925. Nulbber of Beta Rays Associated with Scattered X-Rays. PR. a6. 433-436. Oct.1985. Jauncey and Defoe. Precision Measurement of the Change of Wavelength of Scattered X-Rays. H.M.Sharp PR. 286. 691-697. Dec.1935. Scattered Radiation Due to X-Rays from Mo. and W. Targets. PNAS. 11. 285-27. Jan 1925. Allison and Duane. The Compton Effect with no Box around the Tube. PNAS. 21. 56-61. Jan.1925. Ross and Webster. The Compton Effect: Evidence on its Relation to Duane’s Box Effect. ROss and webster. PNAS. il. 61-64. Han.1925. Effect of a Surrounding Box on the Spectrum of Scattered X-Rays. Compton and Beardon. PNAS- 11. 117-119. Feb.1925, The Compton Effect and Tertiary X-Radiation. Y.H,. Wo. PNAS. 1. 183-125. 1925. Modified and Unmodified Scattering Coefficient of X-Rays. in Matter. Jauncey and Defoe. PNAS. 11. 517-520. 1925. 1925 (cont'd. ) Sl. 82. 83. 84. 8G. SO. co of X-Rays Scattered by Mo. P.A.RoOss. PNAS. 11. 567-569. 1925. Unmodified and Modifies Lines in Scattered X-Hays. Ross. PNAS. ji. 569. 1925. Ratio of Intensities of Unmodified and Modifed Lines. Ress. PAS. il. 569-576. i925. An Attempt to Test the quantum Theory of X-Ray Seattering. PNAS. 11. 601-602. 1925. R.D. Bennett. Photegraphic Investigation of Scattered X-Radiation. Ress. Wavelength shifts in the Scattering of Lignat. Feote and Ruark. fclence. 61. 2863-264. Mar.6,1925. The J Phenomenon and the quantugy Theory of Seattering of X-Rays. R.T.Dunbar. PM. 49. 210-236. Jan 1925. The J Transfermation cf K-Rays. Barkla and Knastgir. PM.--49. 251-256. Jan.1925. The J. Phenowenon in X-Rays. Barkla and Khastgir. PM. 50, 1115-1135. Nov. 1935. Further Experiments on tbe Absorption and Scattering of Camra Rays. N.Ahmad. PRS. 109. 306-283. 1925. Toe Compton Effect. WNeoster and Ross. Nature 115. 51. 1925. Compton's Theory of X-Ray Scattering. H.Fricke. Nature. 116. 430-431. 1925. The Compton Effect. J.¥.M. DuMond. Nature. 116. 937. Dec.26,1925. of Rays by Atoms. Xramers ani Heisenberg. 681-708. 1925. The Notion of a Free Electron in the Field of a Plane Hlectro-Yagnetic Wave. J.Frenkel. ZFP, 32. (82-31. 1925. 4.2 Concerning the Compton Effect. Rothe and Geiger. VFR, 88. 639. 1925. Brenstrahlung und Commtcnsche Streustrahlung. 6, 'ie. ZFP. 33. 33541. 1925. SS op ' e * 4 43 Fy ae 8 a eg | £2 er] Cy 2 ww Teay Boag o A o > f 1 42 wie fe alg a o ° teh a wi Gg end dnd et aD © os 4 “Qo ae e Cy os 42 we GS + cf FS a oe 13 4 hg av] S460 Q er) ort OF 1) peel bo gg Vee ° £3 © Ley) ap Os od te coy bite Cy + OD ot red G et © uy cd foo» a2 & ® fal fy & re re P 4} te} aD sa §3 40 Bay OL 2 [?) 3 + et sal of Gel ofl e a) a bed rd 2 7 2 ae > © « a 6 &> Lael (i. Fea Ss E« D. Ba fh e 2 2 2 a £3 a 6 2 a Py ® ° rd wy «ti i} a aa t CS > oe sg QQ fen it 3 co co a> che co ood ae] god > 33 4 goss od ot es ed ed aed rot rd rah 117. 118. 118. a) &? oO Ss lal. 127. 6 {(cont'd.} Diseypearance of rhe Unmodifted Line in the Compton Effect. PR. £8. 6860-625. 9Oct.1925. Jeuncey and Scyd. The Scattering of X-Rays: A Review. GEM. Washington liv. Studies. 8. 103-154. 18286. euncey. Rewarks Upon the Theory of the X-Rsy Dispersion. Gray. Prec. Roy. Sec. Canada. 20. 181-185. 1926. Compton Scattering and the Structure of Radiation. PM, VT JT==2. £67 =287 e July 1926. Eckessley. The Compton Effect and the Reflection of X=Reys by Crystals. £.J,Wiliians. PM. ViII-2. 657-674. Sept.1926. The Reflection of X-Rays from Crystals. R.Schlapp. PM, WIT-l 1009-1085. 1526. The Conservation cf Photons. CG.N?Lewis. Nature 118. 874-878. 1936. Relativity Cuantur Mechanics with an Application to Compton Scattering. P.A.M.Dirac. PRE. All1l. 405-423. 1926. Remarks Upon the Yy-Ray Spectroscopy of the Compton Effect. and the Pseudoline of Clark and Duanae. 4H.Seeman. ZFP, 35. 738-742, Feo. 1926. Concerning the Characteristics of the Compton Effect. ZPP, 38. 120-145. “ar. 1926. Kallmann and Mark. Concerning the Compton Effect in the Case of Canmma Rays. ZFPP, 36. 261-258. War. 1926. G,Serfman. Remarks Upon a Dependence between Duens's Quantum Theory of Interference and the deBroglie Waves. P.Jordan. ZFP, 87. 367-383. dune 1926. Compton fffekt bei Ausgedetnten Streukorpern. Rajewesky. ZFP, 37. 699-700. June 1926. The Compton Effect and Quantum Mechanics. G?Beck. ZFP, 38. 144-148. July 1926. The Comgton Effect and Quantum Mechanics. G,Reck. ZFP. 38. 149-156. 19286. The Compton Effect Folloving Schrodinger's Theory. Gordan. zFP, 4C. 117-133. Nov. 1986. 1926 129. 136, 131. ~ CI mM 133. $27. 134, 135. 136. 136. 141. f~ a n 2 143. 144. L465. 146. (cent'd.). The Compten and Phote-electréc Effects fcr Polarized X-Rays.» PS. 87. 385-388. june 1926. F.Xirchner. The Compton Fffect and X-Ray Measurementse R.CGlockner. Zeite fur Tech. Phys. VII=-ll. 571-577. 1926. The Increase of Frequency of Light Quanta by Colligzion/ with Rapidly Moving Particles. A.Haas. Wiener Ans. 287. 207. 1926. Uber die Richtungsverteilung der von Pélarisierten Rontgenstrehlung ausgelosten Elektronen.°© F.¥irehner. Anu. d. Phy. 81. 12113-1138. 1936. The Compton Effect. Ritta BRunettd. im. 3. 1-11. 1926. Measuremente and Interpretation of the Interference of X-Rays Reflected from NaCl and Al. Bearden. PR. 39, 20.3%, 1227. Theory of the Intensity of Scattered X-Rays. Jauneey. PR. 89. 757-764. June 1927. Frequency Ohangss of Light and the quantug Theory. Py. VII=3. 1306-1384. June 1927, Bright, Ruerk, Erick wedde. Modified and Unmodified Scattered X-Rays. Barkla And Khastgir. PN, VII-4. 735-745. Oct.1927. The Total Reflection of X-Rgys. J.A.Prins. Nature 120, 185-185. i192 The Compton Fffect in Wave Mechaniss. P.A,“,Dirac. Camb. Phil. Soc. 23. 800-507. 1927. Prec. Univ. Durham Phil. Sec. 9.Darbvshire. ”, 11l?. 1927. cwei Bermerkungen uber die Zerstreuug korpusculsrer Strahlen als Beugungserscheinung. Wentzel. ZFP., 4Ce 496. 593, 19327. Uber die Richtungsverteilung der Photoelextronen. Wentel/ ZFP, 41. 888-832. 1927. Versuche zur Magnetische Beeinflussig des Comptens Effakts. ZFP, Al. 872. 1827, W.Rothea. Rlectwon VYelccities in the Compton Effect. ». Lube ky ZFP, 82. 516-531. 1827. . Theory of theCompton Effect. C."entzel. Z2FP, 43, | 4-8, S27. 1¢27 147. 148. De Fe (cont'd, } Remarks Uron the ceattering ef Alpha Certicles. Oppenheimer. 2FP, 43. 413-415. 1927. The quantum Mechanics of Magnetic Electrons. *, Pauli ZFP. @3. @02.623. 1927. Theory @®f the Compton Effect. G,Wentzel. (continuation of number 146) | ZFP. 43. 779-787. 1927, | Concerning a New Development of the SchrodingerWave Mechanics. Berlin Ber. page 108. 1927. YV,Laue. Concerning the Compton Effect. Sehrodinger. Ann. d. Phys. 88. 3857-264. 1927. Concerning the Dispersion and Seattering of X-Rays. Ann. d. PBys. 82. 685-604. 1927. Yallmann and Mark. The Compton #ffect for Eound Electrons. F.Kirehner. Ann. «4. Phys. 83. 969-975. 1927. Guantum Theory of Molecules. Born and Cppenhelwer. Amn. d. Phys. 84, 457-484. 1927. Upon the Compton Effect. A.Carrelli. Cim. 4 1422145, 1927. ND The Solution of the Wave Equation for the Seattering of Particles by = Coulombian Center of Force. ott. Proc. Roy. Sec. All8. 542-549. April 1928. Interaction Zetween Radiation and Tlectrons. Cempton. PR. 3l. 59.85, Han, 1328, The Scattering of X—Raye from Gases. C.S,Barrett. PR. 338. BE<89. 1928, POCKS . X-Rays and Electrona. A,H.Compton. D.VanNostrand. 1925. The E@ectron. R.A.Milliken. (esp. vp. 254-260) Univ. of Chieazo Press. 1925. Introduction of Conterporary Physics. %.%,farrow. D,VvanNostrand. 1926. Atombau und Speetrallinien. 4th. ed. A.Someerfeld. Vieweg. 1925. Cndes et Mouvement. L. defroglie. Gautier Villard. Paric. 1925. EB. Arranged Abrhabetically by Authors... Ahmed,N. 48, 43,- «yO Oe Allison,$.%. 35, 3%a, 73, 78. Armstrong, H. 37. Auger,P. 19%, Barkla,¢.%. G, 53, 8&8, 89, 137. Barrett,c, th ae a 1Sé. Eennett,R.D, S84. Bomr,N. 44, Born,M. 154. Fothe,W. 13, 14, 5¢, 98, 144. Boyd,R.4. 113. Preit.,G. 108, 136. RBrickwaddas pas & tw Lae | Oo Oe fs ra) & re OY CA te fae a ae ~ & t= Carrelli,A. 185. Glark,G.l, 8, 29, 30, 32, 34, 37a. Compton,A.H, 23, 26, 41, 48, 51, 1o2) go 9) G 10 pap) 4 4 . euvillisr,t#. 34, Darbyshire,c. 141. Darrkw,¢.%. C. Devis,B. 72. 17. Detoe,O.k, 78, 6C, ill, Desgauer,F. S76 Dirac,P.A.M. 120, 140, Muane,®. 8, 28, 30, 35, Tuliond,J.W.M. 2. Dunbar,R.T., §&7. Eekersley,T.L. 115. Florance,D.¢C.u, i. Foote,P.p, 86. Forsterling,K. 8°. Frenkel,J. 94. Fricke,H. 39, @2. Seiger,H. 56, 95. Glaser,©®. 39. Gordan,W. 128. Gray,J.A. 63, 115. Hagens. Oe Havenoy,C.F, 48. Haluern,®. 52. 7.¢. TADN, Go Py * £ 4 3 >, i a Eubbard, Ts eken art co = ifs 3 i) end ay Ca Yallmann,F. CQ e Yirenn 138, 1583Y, 103, 1 15. ff,8. ae as a os Rulenk Laue ,. La) <6) wong «oO ay ork vel fy Me -” 11S. 145. 4 od tw 3° 2 Beshamn,P. ig, oa sth Lewis,>.u. Lukitsky,FP. Meislish, Meintner,L.- it} Fe sOtt,N. z até oopenheiver,R. 147, 154. 2 Pauli, 14, 148. Perrin,F. 13. Prinos,J.4, 138. Panti,E.7J., 106. Foas,P.4. 7, S38, 71, 77, 78, #1, 8, 85, 90a, 10S. ALE ar | a 4 < Buark,A.E. @8, 136. charp,H.M, 75. cy “3 iD Cimon,A.%. &6 etiffler,W.%. 32, 37. Stoner,E. 4%. etrauss,H.7 8&, 38. Patson, WH, 80; : Websts ry 20 33, 77, 7& Wentzel,&. 97, 142, 143, 145, 148. “Williams,E.G, 117. Wiison,c.T.R. ll. Woo,Y.H, 31, 68, 79a, 107,