Energy and Intensity of the Gamma Radiation from F¹⁹ and H¹ and Be⁹ and D² Citation Rasmussen, Volney Kinne (1950) Energy and Intensity of the Gamma Radiation from F¹⁹ and H¹ and Be⁹ and D². Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/8tz1-2t47. https://resolver.caltech.edu/CaltechTHESIS:10152025-044853451 Abstract A magnetic lens β-ray spectrometer with a large (~4.5% of a sphere) solid angle and with good shielding against the neutron and ý-ray backgrounds encountered in the investigation of the prompt ý-radiation from nuclear reactions is described. Methods for determining the intensities of ý-radiation by observation of photoelectron and C01npton electron secondaries with the spectrometer are discussed. It is concluded that when their use is feasible, Compton secondaries will give the more accurate values for the intensity and energy or ý-radiation. The nuclear pairs and y-radiation from excited states of O 16 have been investigated. The pair spectrum agrees well with that calculated theoretically, and the end point indicates that the first excited state of O 16 is at 6.04 ± 0.03 Mev. The ý-radiation observed corresponds to levels et 7.09 ± 0.06, 6.9, and 6.14 ± 0.04 Mev. Estimates of the relative and absolute intensities of the ý-radiation are given. The rather complicated y-ray spectrum resulting from the bombardment of beryllium with deuterons has been investigated. The assignment of these ý-rays to the possible residual nuclei is discussed, and it is determined that most of them can be attributed to excited states of B 10 , as formed 1n the Be 9 (d,n) B 10 reaction. By comparing the ý-ray intensities with the neutron intensities observed by other experimenters, a level scheme for B 10 is constructed. 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): Lauritsen, Thomas Thesis Committee: Unknown, Unknown Defense Date: 1950 Record Number: CaltechTHESIS:10152025-044853451 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:10152025-044853451 DOI: 10.7907/8tz1-2t47 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 17722 Collection: CaltechTHESIS Deposited By: Ben Maggio Deposited On: 27 Oct 2025 18:23 Last Modified: 27 Oct 2025 18:51 Thesis Files PDF - Final Version See Usage Policy. 59MB Repository Staff Only: item control page

EiEROY AND R A D I A T I O ii INTENSITY F ROM OP ,19 + al- THE A. N D GAMMA :ae9 <· n2 Thesis by In Partial Fulfillment of the F.equirements Doctor of Philosophy 1950 !t is .u plea.sure to &oknowlsdgei tbe act,ive p&"ticip.ntion of Prof@ssor T. Lat.u-its(.:ln in most of the work described in this ·t.hesis. I am also &;reaily indebted to Pro.t·eiseors c. c. Lauritsen, R. F'. Christy, &i.d w. A.. Fowlar for much advice a.11d assistance. A:3 is u:;;"tJ.31 in proser.it day work in nuclear physics)! th(;, construction and succ1%sful o~ration ot the beta-r~· spectrozr~ter 1-.;isuJ:ted from me joint, 0.1':forl:.s o:f fJIZlV@ral paopla. In addition ·to thi.l: faculty m,i:lmberfJ lli'\'.m- tioned, Dr. c. I. Chao of the Institute of Ph;y~ico, Academie. Sinicu, flanking, China, Mr. C. B. Dougherty, Dr. W. F. Ho~e.k, and Mr. R. G.. Thomas he.ve, ~t wm-ioua times, giv,~n valuabl® sssistanc~ 1n construction ot the £.1pectrometer and in int®rpretat,ion of thia results obtained. lVlr. L. J. Oililla.ndJ) fa . G. P&l.stle11 and r&r. J. F. Hill of the Kellogg Laboratory machine shop, Mr. w. D. Gibba o! the electronics :ilhop, and Mr. v. Fe Ehrgott,ll Mr. a. L. Dorr, and Miss J. Antz of t.lw drafting department have ill, at ·variou;;i t:urt®e, been of considerabl~ ~ssiatan~Jo This work ·was suppo~d by the jo:w:t. progrmi1 of ·c.hs Office of N~vu R.0s0arch and -~he Atomic En@rgy Comrn.i.ssion. Ent.irely as,~de f:rroui t,he meirit O't:' laclc of merlt of thE) present thc~sfoll I ·would like t.o truce., this oppor- t-e..nity to co~riend t.h.GfJe two govEJrnri:ient a.~--encios for the.;ir far--1:iighted snppor't of h,1~1ic f.;<}ieJ.1tii'ic re1;;~aTcil. Finally., I am ind0bwd abo~"' all ·to m~r '1r'.i.to, Janet.ta., without whose help this thebiG wo\.i.ld neither h-avi~ 1'.xien written no:r -1.,~~d .. ABSTRACT A magnetic lena '3-ray spec-c.romater nth a large ( ~ 4.5% of .a sphere) ' solid angle and v.rith good shielding against the neutron and y-ray backgrounds encountered in the inv0etigation of the prompt y-radiation from nuclear reactiono is described. MethQde for determining the intensitie3 of y-radi~tion by observation of photoolectron and C01npton electron ·secondarias with the spectrometer are disc\Wsed. It is concluded that wbeN their use is .feasible, Compton sacond.ariee will give the more accurate values for the 1nt.ensity and energy or y-x-adiation. The nuclear pairs and y-radiation from 8=tcited •tat.es of ol6 haTe ooen investigated. Tbs pair spectrum agrees well with that calculated theoNtically-1 and the end point indicatelll that the first exoitsd stato of ol6 is at 6.04 ± 0.03 Mev. levels et 7.09 .t o.06, The -r-radiat.ion observed correispond$ to 6.9, and 6.14 ± 0.04 Mev. Estimates of the rol&- tiYe and absolute intensities of tha )-radiation ara given. Th<a rather complicated y-ray spec·crum reoul ting trom the bombardmsrrt of beryllium with dauterons has been in'nlstigated. The as:!ignmsnt, of thEJse y-r.2ys to w possibl«:i rtesidual nuclei it, discussed, and it is determinsd that most of them car1 ba 4attributed to excited states of 5lO, as formad 1n the :ae9(d,n)Bl0is- re~ction. By comparing the ,-ray intan3ities with the neutron inteizwities obsarved by oth@r expsrimenters, a level schGlOO for BlO is constructed. TABLE OF CONTENTS Part Title Page I Introduction 1 rr Spectrom.3ter A. l\f.!,J,gnetic lens type spoctZ"Oll'JGta.rs B. C. D. E. F. G. Discussion of techniques D,3sc:ription of spectrornetl.:,r ElBct.ron tra,jectorles Two rwp.u-ated coil cm1.:fig-.ir~tion Four sopac-ated coil configuratio;::. Comparison of vario-us field forw~ 11 16 H. Use of. apeo"t,rometA'.lr with el<!l{;t.rost,.9.t.:i.c tAC•Col,':!rmtor 18 III 3 h 6 7 9 Mcasure:ro.en.t of C':tl~-R.ay Intensities A. B. D. .Introduction Photoelectrons Compton eilectrorw Positron-el&ctron pairs. E. Effect of instrmnent window F. Yield~ o.t' nuclear reaction.a c. 21 Int~rnsl conv~rsion 23 32 33 35 41 Radi~tion from Fl9 + al IV A. ReactioM B. Exper:i.mentru. details 4) D. Rtisw.t.s - Nuclear pair~; R@fnut~ - G~'l.m!la rooi.'l.tion Dbcw:;~ion 45 c. E. 42 48 5J V A. Possible reac•bio:us. Su.."'Vey of sa.wm-rsidia tion B. EnGr gy determination Co Rel&tive 1ntensit1\;rn ruld yield~ r:. High~r onorgy lioos E. .Assig..:im~:nt of gw~Inia-rayo to :re~iidu..1,l nucle i F .. First, e:-:ci'teid s-c,at,e ot Li 7 55 59 69 81 84 92 100 Appendix I 103 F'igureo 106 -1- I. Introdu.c·Uon Recently deV®loped ma~tio spGctrom:;ter~ .for ooali:1uring too ooorgie~ or heavy particlea< 1 , 2 > and g3Dlfta raya0 14 ) produciad in nucl®ar ree.ctions haw made it poseible to determine many more of the pertinent f <1ct1., about the excited levels of light nuclei. »&any such levels have been identified, evsn with earlier end lees precise techniques, by observing N 8orumceti 1n the yield as the incident particle energy is varied, by oboerving vuiou~ particle groups ot different energy that represent end product.a or Uw possible nuclear reactions, or by measuring the energy of --, -radiation tiult may be emitted from nuclei left in .m excitGd nt ata by the reaction. The heavy- particle groups, or re~onanceu 1n the simple capture reactions , indicate tho~<D lsvele in a certain nuclews that are exciud °b'J the 1·eact,ion. If y-radia.tion of !.l. single energy is emitted, we i..1uroodiatel y mow the loca tion of the l Gvel 1n the nucleus. In s ome caooB , l ""vel ~ i nitially t1x- cit od by a beav7 particle reaction decay by cascade y-rad.iation. Wo must thim Compal'9 the energy available in the rosotion, as given by too differences in mass of the orifiinal and li.nal sE>ts of particles , vd th t hs en~r ~· observed aa y-radiation and heavy particle kinetic energies, in trying to decide where the levels are located in the nucleua. It ia clear tht:l'.t the increased resolution and accuracy or the most recent methods rlll make this taak much easier~ and much success has been attained in locating energy levels by these mthods, as revie\l'ed b'.f Hornyak and Laurits•n, (5) and 6 Lauritaen.< ) However, we still encounter certain ambiguous situations 1t1hsro the determination of particle and 1-ray energi eru i s not sufficient sever-al possible locations f or an unknown number of l evel s . Further experi.m1mtal evidsnce ia then required. COO possible approach is to in- veat1gate particle-y and r-r ooincidenoelll. Very littl<e work of thia potentially fruit.ful kind haa been done with nu.clear reactions., It i&l anticipatsd, h0tmver, that one would b.ave to use methocls that give a large eolid angle, and consequently a low energy resolution, to get reuonabl• counting rates. Especially in the more complicated ca@eGJ 1 a UNful alter- nste approach to thus problem is by il}lb&llls of intensity m aaunments, where one determines the initial population of a particru.a.r level by measuring tho yield oi' the corresponding bear.J particle group and then matJUrEia th0 yield oi' ·l.ho various y-ray lines th~t may come from thi~ lowl. If reason- ably ;:.1 ccura.w int@n6i ty meatnirements ar-~ available , tllon the construction o.f a unique l f)vel s cheme will i..suru.ly be possiblci. ThGll present thesi.8 u concerned baaicall.y with f.mch intensity ml\suni- mants-in particular with the rrJeaauremsnt of y-ra.y intensities by Ean5 of a ~-ra;y spectroa:etar. Mo great auccee!l can be claimed., in good part 'beCWiuse equally reliable values :tor the corresponding heavy particle intensities, IU"9 not :!vailable. It is shown., however, that this approach 1&i both practicable .md potentially fruitful., and the techniques required tor the meaaurem.nt ot y-ray intensities are 1nv$etigated in some detail. II. A. Spectl"O-mte,! ,!k~et1e lentil tl}2! s~ctrometfirs Sevaral p-ray spect:romoterlll of the :u.gnetic lens type have been recently de1PJcrlood in thfa literature (e . g.-Re.te. 49 'i'-9) . Tbsy are all oharactari~d by & ~ t i c field with cylindrical symmetry, the @implest ~ ~ case being th.at of the uni.fora i'iald, B • Bs e•• It is -well lmaw that th® uni.to.rm field Mkl :focussing pro()@rties ; oo electron originating on the its initia1 angl€,1 vri. th thtti z-n~i s . By introducing appropria't•J; 11.Jld. ting cl.s o havo foo-.ts i.ng prcp--er't,i6s , indeed, tor electrons who~e :ill:ttiru. aagl ~i witJl the a r l,-;i i s ~'7.00ll it i~ only oooos6lm-JJ a ,c; shO'W"tl by Eu.sch, (lO) tlu.rt. th.e field have cylindrical ayiM!Stry. Each of the threo geooral t~m of !bld form ha.a itLJ particular marit.s. The nthi.d lenstt type of Deutsch, Elliott and E''7l.!.M» ('I} for example, .rill .focua the maximum momentum elaotron.D tor ~ given eA-penditu.r-e of power in the r,w.g:net coila. Too equation:© o! rootion for the electrons have particularly aimple solutiontJ for the 'l'.niform field, so th&t trejector!es may be calculatad, and &i abaolute calibr~tion, based on a simpl.$ current msasuremnt is possible. The; other extreme in field form, too U-sh&ped field, strongest at the source and im.aga, n£~ oo-an diooue sed by Siegbahn. ( 9 ) Using the usllitl. "pc.in't,l'I focuB, Sfo gbrum, and L&urit~e n and Chri:Jty(ll) have sho-<m th.at this fi eld .forl11 gi,teiJ a larger eolid atl[-_:l e (fre·c tion of a sphere into '«hich electrov...s o.an be omitted and t M.n lens or u.rAii'orw. field 8poct rom.etor. An impo~t reoont dtivelopnent is tlw i;.niggestion of P'rankel (l2 ) that m.ruting a larger initi~ .imgle with -J:.he axim na.ch the ~ i :d ~gain at sm:&llsr 6. '£J1 ;30 ..:~ that tht1 paths for t,)'10 c;i ven initial angl es a. 1 and a.~ tnru!)t croos at in~n-r~di,!!t,e point (more pr~-porlyJI bmc2,uoo of the cylindrie-tl eymuetry~ a circle). ' With .u .finite r~-ige of a, thi~ circll.':) oooooos ~ rtOM or nrii.'llgiv tooa<J that i G appreciably sru~ r than th,;.. :.focus on tho a::d.a . Tlw use ot ' t his ring focus for a unU'orn .f1(9ld ~➔pectromet.a r has been disCUS$6d in detail "by Psrsico(lJ} a n d ~. (l.4) TM ring focus ha..~ been used 1n t,hi.5 l .:2.oor.mtoey nth both thin lens and U-~haped field $peotr0mstera (see Figs . B. ·n1scuasio~ ot techniques SOm.9 mention of th~ general techniquefii of working with a le!Ul type ®?9otromter 113 parhaps in order, and will werve to colleiot in one pl:.108 d.ai'initiona or ?uimui te?'DW that will be uaed frequently. through the le,w coils . 'rh© "tWa of iron Thb current i s dotermined by me:a&uring with a poten"t,iom.zrter tru.'l potential drop acro~s a re:;;i.stor ( al:nllrt) with s lo-11 w1r.-iperuttire coo.f.t'icient . 'i'he momentum ot the electroruii focus~d is di.Nctl,J· propor'l:,ional to the m&gnetio field, and ie ela~t,icru.ly msasurad in units ot ~trengtJl}. Calibration is u.,sually ill terms of ooo or moN elf.llctroo linem of knmm energy. Such line a SN the internal con,rsrsion photoel~ctron linea i"rom the natural r adio~tive slament$. Very thin (a:s~ntil!Uly mono- molectu.&r) sou.rcss of certain of ·t heae el @illenUJ can be prepared by el®ctro- -sstatic collection from the fi!maruation (g.a.~Jsas thoron and radon) (P~i.'. 15, p. 560). Them~ dopcsit.s a.re Uj)ual.1.1 madt.:, on thin fl.Bt foilc which aro pl&e0d perpandioulu to the 3psctrorootar axiu. Thil:) il'lt,ornru. conver.'.:Jion electrons from such souroes are very nearly mono•,mergetic and ·their cmorr:;1 has been m,H,sured quit& e.ocurately (sati., for aY.ample, Rei'. 16). If th® spectrometer 1'1.eld b set to corrempond to one of thes0 lines, it i'ocw~s all electrons ot t.his line emitted wit.bin a C@rtain anta;u.lar range of tha uie, the aocept.mce angle, the corresponding solid angle being wrual.17 expreoead in per cent of a sphere. The electl"Ons r ocueed are reoorded by a thin-window Geiger counter (which counts practicslly ill the elsctrozw received, as long as the counting rate does not get too high). U the fil.i)ld 1s ollanged sl~btl:yi the number of electrons counted i:-, reduced, but dooa not go to zero, even though no electron& of this di:fforont momentum aN being emitted by~ eouroo, as a simple result of' the finiw rs zolvillf, powir of the ins trtment, which i s e xpressed most eooiple wly 1n terms o;f too jiwindo~g~ c ~ , or the plot or counting ra-w vs. m.:zgnetic :field in too neighborhood of a monoenergetio 11.ne. This window curve may be ~e symmetric by adjustmsnt of the variou1£1 c.tperturso md iB then quiw cloooly appro.rlm.a.tcid by ..i, Oaussie function. Tho nreaolution" is oo.finod as 6.p/p, * the fu.ll width at hill maximum ot the wind07J curve (~uru.ly 0xpressed 1n millivolts potentioaeter reading) divided b:y the p~.ak value in the same wtlts. Thie tu.ms out to be a constant, independent of p. It one 18 ex- udning a continuoua electron spectrum., then the curve observed b diatorted by the instrument window. * Ideally-, one would like to romove thia distortion The Nciprocal of this quantity i o !Nquantly ccll~d tha res olution. completely and l'nppro::dmate methods for doing thb e:.dst (uthe~tioallyg 11 u.nfold1ngH) hut ar0 laborious. If ohani'"SS in t.i:le continuous spectra wit.hin. too iruertrumi.mt resolution are aull, however, ODe mt.;, remoV® t.M ili'l}:>Ortant part of the distortion by divid~ ·the oounu-3 at a given iuo.oontum (millivolt Z'Elading) by this momentumj ·t.'lU.$ t&king account of the fact. that 6.p/p i$ a con®tant. It may oo noted th;;vt, ie::1.oept tor the diNetior, of rotation of the tipiral path, i.}lll'Jctrozw &nd posit,roM lll"S t.r®.:z.rted iUik',i,l in the l®Wfl typ© Too i113gnetic: l0n('J t.,<,rp~ ~,p::ilctromoter u 1.: 1-~d in th,J@a inv,.111;r/:.iia.tions has wen pr0viously described in oo·t-~il. (l 7) The m.gMtic .:t'LJld Nquir0d :ls furnish0d by four coils, e.:loh of S.6 inch inner r adi m:i ., 1$ u1cb outer radiw:1., and ih2 inch l@ngtb (®.;-tcl'O.sive of ·the opools on which wy are wound) and consutirig ot 8$0 turrus of /i6AWO double cotton covered ugnet -&dr~. The ncuum chu1bfJJ" is a thin-wall br.ass ·tube ot $.O inch insioo rsdi~ mlcl. 48 inch length. Sin~ the !our field coila m-0 entiNly ~ - r.ll.ta, one ma.y get .t'ield f.orn1@ ranging from the thin lens to the u-shaped .field. Tl.1.e thin lens arrang~@nt (.3'it.h Frankel's ring foc·u .g-eee Fig. l) which .,ms used in 5<mie of the axp0riments to be di$CU3Hd is de~cribed in Raf. {l 7). In some Ct!l~e::11 .11 it was el8&1r th& t ~ considi9rable incnnMae in D. _Electron trajectoriee In principle, one must cal.cul.ate vari011a electron po:tbe w determine the location of the :ring focus, such calcmlations being long ·ana oompli- • ca.tad for the case of the U-shaped .field.* IIOV'J13ver, it l1Mil,1 be noted that the ring focus 1$ only a poorly-defined intersection of rays with a ~ divergence, ao that. it would Nem·possible to trace -Yarious raya 8XJ)(@l'imental.ly with suf'f1c1ent preoiaion. This wae indeed tound to be the case, 11Jxperimlilntal. details being g1Yen 1n App. I. The oomplate trajectoriee £or this .field form an of im.enst in that they account tor some of its iinportant properties. The :r-componente (OI" envelope of the twnily ot trajectories making the same initial angle with tb6 a-uia) of two trajectories an shown in Fig. 2. Thea 119N obtrd.ned by a mt.hod, suggested by Dr. o. Y. Ohao, dGlpending on tho apparentl7 llOt well-kno·m"A tact that the equilibrium position in a magMtio field of a taut, current-carrying wire ia the sams as tha ·p41th of a tree electron of IBCR'ilentwl p • - eT/I ( in the sazne field) provided orily that the mass an\i stU'tnees ct Thi.::, condition w.u, sat1s£ied in our ca~)€l with ~ .OOJ inch dumet®r sort coppr~r wire carrying ~ l 1/2 amperes ~ with $0 ~ree through tb.e tield ooilfil. Too 'N-ire wu nm from the source to the de@irad image position, m1d its cibtance from the axis at various points was measured (no attempt was Dlado t.o maaeura too rather small tension in the wire). It was noted in.particular that the plotted trajec- tories e.ra al.most parallel. (neglecting rotation) to the e.xis for a oona1de:rabl@ part of their length. This is of 1.mport&noe in that it reeul ta in a larger range ot acceptance angle (larger solid angle), as it the source to * The <l\ppro:xi.nmte equations .for paraxi&ll rayo, as usually used in such cillcv.la.tions, would probably not be ouitablG WdN. 1--iS diate.noe wre much smaller., without iactually reduciniz tni1.:1 di&itanoo and coMoqwmt.ly the &fllOWlt of ishielding th$lt can ·b© uwed between t~ Dr. CM<>, in soma unpublished work, ha$ .aliiio developed -ta swni➔r~piric&l expreresion that enable$ one to Giiitmte the effect on tkw nsoluUon or th® constrmt) . Tll®n 6. r&, ~ contribution ot the sou.re~ to thtJ i"ull width o.f the window curve (Ml width a.t the base of the ®Q\J.ivru.t)nt triru1~;l@) is given by !~ ~ f3e£~&-ood ooil c:onf1i~a~i~n With the ~epm-"ation of the coils fixed at, the ~p&c:.tng ®hwn in F'ig. 2 or!e i.m!y f.litill vary th0 field. form by ur:.d.ng only part of the ®.V'i.itllablei turns. 'i'h@ i'ir~t @;;q><r~rim,anis with uwi u-~h&I,>®d field ·r.~re F ~ ·,,u~inc1 only the ou·~r p~ir of coils . Althou{,,il t,."lis configuration proved to 'o~ net too us~fulii rnostly OOOll.US@ of ~ lizl\i t on the meud.mum ~ru.,rg;.7 <':.t l ~1ctrons tbat oould oo focused (~ 4 ~v) aoo tiec.:.,r1.1~,G it, W@.u too sv}t'i;:.ii·i ivci to source siz® and loe,u- 'l;ion, soxoo of i ts propert.iwfJ ;~ int~rasting . In partioulu, thorre ·.v..as evi~3t\OO thst, the out.or p~rt of the t rar:ttiJ1TI:l::rn1i ou. zo,nr~ co~, apond{l'.ld t,0 a m,irpris L."ls;ly larg;s solid w".'l1;~l 1;, . Fig . 4a, for e.:~:atripl c , was obt,ed.ood \U.d.fl€ & • mnall source mid oo'W!ter op,.mine; (0.078 inch) and <lit troJW.Smis sion ~ooo from 2.$ inch to $.O inch radius (in the plru1e mithrey between source .md counter). When the ;;:,ourCQ md counter openini an ,.:dally ~ymmetric with N spect t.o the ma~netio .field coilm, ti prominent peak ~pears 1at th.@ lo-~· cw-rent f3ici0 of the nictn.ngular distribution (thia shape i a f ound beca'\1$6 ~pherical sberrstion mak:eGJ the ~&.-e much larger t han the counter opening). The dis- appearimce of" thiw pGJak irmen aeyw.ie try between the source and counter i s introduced i s not surpri:t?ing it one notes the bemiwior of the trajectories &.; ~hown by t.he eul"Nnt-c~:i.g wire . It tlu, wire i ;; fixed on th® G'.k'tlfJ eat B)"m!l:."®tric points, twm it i ii, syr.wt~tria ov~r i to li<iiole l ength . n· om (or both) of th@ rudll!l pointB :.ar,n moved tlong the axis (to the rleht, say) th,3n ·the point ot uwJdrmJm m.:curtaion .from '"he ad:;;, 12iovee, much further in th.q; s~ dinctioni1 and thr:,; traj~)ct.ory 'ooccnl€'JG R:Brl<sdly :... synm:iot.rio. lo d<et.m..lt~d EOO.nsure100ntt; ·a~re made, but it we.is ~stimntliid that a 1/16 inM dbpl e.0011.'-::;nt of tlie a:dal point:iJ resul ted in £1 l zrudr,ru.in axoursiou. t ,0 2 :'l.noh dbplaef.;:\oon·t of th® point of Soms ~~ut..u.r'\9 or tlw 1,;u,s-jum1etry was also obt~iood in t,h~ oour~ of r ~-.y tr~cing (i.MJ in App. I) to ~et up t.he ring focus., m1@n i t 0~.f, found t.hl:':.1t in the neighborhood of the co'!ll'lter, and .for s ray of m:d.inu:i'il excuroion from the a..'tis of J 7/6 inches , 68/6r, a .077 r ad./inch ( cn.:mg~ in .m;.gl e with the .arlis ~li th chmlge in point of inter section) • For th~1 ex- traoo rmye (5 inoh maximum excurs ion) 68/6z i s sever.a timas as large . Ths f'ootwing properties thus change rapidly if ooo m<.,"VGS the souroo am.1.y from the t,yisnetric location and the large oolld angle associated. with the outer reys diarappears. Resulte of a further investigation ot the lsrgs solid angle aesociated with the outer zone are shown 1n Fig.$. Using a trmuunisaion sone from 4 to 5 inch radius, the loc.!!!.tion of t.t.w ring .focus was determined approximatel.y,by the c~ssed slit method of App. I. With a tt ztandard" oo60 source (see section F belcm) a Naolut,ion or 2j .and a solid mgle o:t ~ $.8J of ia sphere ~'9re obtawd. It ru.~o saeimd prob- ~bl® that too width of the tran$11ssicm l!:ooo could bs reduood by 3<>,i ·rlthout a.ppNci<lble loas in solid angle, al though th\9 0xperimont2 L.-wolw113d .mre not conclusive. An 11Px..impl e of thei off@ct of source s i z~ 1t5 81,vam in Fig. 4b. Sla.tis a,,"ld Siogbahn(lB) b.ave recently publi&b.ed d0tdls of oo e:Kt,ond!ild ~rt.udy oi.' a sp.~Otr(M;OOt..er dtb. an even moN e.,,,"'t.ffa)e field .form than ours , for 0 wich they claim a solid ang].3 of 8% nth a Nsolution of 4%. corroborate ours, in general. Their ro.siu.ts HO".v-,ver, they found tba ring focus, if it. cuin still oo thws n&med., int.be median plane 1 in contr&st to our e&as lilbG" th.ere -~~s clearly & ring focus 4't l/9 the source to counter distan~ from the counter. They also traced electron trajectories, U$Uli 1a photographic technique, 4IDd found the type of a~)'llmetries dsecribed ~bovej but regard them a~ Npresenti.ng the focuaing propertie@ of the field rd.th~ point r3ouroog rather than as tbs effect of '30urce size. Since they u:sed e 2 m di~tar spherical source, ·which. ctm ruu-dl;r oo reg~rded 1'.l;li a point source -u- obs©rved .as,aaetry ll!WJt be attributed to th.<1 finit..e source size. Thia i s of iu?portmice principally becaus& it would -ttppeu that their oolid angle was determined b7 measuring t.h.e initiru. ,e,ngla with the ~ for the ext.re• • appreciably. F. Four oepan,t<ad coil configuration could be tooussd, th'M covering the range of intsrest in !l 1.lmo~t ill ~,®s . only the two ouwr coils ~•re used. To mum-a absolute inteneitias of ~1-radiation, the i1olid oo~le from w'aich tl'le spectrometer collects is0condary elaotrorw wet be ~aiourad. Aa d13cused in See. IIIi there are two powsible definitions of the solid angle. 1.b.0 more natural~ end perhaps fflON significant 1n considering thG mri't,s ot a p&rticular ~pectromwr design i"3 as the ·ootal solid langl.® bet.ws~n th~ min1mum and ~ init,i.tl ,;mgleo M eh1ctron can mnke with the -12mru::inmm e.r1gla mAy ~ bii ·U,e a~ as that correr::;pcnduig t.o tJ1~ minil·mun angle). Th.i:a eolid ,i;l,rlgl@ d ll be designated by fl.. 0 ls ol' the !'Dolid angle Too ~eoond definition 8 (which mu;::,·t 'be i.il]itd in urterua:l:t.:r e&lculfttions) afil:l th~ r atio of the nuru1xar of eou.nts at th~ ps5tik of an internsl conversion line to the m,m1oor of 1;:l,:)ctron!'.l per .st-enidi a.'1 en1i tted by the som-~. D. i D u10ui,ured ,,.a::.; ily ;J.nd directly a ccordinf to it, ;; defL.'lition. Can, ciemtly clo se to th•~: :c1ource. 9 , on t,he othf.iX' himda i 3 ~;om0i1hat. more dit:eicult to rnea.su1•..i to the .1;-i. ccurecy t.hat, is &,sirabh1a hsoa,rnm of Uw diffiotllty i rnrolviild tn obtaining .nri intern.al convers ion line r;;ource for ·.vhich the m.::m~1r of ~lectrons emitwd i ~ !lccura¼l.y knoi:m. Although tluitabl& 130uro@u of known total activity (or disini;egration r&te) are available , the number of internBl conv©rsion ~lectrons per disintegration is dU'ficul t. to mai\,BUI'G experimentally and 1'3 geoorall.r not k..,own to closer thui 10 to 20%. For oourees of koown 13-activ- it.y (continuous spectrum) or y-activity, the method@ or Sec. III may be ueed ·l;Q Jllied.&Ure e. One may ru.eo obtain a f.airly UOCur,!!,te value or 9 b7 dewr- mining th~~ nw. .ld..mttlii ro1d minimum initial anglM 'Wi't,h the &¥.is of 81.ectrorui oorrespom:lL"'l~ to too E,:.ak of an intor.nal conver s ion lin0 , onlouletinf]; th'1i correH-ponr.b.ng aolid a.1ele an.cl subtr&cting the ®i'fa ct of. obsti..-uctions s't-1.ch as too helio:..l "o;u'!l[;.itJ and :su:pport~; for tho eentr1.,1l :£itops . Bec(l'.uz,;c of tilG l:.;.ok of ;,;ttitnble sot.u-ce:) 1 tids l a:'lt rn<J thod was usud to ltx..o;c1;0·t:i.r® bot,.h n and (8 .t'or our apGCtl't)rei.:d;.c:ia-. An annular ap,;n•tur$, ~,;hcrw.n in F'ig. 6~ -~,as m;ed. It vms arran[:[,~9d i;:;o t,hat, it could be mov--.¾i .accu.ratoly ::naa~ured dis t.anoos uong tho spectrometer (-1 ,.i~ and '¥10uld ~~ ';,ell centered. J1n 0.02-inch di.smr~t.er ThB F lina source WID.~; used, the c--urves cbt~ined tor v.arious source to 1:ilit dist,ancorJ ooin;; $howz1 in Figo ? . -13Tcaking account of t h.0 c.hanga in r,ol1d angle s-1.i'btendad by the annulus ·rd th chang.ais in distMce from the source , one c&m ealculatG .from ·these curvec corresponds to cl\ i~ource to 5lit distance of 0. 9.$ inch, which givea a factor of two reduction in peak . height. netio field (28.6 mV) u Since this pea.le occurr; at the sams n&aGt- that. .for t.he whole transmission 21000, °"min is the minimum angle appropriate to both .0. and G) • a.' mrut corresponds to a source to al1t distance of o.$0 incht were the intensity at 26.6 mV i s dcr.m b,one hill, and thus is the ~ tmgl.e to UDO in ccl.cula 'l',ing G) • ~ , on the oth0r n~, oorrospondG to the &ouroe to slit distsnc~ of o.475 inch at ~iiich the peak heit ht is dcr.m by one h&U'. Since the peak has shifted (i. ,fi ., is now at 28 .4 mV) a.i'mlX is tbs ma."tbrum nngl.0 to use in calct!h.ting !1. Cer"in relative positione of the source and slit are ~ho~n ill Fig. Sao I t ID.£-:f oo noted in particular that a source to elit di.stance of l.00 inch should lalso have been triad, to ascertain pos itively that, thtz pau h@ight was f alling off more rapidly than would be expoct~d just .from too dacI'lease of. the solid angle of the annulus with distance. From pUNily geometrio considerations, it 1a oortain that Clain i& not l0!lls than ~ 1.3°., and the error in n. and e from thia cause i s less thEUl l()j. The correction to ~ !or obstructions in the t r ansmission zone i a estimated a& 20 ± sio 8 Thim gives n. • 4.4S .t .2j of lnr stersdiano and = 0.80 x J .81 ± •2% c: J.O, ± o2J of 4 11' s ter&\iane. It may be noted ~ t th~ source used was so ~ thmt effects due to it8 si ae ~ere negli- el ectron paths could be cons idersd as strrlght l!n~s , and that, ae illus- The same source vras also run with the slit.Iii moved complGtely-out. of the tran~ismion !§one, as could be done without moving the source. The ratio of "P@ak h&irthta without the slit.a and with the slits in roughly ths center of the ~hole acceptance conej) then gives ~ ., in terms of the solid angle ~ubtended by the slite, as 0.80 x J.65j • 2.92% of 4,r. some question u There 1a to the ~-alidi ty of thb methods and 001&:ll errors in deter- mining the solid angle subtended by tbe alits bacome imporumt, iao that it is regarded mostly as a rough check or the oth®r re eults e top, both tltt,ribu't,ed to Bl ight &<ilali gmoont, which is v~rti"ied by othsr rn.ns used to ctetormine tns solid a.--.glo of oth~r spectro,..n~ter conligur~tions through the inte~dia.ry of a nstancford" 0060 souroo (hal..f-lU'a = 5e3 roars). This ilourco* oonsuted or a !©\V ~om2 of coc1 2 (natural co + radioactive eo60 ) precipitated in an 0.12 b;r 0.15 inch r-._,ctengle on 0.001 inch copper, held in place by shellac and covered with a J/8 inch d:J..amoter thorillll foil or super!ioial density 16 '11J£/c~. Pb.otoolectroM from the two y-rays of co60 (1172 and l.331 k$v)(l.) are ejected from tho thorium foil over an ~s whose effective di~ter i ~ estimated sa ~ 0.15 inch. In oome oaee~ the ThB X-11.m was tu.ed instead ot the 0060 , the act,i vi ty of the souroo being masuNd by a monitor Qeiger cou.n:oor in & stan~rd por:sH,ion. Th@ dif ficmlty * Kirtdly pNpm.r:~d by Dr. J. H. Sullivan of th~ Ch.,Jmi stry Depurtmen t of tbG Cru.iforni<-l !nl3tituk. frgm co60 r.:1u.ppl ied by the Atomic :f:n3r gy Commi:f;sicn. of reproducing t h i s geometry roade the method not too satiefactory. In 1.u:ii.ng these sources, it was a:Humsd th&t both .0. and e qre proportional to the peak height, the tactor being given by too rneu.Jl"ements ot G9 and D. described abo'Ye. To datendne the effect of Gourco sizs and al.igmaont on the N111:1olution £or the tour soparated coil configuration, a small F-line source was moved riildially off center by meaaUNJd ~ounte. and in Table I. The results are gi-wen in Fig. 9 fhe width (Ile determined by thG extrapolated edg~@) at base of the window cune with an off-center source should be rot'@lly tl-16 the ellll\e as that for a full source whose radiu.v is eq'Wll to the distance of thli extreme source point from the uia. Chao's tormulaa (Sec. II D) uy then be ueed to calculate this vidth. Table I L 6L (inch) . 5 ·lf- 6. + L ~s 6. t ett 6.s (J) (inch) (j) (%) (%) 1.60 .06 0.47 2.1 3.$ .23 1.60 .18 1.4 ).0 $.1 .2J 1.60 .JO 2 .4 6.4 . 23 1.60· .42 J.J 4.0 4.9 .2.) , * Calculated. f ¾ c'bs. 8.1 Note that S b the source diameter. It lllUJ be noted that@xp<ariment.al.ly th® width at tbs b~ 1e generally found to be e01.00what l oss than twice the full width e.t half maxi.Dma. -J.6- A ·tabulation or the reaolut ion and solid angle experixaentall.7 obtained, a:,:l .;;ivs n in Table I!, may oo of interes t. The widths at the base ot the the ex-per :lme ntal r esolution must lxJ regarded aa an upper limit-it cannot oo gua.rmte@d that t ht3 al.igmoomt of tbs source and stops with respect to the m,,,gnetic field was perfect or that the ring focus etop3 trore located at t he opt imum po~1t1on, al.t.~ough in no oua would more improvement 1n the re- ;;;olut.ion th&n about 30% be e,xpeoted under optimum coDditions . Cbao 1 1> ex- pre ssions thus give oonaistently low Yalues as would be e.xpeoted fro11 the s,naral. simplifying assumptions involved in their der1Yation. They are still o! much practi cal 1.Ulti in estimating the change 1n resolution for a given change 1n source aize , however. For our work, the main advantage of th.a U- :shaped field o,rer the thin l&ns is not, u would 588m at first glance, . Uw l ar a,~-er s olid angl e , r or th$ s olid angle of the thin lens may also b6 incNs[_,ed by daoraasing the s ource to counter distance,* but the large i~ot.U-<;;~ t,o counw :r di~tance st miioh that solid angle io obtained. Thi6 is of 0or;:0 i.mpor t,anoo in cut.ting down background from sc11ttered electrons mid y-.rJ;;t(, and 18 oi' special i mportanoo when weak y-rays from nuclear reactions wi t. h a J.ar gG neutron background are to tm s tudied, for our attempts to re- du.00 t bi o background {see Seo.VD) have shown that tba most useful type ot !tiaihi eldingii is the 1/r' decrease ot neutron nux from a point oouroe. -- - - -·------------------------·---* .Aaam.rl.ng t hat the diameter o.f t he vacuum chamber is fixed. The prinoi- pal di ff iculty a.ncountorod in set.ting up such a con!iguration would be e)..rpeow d to be t hat of !inding a large enough thin-window Oeiger counter to count all the rays th.rough t he ring focus zone at a given field set,t.ing. Al~o1 the baokground r at.a o! web a counter would increase with i>ize . -17Table II " ( i nch) ,!., 6t s {%) (inch) 6. L + 6 s 6s (j) Point1v e34S .47 .2; - '-~ 2. 8 1.s 6. p/p (~) ~13 ·~ 4 2. 7 1.9 C 2. J J• 4.0 3.5 0.1 0.1 . 12 . 12 b ng,:.1 om • d (% of L;,r) Thin Lins l ~) ..12 o. 7 focus 2. 2.0 obs . on (%) A. 11 6 2.; 2. 2 1.4s ~ 1. 6 ~ 1.0, -;: : 1.5 :::: 1.05 B. ~o ooparatsd. coil:3 »Point" focua a .24 .15 .l,$ ~ 1.5 .os ~ .15 ~ .04 0. 96 .96 ~ .12 c. 1tpo1nt,., t'oO'Wil a .083 o.$9 l.60 1.60 . 2.3 1. 60 . 23 .23 A . Ta . ( 6.I) I~ R l Ill: . 0 ! , 9 ~ .os .12 .12 f::S • • 15 .02 inoh-lJ ( - - l.8 0.48 3.3 ~ 10% 1.44 1.44 2.1 3., 2.40 ~ 1.$ . 9$ .9, 1.54 2.ss 2.os 1.1 4.2 2.3., .16 1-.76 l.90 2.78 1.18 69 63 ) l = O i ~ = 12. 5°; R 1i 6 l • . 4.1 3.4 2 :, 111: a. . o. d. ~ s.s _c.9 -• f J lJ E;.2rti.Intrt©d. 11.ne:iar ex·trapolation o t front and b&clc l;il~i@f;;l . lllech.amiool uli gnnwnt lJt'.MJJ app~ntl;r quH,e b;ad. No &llowanca for ~ 20% losl3 in oo.fi'lf.is md t.ro.pporw . See Fig. 4b. f. For rsy-~ with mrutimum e:.tcuridon trom ~\.Jd tJJ • 4., 2.1 h.4 4-4 4.h ~ 31°; R m 2. 6J :t.,ch . From e. ~ l J/16 :inc.t'l. c. b. ~ 6% Four separated coils (M.)l = .064 1ncri- (~!-)l • .071 inen-l ! 6R 2. 2 1. 2 2.1 ,3 . 8 Trtanemia'9ion :IJOM 4 inch to $ inch radirui . J 7/8 inch. -18- In the inwietigations described in this thesis, the ~-r~ spectrometer u~ used to investigate the y-radb.tion produced in nuclear reactions resulting fron the proton or deuteron bombardment of light e l 0nmits. Too proton or deuteron be.mu was obt.aiMcl from the l.6 Mev i!eµogg Radiation Laboraitory electrost.at.ic acoelerator.< 19 ) The beam is analysed into its atomic and molecular ion components by a magnetic defiGction of a tew degrees, and the eeleoted component is deflected through 90° by a mecond magmt. Thies umgnet ®erved to determine th~ energy of the protons or deuteroWil to about ± 0.2j. BJ' means of irwulated slit ~ plws suitabl s corona cont r ols the variations 'rl th ene r gy of the de.fl.action of th~ oo.;im -were used to control the aeoolerator voltat;e .< 20 ) The analY'Zar magnet w~a not csli= ' bra:tr~d. Rough Yoltsge maasurements were made by rei'erring to the gener..1t,i ng voltmeter< 19 ) and fairly accurate m.<.HUjurements could bo madu by holding 't,oo voltage as n~asured by t h:S geoor ating voltrfi.3tsr constant and S11i tching too beam f rom the magnetic anal~er ·t.o the el ectros tatic anal;r~@r deis cribed by Fowler, 1at u.(20)* Excitation tunotione (variation of yield wi th vol tage ) oould be meawured by ciumgina; the voltage by equal steps eitmir with reference to t.?.ie genar .ating volt.meter or the curNnt through. the field 00il~1 o! the analyzer magnet, t.'irie latter method being more eatbfactory ao long as hysteresis et.tacts in the iron of tha magnet were £voided. Because of th~ la:&•ge stray field of the analyzer magnet, the a;pe otromter llad to be placed ;aioout four .feet from it 9 tho beam travelling thi1:1 distance in a 1-inch copper pipe open to both the s~ctr<:mie~r mid acoeler- ---------------------------·- - -----* A~ deocriood in {20), a portion of ·!;.he lomr el f.1ctrost.atic anal yzer de- flect i ng pl ates could be moved to r-. llau the bsa:n to come s tr~gb.t thrm1t,;h. The beam v1ould then enter th~ magwirUc mal.y-aer. -19by a system of sdjustable slite at distances or 6 to 21 inches from t.ne outside f'ace of the spectrometer end pl.lite. Sines it. w&5 found that the thin-window Geiger counter in the spectrometer was sensitive to th@ sof't x-ray;;; reaultini when protons were scattered off the edge of these slits, an orif ice only slightly l a r g~r Ulan the bea1 was placed at the spectro- mter end plate and wrus found to oliminaui s;ich counto al.most completely . Targets to be bombarded were placed at the source position oft.he spectrometer (see 1''1g. 2), any converters desired being faDtened directly to them, and this whole assembly was supported by- a fine copper wire t.o ayoici elt- t.ran0ows converfilion and scattering effects . 'fhis wire was insulated so that the bee current to tbs target could be meaemred and was kept at +100 to 300 volts with respect to the epectro- meter to collect lo• energy secondary electrons ejected froll the target by' the bee. When a thin target without any backini or convarter vu used, so that the beam penetrat.sd completely through the target, th@ b3am current ·' was ma.sured by an 1nsul3ted plate$ inches directly behind tm target. _Currents measUNments made in this manner were not reluble, probably oocause of seconderJ el@ctrons from residual. gaa in the vactrJm chamber. Spoetromater count~ wre taken either for a given integrated beam. current to tha target or for a given ·t.otal y-ray yield from tho reaction, a~ 100&1u.red by a shielded y-ray coWlter &, appropriate dist&nce from the target. il&ost of the beam at the target poa i tion was within a rectMgl® ~ 1/8 by 3/16 inch. Thia was usually trimmed, by eetting the iBlit$, to ~ O.l by O.l inch without any large loss of current. Target.s md converters, except where specifically not.ed, wen O.J to 0.4 incb in dimneter. Th\'J a.xis of the spectroi~ter ·.1·as horbiontal a>1d alont th8 ,n.a&;: le tic meridian. The vertical ooroponent of t.ha e~rt.h' s f i•old and the l'>tr ,:ly i'L1ld of ti'le analyzer msgnet weNi approximately cancelled out by two p.airs of lar~ie reotantulm- ooila, the criterion for satisfactory cancellation being that rasolution bo the Smll,,$ for a 150 kev electron lin,;; and a 2.50 ~v line (internal conversion 8 F11 and uxn lines from a ThB deposit). A @ dis- cussed by Homyak (aaf. 17, p. 79) a corroct:!.ou was 1:ru1d il9 for the compon~nt of ti» eartb'n fi~ld along the rud.~. - 21- A. Introduction Wi th a ~-ray spectrometer OM ob$~lvves y-radie.tion by obs~rving too seoondary el e ct r ons produced by the radb.tion in travtH"'1~iilg ro.att,e r. The vs:rious processes in ~hich thase el ectrons m-o f ormed a.I\~ ~ell under stood, mid thGi probabilities for th81r ocour:mnoo have been calctl.la.wd , ias such calculation ifs tea.sible . insofar The bru,ic relat:i ons between tl'w enur w- of th@ y-qwmtum Md th.at of the QJ®condariem aru simple. The u.ocur:1rt.e de- termina.tion fr011. ~ secondary el.13ctron spectrum. of t..he 0n,11:1 r gy of the primar;r y-quntum is, on the other hand not simple becauae of the eruarg;y lossew of the eleotrpns in •ecaping from tbe oonverter, as discu~sed 1n detail in Ret. (17). Thie difficulty ariNe ba5ical.ly from the fact that the con- version probabilities are low, so th.at one must usually use converters ot appreciable thickness to get statistically- s ignificant numbere of al 00trons. Calculation of these energy losses is possi bl e but, ®ven with m.my simplifyisg assumptions , complicated, and has been the subject of L"ltlJ published papers, of which the most recent and m st general i s by Ni el s Bonr.( 2l) There i s also vary littl~ experi.loont al verification of calculations that ha.ve been made , not so much because t he expsrimiants am difficult as bso...2 use they represent~ case where the bas ic physical principles Geem to l:x~ wall Ull(Wrs tood and where detailed applicati on would seom t o oo not, too fruitful . For a dli>talled d1sewlt31on of t his probl~m, r eference is made to th0 paper of Bohr mentioned above. here, however. Mention of the salient f es.tures may b@ mdtil A .tut {velocity ~velocity of light) electron traver si ~ matter loses energy principally by collis ion with free electrons and by exoiting and ionising the atoms of t he ms.tter (radiation is also possible , -22- w:l th other eltJct.rcn.."'i, eudrt::r losses up to t1alf its original e;:~ r &J" are pcasible ( for greater loss e s , t.he g,truck electron with more than hall' the anergy replaces t h.e original electron) anrl los~e ;;, of s ever;tl t it>.06 the .average ionizat1.on ener ~ of t he 8tOl:'\ are prubat l ~, al though n oi; ~s prob- abl~ aa euw.ll~r los,';le;:;. For a given pa t.'l l ~n~:th, .£. , bot h th~ n1.m,h;;:1r of collision.::; and t,he amow:i-t of 0n'\1:r ;,:y los t in (-,ach i..r t: subjo c't, t,0 s t,;rl',1::;tic.ru. i'luctua-tions , or F t,ra[;gling . The t.ot,~1 i:,ner[;y lc~t by the a l i: ctron 1n the dist.moo .£. can be ?'{apre::.K,z:rted by a Gau.'3~ian probEbility di s tribution on ·. rhich is m..:.perpoc.i0d a long ta,il r 0presont:i.n.g the Nlativel ;r Lq,robabl o l r1rc,a ene r gy loss oD. &lid '!'he pe:ilk of the Q3uasi.an i s 'i-hr: 11 mos t probt.\\ble 11 aoore,.Y loac is a tunction 0£ i as "R6ll a~ o:t t.he stropping m,a·i;eri&l.. Om r,:,.'J..V alf;.,O t,ake into ai.ccount the t&.il an<l oal.eulate the "average" eoorgy lo~rn, which ia t he quantity l'llOre oo:rr:imonly g1ven. The path £, will no't, correspond in lii!ngth to n s t.r.ai~:ht line in t he oric.:inal direction of the electron, !or t i:1e electrors also inwra.cta wit.h Coulomb field of the atomic nuclelli'.1 1 with a. probability roughly propor-tional to z2 ( z • nuclGar charge). Since the $lect,ron ia tlm.ch lighteir than t.he nucleus, i t doe& not los G ensrf;Y but doet:. change direction. Thi;; :scatterinf. , is al. so subject to :-;t~ti::;ticcl. i'luctu.a- t.ion& which a;:pear as vsriationa in the increaoo in path l e ngth and con- tributi~ .furthe r to u 1e s t ra.g{:;ling in Gnairgy l ow . \.'tb.,:n tl'1e ele ctron in i.i.JuiJ ti on i::, orJB th <:: t ha :., b,ian c j e ot.0d by a ·',quJm'iu.rr1. &.'lid oount,"1d by the 1specti-•ol1'. at,1,ir, ws know only that it. 11&> been 0jscted somewhe re within UiG convc.rw r .u!.11d em-,erg~d from it 11it.h its dir-.c)ction .&id momentum wit."lL"'l. certain apprcpriaus range r; . It, i : :< cl.s.ar th a t it, i s not a sL!,,I)l e m.atwr to d,;_;iw:rmioo the energy of ma primar-J y-radiation (i'):J,.:,; il,;: und a ccura,tely .from a oolloction of such dsu; . A re~;.,onsbly accurate -2.3- solution of this problem hae been obtained by Horcyu.< 17 ) It is al.so clear th.at th.er:~ will be some difficulty in determining the intensity o:t the primQcy' •r-radiationll since thS.s requires e ssentially that ·rre account for all the secondary electrons. B. Photoelectrons 'I'ha most generally useful secondary electrons for detecting y-ra.di~tion from .a tew kev to ~ 4 Mev with a ~-ray spectrometer ar0 photoelectz'Orus oo1 ~u.ae t.hey are initially prac'liically monoenergetio* and their inten~ity co.1trp.vea fe.vora~ ·with that of other oooondsries in this energy range . Sauter( 22 ) hae found the dilterenti~ photoelectric crot:Js section to oo (l) of the e j e cted el ectron in units o:t ·t,h(S velooity of ligM,, a.."ld w = the miglo ootwaen the qu.anturo md the e j e cted electI'On. This oxpre~sion fa relativiaticall;r corNct, but has been derived by the :Som approi.im.;i.tioo 8 and thus hold$ only for (21T Z/137'3) < < l. ThG zS' dependence indictrl'h,s tlwt it will be desirable ·t.o use the largeot poaeible Z (e. g. thorium., Z = 90)., where Sauter• s result is not valid. However., the di.f.fe.rentbl. cro!ila i&ect.ion hae not been calculated to any better approximation, so t hat we &l~ forced to us@ his important result that, for high energy quanM. the photoelectrons :are ejec.rt.ed mostly in the direction of the quantum» half of the electrona * It may be noted that pbotoeluctrons @jeoted from the JC-shell ariv of' tilltl order ot five t,imes as intense as thot:;e t ~u the other shells, providing , of eours3, that the quantum energy is groat,er t..'1an the K binding em:1 r gy. by Hulrr~g et al . ( 2.3) Thay ver ify t tw V:!?lu.0;t, ci~l eul a½d from 2 :t'orrr.ral a due ,(;O Hcl1( 2li) and \ 'I.ii$ Hsl l ' s e::,_1,ro:::,s ion t.o irrtb rpol.nt"1.l bet.w·0e:n th>:::ir oz.lcu.- ci1acksd, according to Heitl 0r (Re f . 2$, p . 12~.) at t.~o points . of' t.he oo.ovartGr . The comrerter i.;6lomet r r i s shewn in Fir .. lOa . rsdiati on i ;:.; conaidered to be 1eotropic anci 1r1.onoener,ge·Uc. Th~ y- 'l'he ooordinot@.1 needed t o de s cribe photoelectric conversion 1!1.l "S SllOWfi in }?ig. lOb, ~here . E. = the angle between t he y-quantum end t.h a spectrou,€Wr axi. ~J o 0 = the ruigl G bst-ween the photoelectron and th.o spe ctr ometer a.n u . w • the angle between the photool e ctron ,:1.nd tht3 ·(- quau"tv:m~ 'P = the az i muthal angla of the photooloct.ron abou t t ne dire ct ion 0f th~ r -q w:mt uni 0 :L-! t t' :: - cos £ 0) If ¢K ( W ) i ~1 thc'.l proba'bili ty p~r K sl u ct:ron that oz:.e qu.an t.1.nr. !X·J1i."' uni t • number of' such ~10ctrons b g,iv~n by (4) COti 9 - cos w 00~ E + sin w ein € (J\')$ c.µ. (5 ) Dif.f'erenti ating 11 putting dE e dw = 0 and elimiri,ntlng sin: ~ one obtai ~, a.ft.er ~ome simpl ification d~ = ---------d~_;_P_!_a_)________ (6) [ cos( & - <.0} - co:3 €] [ cos E Wh~n t.hi:;; is ~u.b st1t,iJ.ted in (4) we g.at ~ = _h_n _n_t, d( co::_ ~~5 co~ w) d( 1:_os ~?~.- OO fo; E • V[coe(Q - w ) - cofl E] [ 006 E - oos (Q + w )] ' ] de f dQ f dw co;;., 6 U' ( 8 , ~ , w ) .. -.--.--~- ~.. ! de Jd8 Jdw 1 • ( 0, e , w) (7) (8) -26- to 'tho qu.mr:rtm."l direot iono a-."ld b b It a- K i s tha t.otal zt-pho'l:,oelectric cre sts section~ t,he Dirac delta function., t'.1e11 ·th~ 8Ube1:.i t'4).tion can be ·written as ' (9) Int~gration over w ·then f; i Vefi (10) (11} IOO i:,t import.ant i t':J that the ph.®ncwnon of s cattering ha: :-J been n~gl acted. Except ti.url.:, if Eru.v.x ➔ 1l' / 2, t,he ,;:.1,ppropri,a;to l l!:d.t, i B tr / 2 - 8, wtw I\"1 8 can. b,.3 eie timated from the :at;t em.1.B-t.:i.cn. of the y-r ~'td:i.a tion i n th0 converter. This i :;; an ex"~ r.1G caw reqv..i rlnc ., for e, :.simru.o , 90 = &JO, .\3EAd photos l e ctrona of < 160 Icev. fol low$ . For very thin f oils, i.n m1ich s02ttering fa negli ibl e , only appreciablt1 . Then ti.v.;i root i? "an ;3qu..arf1 soat.t.el"inc &.."1f,l<:i , ~ , i s st,ill sn11:u l th@re is nc noti,;0abl o effect ( ot her tha."l the l i rwar varhticn rri tb fo i l thi ckness) :1 the rJ.'00!.00r of s l ectr ons DGS.t'.l:,erod ov.t of ·Uw acco ptan~ ~ zone from these :c·ange sj s i nae ttw numoo:r of <Sl eot rons ori -;inally ~jec-wd at an angl e 9 is proport ional to \, coa""~ @ - 2 COi'il • w O , -1/2 ~ cos vn-1 • ; ih~ cases vlith which W3 are concer ned , where f3 f or the e l ~otrona is ~ l and Q 0 ia sm,all ( 30° or lees) i1 t,h.(1):rs are a. lffg® number of elGi) c t rone .at l arge 9 [ ~ (Tl'/2 - cos- 1 ~)] th.m.t were e j~ctsd by y- r iaye travellin£ r ou.grJ,y parallel aro cHJsttored into the a.ccepta.ncis zone , a rapid inc.reast, in t.,he m;,moor of phot.oel 0c::trons counted is e xpected ( and i a obGcr-ved e.xper :bl'i))Iltru..ly) . • down in the conti nuous backgr ound. of Compton ulectrom., er scat " erod J:1hot o- thickrusss 1 thi t:J second af'fect becoru0s prodomina.·,:c. , and we reach a 1lnat.ura= tion 11 thi clo.1ess ooyond which ~ddi tiomtl. oonire rte:r produc~e no ef.fe ~i on the t - 28photo-peak (tmtil, eventually, attenustion or t he primary r adiQtior1 becoi!'tes notice.a.bl®) • * The problem of sca.tterint , wi. th iiJ!'Je:rg y loss neglected, can be treated toooretically by considering Bothe 1 s< 26 ) d1.f'.f'usion equat.:ton, which may be written for our C1¥:U.lle (12) Here f • t (JJ-,x,1) 1$ the distribution !unction (pe~ unit solid .iingle) ➔ !.'or electron.e o:t' veloci ty V in an in.finite plane sheet of ruaterbJ. . 'l'ha x coordinate a.us is tuen no:riruu to the plane and p. is the cosine o.f the angle between the .face x 'V and the x- ald.&-} . Electrons are presumed to originate at = 0 and to have an initisl val.us of µ > O. 1 i s thG ~etumu. di stsnoe travelled by an electron in going from x a O to x. x and i. an both me,1U3'lll"ed in uni ts of the di.f.fusion length /\ , de.f i.Md by ½= angle . '2 n 1.l[(J" <a.,V)(l a. CQGi a,) sin a. da. . (13) The lQ\'i/er limit on a. is set by the eoreening of tho nuoL:.3..u• Coulomb .field (scattering field) by the atomic electronm. The upper limit , of no as rr/4. Sol utions of this equation h&ve been diac-.wsed by Bothe< 26 ) ru1d ey JJ@·U1e, Rose .11 and Smith. <27 ) A particularly isimple tlpproxilr.tJtte [1olutioni -29wo:.."k dooo .!lt t.'1b leborator-.r. He 13t8rts by as sumine that the 3eoond der:i.vative ia aronll, and tr,s t for tt,e region of in-wrest µ.. ~l. The fiJ:• :3t order equat.l.on t:1us obtained 1s oasily solved by standard methods. rr f 0 (JJ-) 11:1 t he original. distribution of elsctroW3 before any scat.terinLl, then bB get.a a relation b-istweEJn 1 and x ( the :1umrag 1.'actorn) (14) whe1"0 ''ni is u scattoriug length defined by (15) and au !.iil Bctron di::-;tribution {16) Now ..1ocord:1ng t..o eq. (11), f 0 (JJ,, o) is given by {17) Thoa(E) elaotrooo originsting .at x m O th<aiu have a diilt.ribut,ion (18} One thing particularly no·t.abl~ ;,;.bout t.hi r; clfotributii:m 1u that it b.aecr:l'.': ~J infinite at fJ- - (x/:s.ti).) = ein2 w • 0 This we know to be too extre100. '!'horn.a..! thtir~:f'0re expand;;; f (µ., -:t) 1u a po'>ler scrfo ::J in :1./ ¾ and k~f-.ipr..; onl;r (19) -30Je can ·t.11erefore write for the number oi' electrons formed i n the co.nveiirter .and 1;;1merging from t,he face at :x = t, and at t.he angle 8 0 ( acceptance angle of the spectrow.tflter) {20) cos €. Thb expnission i s not ?e,oo -~ccurate, s ines the appro:id~tion::i inooe in the dif.fu@ion equation .!l.N not valid whe1"6 i t will gan~rally be used . How- @ver.11 it is simple and easy to ue0 .11 and its general behavior for vari~tion~ in converter thicknea,s see~ns qui ta reaaona.ble . It cer't£inly contribute ii! no more error.11 Md proba.bly much less , than the original ~~:i.u;..•·1ption we n N forced to make in deriving it, that all th.0 el@ctroxw corre apond:i.ng t,o th!ia known total photoelectric cro3s S(ilction, o-K, w 0 ~ ej0ct.ed at the m gls = cos- 1 ~ to the y-quantum. The order oi magn.itude of the or-ror re1:rtltL"l.g from t.hi 8 approxi~t.ion , which i s th~ se cond source of ®rror to be consideredjl tna,,r be estimated roughl y . I f one cru.culatea from Sautsr • s 1a:r,:pre:.:;aion. t,he r ati o of tlYJ dif- w • T( / 2, coo gst s :tor 400 !rev ®lectro-oo (~ a o. 83 ), for @Jt.:nmpl o , d o- (w0 )/d(1" (,r/2) = J6. With our converter geometry., it i.w pos sible f or a ~r-r&J at, wery clooo to 90° to the ~pe 0tromet,0r a.xis to have a path t,hrough the converter w;ry long compared to the conv®r·,~r t hickness ( n factor of -Jl100 itJ possible, and in pract.ioo thiB .factor i ~ probal:ly bet.:re~m 2S aa:l 50 ) , 'l'h:is will give an app:rociabl~ number of ol .act:ro.n~, that gr,e not accrn.::.nt;;:.id for will be compensated by scattering in. Eq. 20 may b0 t,hen n::m--it,ton :;.o (21) evaluaU'Jd ein:pirical.ly-., as in Sec. V c. -32- The situation as .far a.st.he use of Compton s15condary electrons i s concerned is muc:h better. The diffo1"f.lntial cro s6 s~ction i :;, civen by tb0 well-known Klein-Nishina formula for any enor gy or conwrti,r of interest in the present type o.f e:.Kperiment. The number 01' Compt on secon<la.ri o6 eje ct'Jd depends only on the nmnbar oi ' electrom; in t he, conve rtor , so ·that 3flY element is roughly equ.al!J· suitable as a convert~r, and !iie can t.hus avoid the heavy eliaments and t,he associated large scattering. * SinC'..e the Compton ~leot:rons have a continuous ene:ir gy epectrumi th~y are not am conven1ent 51 in some ways l> as pbotoelectroM . Thera i :o some preference., which incre~aiea with increasinf energy 9 fer 1:11.s ctren~ to be e.ject~d with the rr.:.arlnru.11 possible energy , but below about 3 ~ev., th.® re- mu ting peak i s not as prominent as the photoelectric pe8k from ,a heavy conve rter of equivalGnt tbicl.1ess (me E.>.sured in unit:, ol' t,lectron ~ne r gy loss ), 311d the cont inuous sr~ctrum introduceu 2 troubluso~~ ?ackgrcund it 1~or0 than ooo y- r ay line i s present. The Klein-Ni :shlna. formula has been a ppli 2d to our ~➔p ::i ctrometc r t.-u'ld 1 by • (22) a+ (1 + )2 X = COS ~ Th~re i s r.1 0100 &<!vantage ll'l us ing alemente in th6: neighborhood of copp0r where the a~rgy l oss of ~ .fast ~le ctron psr con:ver ter e l e ctron i s .;i. minlllMno - .33where Hen dW' / dp 1a the number o! '81l ~otrons per unit moi"ae.ntum interval aj©oted into tho accept.a.nee angle or the spectrometer ( e1 to e2 ) 'by one quantum or i s otropic y--radiet,ion per unit solid angle11 a is a convenient parameter, and I\}= number of elect rom/ooJ, t = converter th icknes s, r0 = class ical el ectron radius , y = pri.Jnary qwmt"Um energy in uni t s 0 1' file, c2, µ. • moc2 . <llf"/dp i s the primary c;pectrum, betore the ei'feats oi' thl.'; :t'initf;;l N @olvillfi p0111er of the spectrometer a.nci of energy loss in the converter ruavs been considered. 1n Seotion E. Tha effect o! finite resolving power will oo conaidered Energy loss effects will be considered l ater, in connection with experimental resul te. D. Positron-elc.ctrori pairs. Internal. conversion. y-radiation of enGrgy greater than 1.022 Mev oar1 w.so be de tecriA')d by pos itron-electron pairs creat.ed .ns t ho r adia ticn traver ses matt,~r. Thia positrons and electrons· :iiepara tely exhfbi t a cont inuoue dhitribu.'cion in ~ner gy ( the total mwr gy of the t.,10 components of 011c p~ir t'.!UDt add up t o • the y-rr,ry energy, of couros ), so that a largG part of tha wholo qx,ctrum :JC t.ri.at we tu'l.ve not found pair.s part,itm.l~ly ttsGful in our work. An ~3:r.ci•ted nuolau.s that 1110uld normally dsca;r by r-emiasion. ~Y also pointro out, th at the ctlr~,c't, interaction is ttrn naore probable, and inore~oel?J rapidly with th® ml.i.lt:Lpola order of the radl&tlor:j so that. tiH~::,e so-called internal colwer~ion electrons c&rmc,t be ue0d to m®a.£;u.ro y-ray intensity ·1relocity of the e:;~ci.ted nucleus, that deoa;y- by quantum em.i::rnion ro,a;y occur i:,Hfore the m.wleiUJ b.as picked up any atomic ehetri:,rOJl:£). Tho y-re';)'~, from th0 ru1tu1~ru. raidioacti·1r·:;; ol,w1c;ntB have a.lmo:it £.J.1 b'i:HSin idont,l.fic,cl oy th'i:J int.:J:rnal ccnv0rdor. line G. S0e ( 16) I} for cx.Hro:pl~J . the p:robabilit,y of for.rlng :suer, pairs does not vary mueh with t,he mi..u tipole order or the transition., they may oo uaed for rough intensity rueaaureroonts or.9 with consider~ble care, f or det.erminin[; the multipolG ord®r or the radiation when the intansi ty cf the y-rad1ation is kno":m. 1.n cert.ain oases, both tJ.1.e excit(&d izt&t-:D a.."ld the ground stat,e of th® nucleus mc1.r nav~ a total spin equal to zero . Transition bstwe©n thEJ:se two states by limi:mion of a s ingl e quant-t!ID is t..heu absolutely .fcrbid.d@n . It there i s no inter 1i.<:ediata state of di.f.f,.n'ent charae·ter, th0n th1.-~ t r ansition may be by ejection of an interrutl conv9r s:l.on e l ectron,* by the a,i:im:rion of ~ an electron-positron pair or by th~ omi ssion of two qu.a.ntlil with a con- ' tinuous energy dist ribution in a doubl e transition through intermediat,o s tateliS of higher energy (poaliiible because of the uncert.1inty principle ). E. Etfect of instrument windOllT Even U we know tne primary energy or momsntum spectrum per y-ray- or the secondary electrons as they <9ln1'irge £rom a oonverwr into the 0ona cw.fined by the acceptance angle of the apectrometer, n are still not pn;pared to say how many electrons will appear at th~ ccimter &t the other end of tho spectrometer st a certain setting of the magnetic field . To do thia, ·.wi .:m.wt inves tigate the effect of the finite resolntion of t.he spectrot!ieter • .l'i..ne.l.ytic .function~ for calculating this mf! fJ Ct h:ave be,m giv(:;in t·y Owe1'l snd Pr:b.i.a koffCB) and by Horn;,r&k. (l 7) Toe discussion here i s .from a 5lir htJ.y differ~nt point of view, il:1 oroor to ~mphas i ze certain phys ic.al features ct the r e stu. t. * If no change in parity is involved . Ellis and A5ton0 2 ) report @n 0 x- s.mpl~ o;f thia in the 1.426 M®v level iti. Rae. ~ A~ in. tha F19( p,a,)oJ.6-~ reaction discussed in Seo. rv. -36- ,nu•::.iua rMJ,gnatio i'ield (or current, J through the fi..::ild coilB) in the neigh- The valua of j givini.i the ~um. counts is usW111ly taken as j 0 {an ut<f'Jrnat.e choice ifl the atrait;~t line e:rlrap(Jlation ot the hit;h current edge to h.ali ~um. U w,e now detilrmine the window curve with an in·wrnal con- version line of different momentum, p 0 ' , .ve find that the :r,.-..eak b.ei£h,t (cou.n"l',s p0r ~lec-c,ron from th~ l'.louroe) and o- are unchMged, a~ followr:; from We rn1wi:; decide what thB consta.n:t of proportio:n.9.lity is betW>Son tlw peak counts and th<i total. number of electrons f1llr steradian emittod by tbe and is eq·ual to it to a .firi.;;t 2pprorl1.ration. When we atton,pt t..o m.&\lce a better s.ppro;d.Ir<J,:tion, -we encounter certs.in diffioul tiei"1 which are e0sentially resolv-ed ·uh.en we real.be th.at the solid at11;-,l~ i;;; not well def:tned, evll¼l abcolut.®ly l'jSt.enti:tl if th0 ,:;pet:rc.t'IJ'lI,i.'l't.:Jr ic: to Le t>.r3(I;cl in ob.i.i't>l'Ving i:.;e1condn.r; ®l~ctrtinD t':.-,:m, y-rad:L,1,t:lo:f2.. lu'!..:f :s:-np.•, in t.~:i f,pt~ot,ronbS·treir th@:t 8re irr~dial.i-2:Jd b;y -r-radiid,ion •,l/ill be i.<H.~onci£,r:,· ::;,,1,u:•t1J;::i o!/ 1Jleot.rorm. Thc;,i iJ.Umb,Dr tiff.' fuo::,t! ,;.le<rt.ron~: oouxit:,d in th2 :Jp c.: atr(g.k , t...ul" Thia b will b0 la?'fte il t,he ~k cond:?..l'Y sourc~''-" ;c,,r0 l,oo clc11", ·to t,hG tl:"Ld ':•,c,J.re& ;x)si'l.:.ion. - 31- ooterwinecl by the el ectron path:':1 and ·t,he uefir.d.n.g :,r topc 1.n t hi:'.i middle of 't,h~ curvatu1'\1 of cll electron paths will be L."1creas~d slightly. Si..l'.lCG thv t10\ll'OO .rt s-. ::;lightly larger un~lt1J, g!YID-X + be, vdll be abl e to t,) t , past 't,he f inrt de!inint; i,top, and will oo oour1ted if 09 is not too large ( 9m.in g 0<.JV t o 8_,. ~ + be•, with 69• > 68, at the Ga.!!'11:il ·time, ~,o that there is a· nut uw.d lo~ZI! in covnt~ to correspond to the oooervstlon that we have mov ed off thcJ peak of the curve) . Thus although the naturru. definition of tl16 solid angle of the· spet:trometer i~ as that. oolid r,,;(lf&le corresponding to ·l;.he maximum ~ci. n1i nimu."U valusl:) of 9 for a.11y curront,a in the neighborhood of j 0 (thi m solid angle will ba deaign.gt~d by n. or ne.f'f oopending on w'n.ather or not the effect of obetructionr.:1 in tho t r ~ 1 ,,HJion 0000 ha:n wen subt r acted ) , for our prta sant purpo~es we adopt the moN rest,ricte d ds·:tinition t hat S.t oorre t1pond3 ·to Qm,.qx ,ind 9nrl.n for j 0 » t lw current cor~:..,pondin:; to 13ou.rt.-o , or th;J).t i t ta by cie.ti ni t i on <:iq..:.al to t,he ratio of t he number of count::, @t this pe ak to t he number of. el ectrons per :.:;'i cruditID. Gmi tt ed by and is i n sters.di.i.ms . amount. In particular, it i s to be noted that the are a under· the various curves is conet,ant (and will also be com;tant , because of the small rMgo of currents, if we dividit the ordinates by the cur:ront) . unde r the curve will remain constant . Thus if we in- How0va r, we will P.J. :so observr: some flattentng of the . top of the window curve ( ~ee Fig o 4'b, im1~ r:&; the too s ources are ~ of the Emoo activity , for an exwrplo). Thi$ flattening may be reduced., if desirable, by increa8i ng the separation of th0 ring i'ocu.a s tops, whiol1 will incre.aBe both n and 8 to e. ,:.m,.all extent . tie a.ra t.hu:s led to t wo l,1'Gneral rules for- obtaining valUf;I) of 8 for va.rioua souroe meru:rured with a ~o·uroe givinc a half-width (]' 0 , and ii' t.he change in source size i s sm~ll enoug,h BO tha t. the &"1apt>J of the .rl.ndow curve 1:s not chm1.ged g:reatl,y, we will havs from t..1't~ equru.i ty of the t.wo arc:HiS for s ources of t he :iHlrrrS ac+.1:111 ty (24) a s ource of mow a.cti'Y1ty and of the dimv,,r oor deeired. * Two quailli'icati ons may be made at tnfo poii1t . For low ·8~ r '-Q' el e at.ron:3 scatteri~ in the spectroma·t.Gr 9 b~ck-.scatte ring i n the so·.irct; , raduction of the cowat~r eff iciency (because ,,f the counter window thicknCv~s L, and stray !lU!gnetic fields iuy all contribv.t® t o a dist,or t i on of the window curve that must b® ta..\ten into account. 1Uso , the mat.hod .for !l!easurin,~ 0 &ctu.ally- used, as des c:dbed in Seo . 11 F, i s applic,sbl e only with 11 s:;n&llr. sources . -39It is ganerall.y observed with l ens ·typs spectrometers that $/hen the ring focus stopa ar~ s r!t t.o i ive a window curve of t hts mrud.It,m:, t,hsrpne9s 0 W(j 0 ,j) = exp 4,r (25) W(j 0 ,j) is t he probability th.st an electron of momentum j 0 = p0 leaving the source with a random dbtr1.but1on of initial angle will oo counted -m-10n the spectrometer field current ha:, th3 valu® j o Because too oa,u ssizm is only an appro1'iima.tion to the windcrw curve arid i s probably not valid unless ~ << l_, it will oo ast-mmed '!:,hat the denominator in th<:; exponential can be writto-:m ru;; ooy of ·the i'onu;5 D. 2j 2 :! 62p2 = D.2 j2 = A2jp. 0 W(p 1 j) ~ 0 tor eithar j -+- 0 or p ~ O. I.f wo are o·bse rving an isotrop ic primar-J distribution for which tho nuwber of eL.H:trone per sterad..1..M ht.\ving momont..n betw~.K;n p and p + dp i s given by f(p) dp, then the number of oountliJ registered by the spectrometer at & current j will be 1 C(j) = W(p,j) 41T t(p) dp (26) p Ii' b. << l and if t."le primary distribution doe s not change rapidly within a dh;t.il.uce pl\ (if of/op• p6«f(p)), then Hornyak(l?) has shown t.,hat this inwgral can be avalW1t.ed s.ppror.imately to gi w C(j) = 06 -..fir j f(j) (27) - 40- a.oo for D. <<. l (with no .restriction on the variati on of f ( p) (28) where wa note t.hat. the intei -ral on the right is t~rn total number o! ele,._ trons per star«idian from the source , and that on the l ~ft is the a.N:a under too experimar1tru. counts per unit momentt.m intarva.l versus ~oment~ curv(:l . tions for Eq. 27 are not sstisfi~d, it will not always oo possible to perfor&n tho integration of Eq. 26 . Th 0 integral inust then be evuv.atsd numerically which may be t.e;dious if ~ large range of j is to b® cover<.ad, because of the term ~2j 2 in th@ ~:11:pOrumtial- i . e ., becm:w.,e the width o.t' 't..'1~ window ie a function oi' J. Professor Christy h.&2> pointed out t."tat, i t i ® quite simple to plot fas a function or im. p and to fold in a window curva _of cone'l;&nt width and height by numerical integration. Thiti is equiva- l ent to folding in a window of conet:mt he i ght Md constant percenta.ge width in a plot against p, mich is precisely what wa wlllnt . The process i a illti&- trated in Fig. 11 for tvo r--3c-t&ngul.ar primary distributions of equal &NM (int,Qru;ity) but difforent momenta . The r®sulta are ahown in Fig. 12. 'i'hs only approximation involved lies in taki.."1g thi1l window C!J.l"'ro ~s Gaussian on ~it.her plot. Anuytically we bave (29) -41Suostituting and t-l) 1-f=l-e ~T)-~• Thon (30) F". Yieldt: from nuclear reaction~ The ioothods described in the previou.a section for deturi:rdning the intanl1ities of y-rediat.ion are applied in t.his thesis to y-radiat,ion arising from certain nuclear Na.ctions. Here we are interested not only in the ralative intensities of sovaral ;-rays produced .in the sa-roo reac·tion 1 but, also in t,he absolute yields of the radiation. The 8ti)naral techniqU0r.1 -and concept~ of oxperinw.mtal nuoleu physica nave ooen di.scu::,sed in many proviou:;; pap0r-s, of m1ich Bethe' s claes1osl articles in the R.aviews of Modern Phy,:,ici/ 34 , 3S,J6 ) and the recent discusaion of y-ray yields by fowler, La-arit,1'3001 and Lauritsen0 7 ) may be mentioned in particular., f urth0r diacussion will be m:tteiupted h<j l\,, except occasionally in t.hc1 No ooo of a number of excited l®vels \ihoae snbs~:iquent dee&y -to tho J.'l'O'IJ.nd td:,ftt{a &i.ccounts for t.h't3 y-racliation and pairs. Ho Which of the oJ.6 Btat~)r;:i i;;, fox-med long rt:mge a.-particlea (ground still.ta), pair~:!!, ~d y-ray~ hav-cy 't-.-e~m int.ensive- 11 $tudied.(J9,40,4l) radi&tion is pre0UDtably forbid.dan by the selection nue mrnluding J = 0 to are formed in, a dill3ta..l'lc~ ot th(ii order ol' t,hc-) Conrpton wave length £ror.1 t.i.~0 emitting nucleus. <42 ) '!'l:'M) ma."'d.m-Jm encrr::Y of t,h<:i nuclear p3ir;3 of oJ.6 hm,., been d@termined by 6l'oml1ng;on<43) ta5 4.9 .± 0.2 Mwv, giving a level et~r~~ of This section is based on s pape1• by E.asm\t.~sGni Horny·rut:, t,:a1Jl'it,sen, Lauritsen, Phys. Rev. 617 (1950). J.1., l!l.l;M.'.i Capt.ure y-r~ation,1 !r.,;.t!lJ. trM~i tion ti,> f;,i:., e gr,-;.lu.nd @1~<'.1.t.e of ie20 ho'!\13 also ~~en ob$®rv8d.(J8) to be oon.si:3tent with the h:;t1iothesia of their nuclear origin. The angul~!l' corrolation between electrons and pod trons has also been shor-m by Devons flnd Lindsa/44) to oo ooneistent with theoretical expectations, and Devonli.1, Hermvard, a."ld Lindeay< 45) have measured t.,he b.s.lf-li.fe of the at&~ as cure:t.o m:'lt,erminetion of the pair end point and of the momerrLum di&t,ribution. Walk1::1r and McDa."1i~l 0) hsw tzhown that the y-ra<.U..atimi compris.Js two which deper~ on bo-.t1barding volt;agee 'I'tiis ~,sult has r-i;cantly 'ooen confirmE,d 6 b:,y Burcham an.d Freem&n. ( 4 ) who have observed ths co~spondif'~ ct-particle groups but vmo fin..1 indication ?fa third a-group at too 939 kev rssonan~j, suggesting tbst an additional -y-ray of er.iergy about 7 .2 Mev should e,:ist.. The~e oooiarvations have been eKtend~d in this laboratory(47) to ahow that all three groups exist at this and othar resonances, with varying relative intensities. Further mea.surements oi the •r-ray energia~ and 1nt.ens1tieg. as a function o:t.' bombarding voltage are reported in this section., bJr the 0:peotromG·t.er when set ·to -tt1w p-oak o.f the pair di.Btribution. Too rason:a.nce \!ll:nergias quowd w-ei tho:ea o;c Bennett, 8t. al <40 ) muH,iplied by -44- seal~ ~ras obtained by a;;;suai.inf: that r:d.d-point of ttie initial rioo on thi, y-ray curve correapondad to 873.5 kev (sino.~ the target was ~ $0 kev and the resonarice is onl.t 5 lcev wide) and that the anal;rzor current and mo- raentum of the accepted proton~ were linearly related.* Particu.l.arly in the -.irork on pairs, corwiderabl~ attention was given to the prohlam of dil:rl:,ortion of !'.be spectrum by scatterint• The first ex- perioonte i,ere made with a thin ( ~ $0 kev stopping power for 900 kev protons) c.ar 2 target evaporated on 0.001 inch copper foil usinQ; only the ndnizr.mm m:u:11bcr of bai!lea required to de.fine the SPflH:tromt1ter acceptanc@ angle and mmular focu~. The rc~ulting spectra oont~iood a relatively larg:3 u ~ r o.t electrons lli"ld positron~ .nth enorgiss below l il0v. Sub- sequont work w-1 th thti BpiDctro;:;-:e¼r, u2ing t,he w~ll known :sJ..3 positron tron paths for lonr.:; dietanoos. Tho pair spect,rum was redet,emi.nGd somet~ lateri1 u.sir1g the separated coll configurationj w1 t.h particular emphaaia on the low energy region. As a further precaution 8gain$>t :Jcat:t;ering., u 'target consiGting of ~ 0.3 mg/om2 B~ foil Ythich had been eJtpOliJ®d to m,· vapor ,1,"=lS -------------------,--~---------* Too ssoond y-re.y resonmce on this curve b not quite well enough defiood to al.lo-ill one to make a oorrection for too residual 1uai;n0tism of t."'ie magnet, which, ho.1ev...r, io probably quite Dw3ll. for y-raf measuraiients, Compton electrons ejeot.3d i'rom a 2.S0 me/cm2 neg&ti·1re component,3 re sp:actively, as obaf:rved at the 12)6 kev pair reCJon- ance. l'i g. l54i1 and h prewents t he portions ooar th~ end points. Field in- sensitive cosruic ra;y ruid local l aboratory background o:f about)% of the pea..k height, has been subtracted .from the dats pres@ntJ.id. Unoortainti~o in th is background are import,mt ·only .tor the first three or .four low energy points , '\15l}.e re t..he additional error 1!1'.&y ~unt to a~ much as the statistical · probable error shown. The oolid cur-.~<:lf.J in Fi~~ . 14 and 15 are calculnted from the theoretical ®¼preiwi1>ns gi wn by Oppenheimer, (49)* . • modi.tied slightly by inclusion of th& * I am gro&tly indebted to Dr. E. R. Cohen for thsae calculations. Oppenheimer' s differential distribution for -U1e nuclear pain b dN a P+P- (E+I- - m.2c4 + P+P_c2 oos 8) sin 8 d9 dlf• Integrat~ over ill a.n.gles: and 1f·iroaucing the Coulomb factor givee (E+E- - m2~) P+ dp+ 21t' Z~c dloc - - - - - - - - wilere t • --(® ~ {r - l)(e -~-- l)E+ ! l.37 P+ t.ha calculated (•~O) dbtributio;n o:t i.rrkrnal converri>lon pairs ;; ord£rs J.~ad t.o somewhat i'latUi)r distribution:.:,). froti electric It is o! in.t,.sr,.r nt to ob- serve that tho apparent eml point of the positron spectrum ts sors.:1 60 ~)V hi.gb.$r th&n Uu.1t of t,he electron distribution. 'l'lw difference results i'l'Om th® effect of the Coclomb factor, which givefJ ,a non-taro probe.bili'ty of finding a poai tron of in.uimum energy in the primary ~pectni.:m but a probability approaching zero of i'indlng an electron of mu.'1.mulri energy. With the resolution used 1n th•Jse experiments, this appean as a difference 1n tbe end poiuta for positrons a."1d ela ctronll (compare Figto. 15m and b, whGN the spect,r& before folding in the window · cu.rve ue sho,m by ru,,r,hed 11.nalii). The chcioo of' t.hG energy parameter in making the boi:;t fit o.f too thoo- thu u;0ut probablt;: energy lcwa 1:n the copper b~cki.o.g of 18 kev. * Too cnerr::r of the oJ..6 lev@l involved is obtain•ad by adding tho reGt r.~.a:ii o:C too peir Th® :!:ipectro~t.er calibration is b.ased on Bp:: 10,000 gau;:tt.i!•~Clli for tr.iG X-li.M .from a !l."'.u", deposit. The end point q,uot~d was determiw!ld .from t,he data taka11 nt:h the CeF2 on copper tari-et. Du.ta taken wit,h t.'18 'Bef' target give $.022 ± 0.04 Mev . Th~ higher energy points taken vi.th thi~, target hliiV® been shi.fwd dov.m by approxinu:1t;ely 10 kev to f'acili tate comparison ·rith t.11.e oarlie:r. d.Jllta. -47( l.,~) correotion has been included in this value, ;;inc~ oovons, et, al ,'4:;:, tisve shown tiurt. tna lifetbe oi' fois utate 16 7 x 10-ll sac, wh.U e t.h@ averaf5e stopping time for the excited oJ.6 nuclcua in the caF 2 target i;.;; :.1bout 10-lJ sec. the positron spectrum at the 939 kev •1·-resor.snce. The results are sho·wn in Fig. 16 where the wo curves marked "Intsrncl Conver ;3iont1 represent the distribution of internal convers ion pd.r:s from the 6.1 Mev y-r&::.r ii t..11(:i.r contribution to the p,2ak o.t' t.he ob;=ierrl ad dbt.ribut.icm i s taken a~ 10% or • 20$ respe'ctiTely. The upper m.u"-ves El?"'.-3 ttwrt obtaitied by adding aµpropri&k.- l.y norr'1tll.ized nuclear pair di~tributions (end pcint s 5.02 Wov ) ·1;.o thesG.* attributed to internal conversion palri:.1 seem to n t the ct.at.a reascnabl;r well, although o.0e cannot rule out anythinf; between 5% and 15%. Ii' Ot:f.J takes the yield ot 6.l iiiev quanta ss 11.5 x io-8 ,/proton fort.hi~ target and voltage (seo Table IV), one can calcu.late that thifj corresporufo to a conversion coefficient of 1.9 x 10-3 poira per quantum. RoseOO) hb ccl- culat,ed tbese coe!!icientr. f'or varioue nml tipole order1.'> of -y-radiation. Hi&; results for 6.1 r&ev y-reidis.tion .are Table III Rooiation p&irs par quant,um Electric a&ag.m,·Uc El0o"t,,id.o }~ig.net,,1c dipol@ dipole quadrupole q-:.i.8.dl"Upol0 .., 2.J 1! 10-3 1.6 X 10-3 1 e -:..,t, .x 10-:.• 1.J :'lt 10-3 M~·tic 2 p0l~ 0.97 ;\. 10-J * Note thtit pairu from t..11e conver fi-ion of {-r.a.di.s tion in t.h,~ ccp-per !r;:.mld oo about 1/10 th.Id int(;neH.y of the int,~!Fmal cor.v0:1:•dm1 paire. The bock~ ground sketehed in i.nclud3;.; rour.,hl:r the int,ern~l c o.'lv0rBio:1. pa:i.r:s i'rom . the 7 llev ~r-radiation. The efteot of t,h.o wu1dow curve at t..i"l-8 end po:1nt has been estimated for the nr.;pcr ourvu:;; only. yield ciet.erm.ln&tS.on would b® a.voided. Thi::i orie,in.sl purpose of thb par-ticuliU' exparimtmt wtils to deterr,;,ioo 873.5, 939 .:ind l.381 kt:;V &N pre;':lent.ad L"l Figt;:;. 17 and 18.a and b. Sv.!fio1~nt data w :c~ a.lao obtained at too 13$3 kev re5onanc® to :umke possfolit., .m est!- tb.ose calculated from E.q. 22, Sec. II! C. Assumptions mu.et. then be mada as to t.he dist,rJbution in tmorgy loss f or • el®ct.rorm originating unii.'onu.y tt.i.roug,.1-iout t..ho tl'liolrner,,s of t.hi;;i corn,ort®r. J:n view of th.€. hiib energy of t.i:w electrons a.rid the low ate.de number oi the converter, tna dietributi on i1~M3 talcen as rectarignlar and of conDt<ll'.!t w-idth, on a momentum scal.0, over the r0:t1ge of -momenta involv0d. Tha width ot the rectangle was de~r:minisd. e:q,ariioontru.ls' by obsrtJr.;ing ths end point of the nuclaar pair distribution through the eruas 250 mg/cro.2 Bo t..hst loim cru.cula.tad for thi.s thickness of oorr lliur,1. To -~rd.:; number 1.m,1zrt, be: points 1s consideNd. satisfactory dmm to er.nd includin& ti'le peak . t,ype Uiled in Sec. The d.0- V, ~hare to 3 rcctant,r uler distribu tion :tic~what less in yond thi~ value, and a long tail extending beyond thtj) averafo:o ~m-~rgy lo;;',a are adcwd, would undoubtedly giw muoh better result~~ . Th~ f'U, on the high energy s ide is quite inaensith·e to wch !l'!odifio&tion sinc:a both the initial * The Doppler broadening of t,h6 6.1 Mc.~ V y-r2.,;; du:::: to t•:. o t icm of th:.:" -~:ccit~id ()16 nucle\15 in tha center of mai:ls sy;;3'e,cr,i b a.ixnxt 120 k .:::v.r. Thif., i;:; ;;mall r.:,nou.,gh compared to the, conver~r thic!m.:;;;,~; t.J.ic~t :U:.s ,)i'ft:ct i:::; .n.c:,;l:i.r iblo , as is di~cue,:51ed iri Sac. v. in Sec. II F, by m~Ms of th0 'fh.B X-lino, a inonitor count€ll"' b@i:ng used t.o Th::: ;,,t!'.l"<:b to-r low t!lm:,rt-;;y y-riil.ciii~1;ion, <1,hich Jrw'L Ol'\;rl~Ap.s th-.,:1:, of 'BJ'alker and ~cD..;,nit)l,0) gaPto ~sJonti.:cilly nt~ 2:iitiv,,, r0,.n.ut.rJ, ~ h t.'liimn irJ. electron peak from & 'y-ray of thio euergy wotJ..ld oo a conste.nt ind©p@ndent o! conv1e.rt~r t,~ickne::;~ (bGcau:;;s of large snerg;J lo:,;;$ and stl"aggl.'lng ~ffeot5) in tho i,J@condary aleotron apect,ru.rll ®.19 to K-photoel€!c·trons fro111 this line wou.ld be t!1G m~"ll.'.& as if tho canverter aor u . 001 inch thick, all thii photo- = 0.73 x 10-S number of thorium atoms per ci:12 of conver~c:r and er I b tba K photoalc:ctric ubeorption crost; .:section ( 2 K electrons per atom). th€: is:q:,erirnentsl Fro:ir1 19, one geu ') c < 2 x 16 counto per 77 .x 6.2h :x 1ol:.. protons or c < 0.67 x 10-13 counts/py~ton prot-o n I(0.952, ?(7.l) < 0.92 x 10-8 =o.~n 0.)4 x 10-7 or 0.9:2 X 10-8 < 1.5 ?( '/.1) + !(6.1) . = o.06 w ,7 J{ 10-1 i'rom ·gyhich it is ,sppa;nmt 110w rough t.h~ survey of th,1;- low ener.f;J· radiation wa.~. Bee&n2.ae c,K decraasac.i w-lth erierg;11 approx'1.mQtely a.s n1oc2/hv and -U'l@ Tabl(lt IV Elt,nl Ero:.:;. ElS:3.X E y (k(ifjv) (~v) (~v) (£tcv) s.906 6.l;il ± .()4 *'7 .002 .t .06 6.14.t .04 ~-99 .± .06 6.1$1.:t. .04 7.100 .± .06 6.14:.t; .04 (6.10 .;t, .06) (7.0$ ±,.l) (6.09 .:t .06) 6.151± .04 -~. 981 ± .06 6.14 .04 y 87JS 6.756 5.906 y 939 6.8$4 't 1353 y 1)81 r.; 906 _,.. 6.7)5 7.09,t.06 (7 .OJ± •1) ± -Jl-6.96 ± e06 I,/I/w, Ixl08 ~;.018 .± .OJ - 6.oh :t. .o::-; Rolc>,tiiA'il :tr,rk.1nsity- of 6 u:ad y xlolO Disiltt(,;r,;rratione par proton *2.$ ).; l.$ • 120 l 1fflh1 ,r 843 n 1236 H t - 0.49 1.1 1 , ·1 J.7 l .4:i:: I 1\.k~v l'ti.(.liati~n. t Yivld fl"'r.>tt~ CllF2 ta.r;g,--et SO kov tnfok for 900 kG'-!f p1--.;1to::lt:i. tt F,;::.;tim"/<,ed t,hin t;.-a;;,"'f,;0t yi~:,ld from rn.1oc k;,nr o.t.' Q.;:;;,r 2 , uc;:tr,ic tht: ~'.:<Gii:.·1t.:ton P n,..,1-1 , ),~,.:, rd'' ;.:;h,lI&,w,.w.,,; D,n,~y,,n1·.<>.,,·1 (40) ("'J"'i" l;-,., .,. a-1J.CJ@.~,,;)·•~·~";;:-.J. y,,;;,,,,.,,, .,.,,,,,) ·," ER ,1 •') ..·i.~" _...\r.,,,.,,1--f!,••?•a \ ""'i_,..,.,."''-,., .,. h/i./o,,,,~ -v,i,-\.'IJ ('\-:' ..,,,. ,·t-~"'-' J1:.:t-v ,c ~·"""'-t 'V«.--..lh..r,,e I 0 v - i -.. .ii -~.,...;.. • \ \..,~fv1 ..&o.k/). -53- E:ft,£ j y 1o8 X 108 ... 1olO .... :26 26 .320<g) l;; 15 $9 $9 O. ii9 o.s l . Ji,2 ,.i . 0 X . 673. 5 <r ~ 5. 2) 939 ' s.o) er= y lJ6l <r = 15) 11' Bh3 er= 26) 'TC I ( ir o) 0 (kov) .-}_; I 1236 <r = 85) 1 ,., K Y(oo) D yK y-(B) Y(oo) 1olO X 36 4bO 210 17 120(b) 20 160 00 10 250( .:1) 77 326 220 ') 5 .. 106 1{ ,. :ls" 1olO 1.1 ~~ ....... l .57 J. 71 - J.o 1.85 = yiiold f01' Caf!2 wrge 'i, 50 k®V thick at. 900 k®V . !( ro ) = thick Cw'2 targ~it, yield . y = t.hin t.:u"'Z'ot yi@lcl pGJr l.H rii· oZ C<'IF2 • I lt i:i: p~Y"lot:,;;1 Kollog[~ LJ!ibora t,.;r;r tie at:, ,u\,,~u:-..;:rrtc . B = B0!.1Xllf;l'' 1 ~) 11,inlUUl'l:J!T"'®lltb ( nij f . :;il) (,:s~) FrlJ'lii ,,ntlli'<,u-tion. curv-b .;1;~aln~.t t:el(.m itor ovu::rt\/;1' and Conq;rtoa:·.i at 113· n l,,.'1"' i'ros;, ,,-1 .-,,,.ti1"1,;:· i•<1 'l'';; ;:•, . ;; " -c;y r ,, / 7J..7 )' • ~L .- ~.'!.t:,)""' 0 ~· ('o) ;}' .Q\t(.. "'1 \ .,.'v.,:;~:&;it it,, Al°) 4,,.\,t, Fr-om Comptone. . t'm:t> wit,h th.& t h tok target iwrk of Walker ?.nd x£eDru'.d~11 . 0) -54The 1-ray energie s obs~rv~d at th~ 873.5 a~d 1381 k~v reoononcos ~,?,rGe well with those 01' Wal.leer and McD&lie l, whiL.~ the l '3Sults c1rt. thG 939 kev rovonanoo ~ not inconsistent ·n th th,:z assmr.ition that & higr!iir ooor rrt component exists , aa iBuggested by Burcham and F'ream(ill. 'lile ~ }solut ion ..md statistical aceuraoy of individual points obta~d in the present :8~~c: : rimnt are such that ooo can say only th.ai;, the diff0Nn~: t~twc~n the re;;;ults e.t tbe 939 kev resonance and the other re0onMc~~s i a &{})J.,SYAb.at outi31® th® prob.able error. Howewr, Chao, et al 0l 7 ) have cleGtrly ~Gparatram 'tii10 a-groups corresponding to y-r&y etatea 1n ol,6 at around 7 li~v. They find that i:it 'the 939 kev rasonan.°'1 only the short ran~J group i .e o! s i gnil'ica.nt intone.ii ty but that at tb~ 87). 5 and 1381 kev resonances the two group~ are of roughly oqt!Sll intensity. Ueing this information, our r~sults ~y be in't.arproted t.ilS in- dios·t .ing liavola in ol6 that decay by y-r~ en::i.asion at 7. 09 .± o . 06, ~ 6. 9, and 6 .. 14 ± o.04 Mev. Ths nuclear pair lev-el i a at 6.04 ± _0 . 03 fit:;v, 100 ± 30 ksv oolow t,hQ lowest y-ray leval. 'i'he close agre(Jm>2r.i'I;. bet~w,::en the «:-ixpor~ntBl and thco- Ntical. pair distributions contini:IS th ut t.h~Be pairs. ar~ of nucloar origins noted, however, th~t tl-10 pair atat>Q mas also de cay by the o~ub sion ot two quanta 1n s uocass iv0 electric dipol~ transition;~. (42 ) Whet.ht:ir or .not such two-quantum decay can compete successfully with pair eminsion dspt~ncw prin- cipally upon the nuclear matrix element:... Since th.ii two quanta would have a continuous energy distribution, a.."ld sinca i t b cl(·W.r !rom the work of ot.b.er80 9 , 4o) tlllAt, their intensity i ,s at most one or wo timsw th&t of t.ha nuol~ar pair6, they would be difficult to detect, and ~ould not hmve. been observed in the present axperiment~. __ __ __ A. - ~?o::',:'3ible resction.s . .. . Survey ot: ~ ,,.-~----,.,..._ , y- rmtlist,ion ,..___.. 'fbe bombardment of oor,1lli'lll1i wi tr~ dGuter one of O to 2 hlev en.irgy i s knom1 to lead t.o ;c;t:e following r-eactionr:H (5, 6 ) a. a 0 9 + n2 -+- BlO + nl + 4. 31 1'18v b. ........ 81';;10 + al c. -+ d. a,:,8 '<ii• -+ Li7 ❖ + 4.52 +· 4.53 'f) I + Be4 + 7.09 Son(G o! tni>J: ruat...or l.Bl in t,til1;0 ;.,ootion h;c;.t; pr<',viously bii!,1.m r tiport,ad in R-.1f:;; . (SJ) t,0 (57) . thick br....,.,r-Jllium ;&:tt,al ·targ0t wa~;;i .oombgwd 'iifith dcHltoronti o.f ~ l . l a'i3"'1. MonH;oring wa'$ by mcil:m.$ o:r a li!}.rui-1VhiE)lood ·y•ray co·rui-wr 23 inche.::i f ros tm t:Sr~~t . The iqooct.1°a oht&iood /QJ.'1;1 1:iihmm in r,'4?3. 22, 2J, ;~-,,d 24. In Fit • 22, ':.,t.e 1t:;,,.i,)erimen t ,::.J. points al"® OJ.'ft.'i.'t/C,$d b@c-aus® tooy ~l~ too clooo together-- lror;. s t,horitun tNJnvart.8r by posi't,ron .ti1mi.h.ilation r adia~io•r.t and th.a 4ll.l ki:vv r ooi.r:1t:i.011 from tha decay of J:u.196 • An appro:rlm.ate cor:re c'c.ii:.:n tor -~ -57determined by inte:rcomparieon of these sewral cal.1brat1orus. Corrections for tbe finite converter t hicknsee w~re made according to Fig. 50 of Ref. (17). It is astiidted from t.he data. of Fig. 22 that under ·these conditions of bombardment ther-e is no ·r-radiation from ~ 120 to 400 kev of more than about 5% the intensi"c,y of the 411 k~v lina. The structure in the curva ju.st above the L photoelectrons from the ?18 kev l1n$ ia ucribed ®it.her to c,-qgen contS11-nination of the ta!.rgat, * or to Coropt,on el ect roR'l~ f rom th(.\) 1022 lmtv line . 10 oint~ on the lowe r (Compton) cur-vs of Fig~. 22 and 23 were furthi'ir. lioo ~ntirely ummbiguously. This p&rt of th(.j spaotrum w.:m 'tim:lref ore re- axamincsd later, W3ing tho two separated coil., ring f'ocua, conti,g uration <ascribed in Sec. II E. obtdned. With a resolution of 2%, the data of Fig. 25 weN The pbotoelactron spectrum from th® known single y-rq from cl2(d,p)cl3'"' W$.S also obtaimd to check on possible sc&tterini or other ei'.fecta that might give spurious co-:mts at the high energy side of th.a (·unresolved) X and L photo-pew. The J.6 ~-~ lina is clearly e .'J tabliohod by Fig. 25. * Unpublished work at this laboratory indicates that the o16 (d,p)ol7* reaction gives an 871 kev y-ray. e Ef'!"or in (Mev) lo·c.i> tini J?ElU (ij~v) .0047 .4109 .;t .0021 ± .004 C .0057 .4744 .t .00:29 ± .004 .6007 C -~97 0 7202 .t .OOLJ .t .006 3".'f'Q 5 .5906 d . 011 . 1115 ± .oor, .:t .008 b 21 .16 4395 . ~()~2 .0088 1.0~:oe .t .007::: .i .009 b 2.~l. :73 5710 1 . ~9:28 d .o.?6 l ·,5; 1•. 4.::. ± .0100 b J9 . oo 82.33 ,1 .009 d .0,31 2.150 ± .0~;2 - .o~:6 b .51.$9 lo I "F)4 '•• 2.74~ .OJO 2.864 ± .017 ±. .o;:4 f<.; 59 • ">S.'\ l2a416 J.2ti7 .030 J.J87 ,;t .ol.4 6J.$l 13,191 J.476 d .OJO - ,3.616 ± .Olli ± .0.40 Bf Electron Conwrt,er en®rgr ~hi.ft from Th) ( g. cru) (ii®V) (Mev) a J?.61 2084.7 .2964 C 42 •.36 2348.0 .)589 a' 59 .U 3293.1 b 15.65 ?!$al< millivolt~ Ey (K-lin9 f,\ b b ... ; , 0 ~ ,:, ,1 Ir Tot.cl errorf {Mev) ....... .01:1 ± + .024 a. 100 mV = 10 A. Correotod for e~·th 1 8 fi.ald by ;:a.u:rtiraoti.ng 0.11! m'f from poter...tiO':A).')V@l"' N,';1,ding .. l A1V li!t 5S.4J2 g&;,lr n<ll-Cllie b. 100 ruV ::: 75 A. Corl"®Ci.ed, .for l:j(~th' ,, iield by ffttbt,r&C'\;ing 0.04 M'ff f'roM potentio~t'",r rew.tAg. l ~V = 207. 7O g~tt~i:>-om. t. Iw:iluckn, .-S.-: ~o.6% for c@l:i.bration. t<rr, ir i:; , eonv®r-ter d:d.ftu. ~.i ;;1.rt:.h ' ;J .i'L,lcl corrrJctic,n ~d lf the sb.spe of th® pho-t0tih,ctr~n lit~ ror Lh?. ,Jztbro;:,it,c:r:.',,d y-r,i;r ;:-1.nd t,hu co~v~r'&:J;r •;:;er¥.'. known)) UJ.(i; ,3.-,_,,c c. 0ffcc'L oi bro,,d,.::,nir"-'c c};:,d.d 'b<e ob·:t..ain<FJd. fu .f,.0\1}13 c.;i.;;;0&, t~:;£,p2 O.i'J.ri i>:i ('.::i.,B.ltl:,'Jci ,51·,T:::,!"i: a.:.;;:,lly (S, :c. Y F). If it could ,;w ccl.cul&i'Gdd gent;r~1ll;· ~ 'th-£,:0. :J i'i;., o.: t::n cdculr,t.&d to ts1-& obcJt'irved c~J~!:> nm;lci.p oi' c,:-v.:r,;e, :,. ,nor·.:, :acc-u.: tit.'3 )"-X',\Y iaIWl'f:.;/ t.h:£:.."1 eit.~ieT th.e ;A.':l,;:Jc or .;:~1.trt:pol2ct·ccd .,;i~\,<3. (i.;;i"V61'! 0 Table~ VII te Bp E t'? (mV :.,) { /J • em.; (ko.n:1) b 43. 97 b 49.04 2107. 2 2350. 2 b 69 . 07 d .3310 .1 301. 6 .359. h 605 . 3 6o5. 4 K-phu t o po~ b 69. 08 d 3310. 6 C 12 .... ;; ,~,.. ,- 4 • • ,(.<J'( 1• .eb . c "'2 ')l 7 ,L • c. St\ift ! 911. 0 C 16. 26 903.9 S857. 7 1318.l 0 J.6 . ll S80J . 6 1)02. 6 C 22. 97 8274. 9 10, 656 12, 3$7 13,004 C 29 . _58 c Jh . 30 C J6 ".1') • --to. Conv0rt.Gr lwOl . 2 (kn v) (lrov) 7. 0 2. J L.lJ . 7 ,;t 7.0 2. 2 1.7 L71 .4 .:t; l g 716. 8 ;t; 1.1 716. 9 ± l .l 1022. J ± 1. 9 1021. 5 ± l.9 1435. 0 ± J 1428 .1 ;t; 5 J.: 16 2151 2868 ± 12 3378 ± 13 JS94 ± 3?. 7.0 7.0 7.0 24.9 24. 9 51 $7 2022 1.7 1.5 7. 8 7. l 15. 7 19 2?24 3229 113 ll.3 34 39 .il4 5 ll3 39 "')~ 4-, Extrapol.atiacl Ey .9 Qdt-i.➔ (mV ti, } Bf Ee ~ ( g . cm) ' e,'-w") (K (Jruv) b l;h. 67 211$.1 JOJ . 4 413 -~: j; 1 . 9 b 70.00 JJ14 . J-1, 6o6. 4 716 . ;?. .±. 1 .1 o 12 .461 4435.2 913. 5 1023 . 3 .± 2 C 12 .431 4424. 6 C 16. $4 5887 $387 C 2J. h,8 8357 C 16 . 5'4 910. 3 1020. s .± 2 1326. 2 1436. 0 .± 4 1326. 2 1436. 0 .i: 4 2046 2156 .:t; l,S'h h h l1 ~') . ! nclwloB corr~ctioo t or sxial conrponent of ~art.h ' s field . lOA = 100 mV t 41.·..mt . l mV = 47 • 924 g . c:1i pe&k . 1 'itlV = 4'l . 349 z. a..u 1,;;.;;:tra.polatr.;;d '3dfe . 7:111. = 100 tiiV shux.rt. l mV == 360 .. 25 g. cm ptJ ak . l mV = 355 . 93 /.• Cf/. ;,::;;~trapolatr.:;d E~d~:;e . Indt:p~nclent d£Jt-:.:rmi n~~tionz a:" t he oo gtnning rod r;m d of t ..n.i::: ,3t!rics of e1~x;d m,:;nts . ,.._ .,.,~,,. ·. r+•" ·,, t 11~ c .... ~, .... .. <I! ,.,, r.,. /C -,~ ? V···1·, ,p.., ~ ,-. _::J f. £• h. fiG:f . (r!) ., fig . li.4. Soc COO:!:,!i.lfltB in te,Kt,., e~Jpae lally Soc . V F . .K and !. lines not w~ll ~:enough resol v>f:ld for det,errt.iua t i on of ·~:....- tra.polat,\:Jd e dge• . ;;. . l>o c. d. \JV~J.V"'.!', F'ro1I1 ,_.,.,_,: ,o ·· ~ , ,.. A i.~-,9 ..i.,.1.1, .A,U O b-. t;' tion V = 0 mo l1I. 2T --0 11 P ... E l', = E = p ::: ,,/1)'0 m: I ·p ·'£ = R + T i;·r. ,!' A ·.L!..,.• (31) ~~o~ ~ E. J ( ~ 100 kov). (34) &N di' 'f is the number of quant,$ ob~sr,r~d in. tho am:tl.l eon.a d.0. ' 0 and o.' 13 the &.1\1le 'be·bfa.gn the dir-oction ot t:1e m.1cLm,.. .;i...'ld th.a diNoticn or Th~n * :rt i :-; ,1urum.~d throi.t~out tr.a:, '(~'lL: ;..1(:;,r;;:;;n.t.,1:1, i s :~~m,,, ;;h,, ii:Jd:J. (36 ) ; p1:"'Jt:::t.:.:'i:.."1;it.ai",, .-z- (37) ThL, iu n rec·t.an&,'1.l.lar distribution in ~r:.er.g;;1;, 0% ..ridth 3~ v•/o. ho no~ i'n:i..t.b.t3r ti;..nt as long a::.:- purt1ly relativistic ei'faotl$ (tenllG in v2/c'2) aN ' ..:!11;,r i.U"J:i:.&\{.c;lsd l'rom tJ.1:J,.;;~ 0:f.t\::ot,._;; smd i·.; practi.call.y a.n n110br~rv:abl,a be oa -..,1th' one of the Sallie ®oorgy !ro::11 a nucl~ru, w.~ kno·:J is v·{Nlth,n~ ( from * t,ion of y-radi,ation except in a :fe1:li ictimple cases where only small (10 to 15%) departuree from spharical eya.._,,etr:J h~v~ beeu found. (59) In general, one is roroed to assume that the broadening is symmetric around the OGnter of m®:IS uhi.f'i oo tnai the additiorutl correction to the lavel 8nergt is aero. di.:1tribution. ffl.lt$N vcm 1~ along V..U.UIJ o! co;:;; E for the Cil.c;~ m:i,;;re one i ~ cb;i1;;:l"'rlx1,£; photo(ciL:icr.rt:ms by noting tllfJ :,1p,.act,rolll'iJt0r a:d~:,. Ol.10 ixiay obt,.:d.n ti\ll a;:;prcillimate that it, follo-ilCJ .from E-q. (20) 1 Sec. IU B, th'i!t i .,; the cosine of tne mean :,:;pect:rometsr accept,arH1.s c>..ngla. for loe1er energy coo'E. r o act,ion or L-i. radioa.:rt,ivG d®cay). * With the notable exceptions of the ff2(p,y)He3 and H3(p,y)He4 reactions. -66leval enr~rgiea (or dU'.farences in. lav~l anerb1.e$) oll'e given in Table VIII. Becav..s0 o.r ·t.hc :-:.maller probable @rrorB., -:,ho 1--rcq eoorgia.s a:r,a, taksa basic.ul.y !rom Tal:>la VII. BocawJ0 of the uukno-..m e!ioct, of Doppler bro,.ning, the \Zixtrapolat~d ii'idga d1~1.€,n.in.qtionJ :i:,\l"..-S i;;'lo1'1d. "i'h0 broadth 8n<l a.ay,m.ctry of tllo 472 k::.iv p0ak tl\r.~ ::.r.).c.h a,:; to 1::ako tbi~ -u..:::ioluf;;~ :for ol.n .::i.cm1.r~:ta eoorf:Y oowrmirultion (btK:· Sue. VF). Tho 717 }mv linJ can bl\ll -~,@ibigu.ou:ity <il.3- t:igned, ;;rt lcoot in 1.-Jl'gE.i part, to the trim;d tion from a ,:;·~at-i in i,lO c.t 700 k0v to iho ground :ztate. &!"1 Th,;~ Dopplli)r broru:k:;niuc c:an ~"lu~; oo calct'!.l.at,ed 1.88% (total width), md ev&n if th~ t.rmi~ition lflin'.l b9tw®~r:. th0 3.6 ~ 2. 9 ~v level:c, ti,e bro-£.daning tmuld bs 1. 1%. R..'l·l;.her rou,J:i graphical. ink- grat.ion show~, that thicl oomt.in.ntion ,o f thic:: broadening imd ;Z!. 1.45% G.aUiHd.~111 window is another approximfAte G~Ul3si&n of 2 • .3% or 1.8% in thet:ie too-o c.e.rm~. Th0 0b1a1ained width o:t the It photo-~3 is 1.60 z .0$%, t..~~ ;;;light increruii~ over th~ m.ndav ~,idtt, ooing mor-.a '.tJla.n adeq~tely acco'l.lntad for b-i.1 energy lo~s in t.he c:onv.arter. Thi~ di~crepi-mc;r m,~y oo the r\f1::..ult ot ;an :mg\il.:31° di,it:ribution th~t. ?"~duceu th<l:l Doppl~r broatkmin;:Z vcr-5 w~rkedly, oz- it, ~ indicaw th:.-.it the excit.;;icl sJ-O mJclem~~ i:.:; :.:,·t-upp8cl, on tha avera?~,;;;, hafona it, t.io:o, as dir:;cuGood lat.(i)r, ii> pr..'.!t:une'tl to b® i:.!let.rt.rio qtwdrupola. '1'l1it hnli'- li.fw ·wo\J.ld then 'tx1 o.f thG ord:'.Jr ol 10-ll ;).JC or grea-uir, wh.i.lta the ~d:,01.~l)iw: ti.mie ior th~ B3-0 nucle\i,.;; in ooryllium IU;:il.Y b~ u~·timtri:.~d ii.1.:; of ·Uw ord,u:• o:f.' -67- sharper than might be exp$cted, but tbe discrepancy is not (mough to do the residual nuclemi. Howewr, one now.; that the arl.rapolated edge and peak detem1nat1ons of 6llergy tor t.he&e tlm y•rrqa agree, which alao trug- geato that the nucleua is stopped bei'ore it radiates. It is quit® porJsibla that t.ha Doppler shift correction should not be made for thei.;e line~. Siu11lu.9 althou.f#1 more inconclusive, arguments for not makin~ this correc- tion for the 1430 ke-v line m.ay .be adduced. * In Fig. JS of.Ref. (17), Hornyak haa ~un.toldsdff the K-photo-peak tram this y-ray. thus removing the effect ot the finite instraent reaolu. tion. ThAt this unfolded cu:n-e shmrs none of the expected Dopplar broadening waa first brought to my attention by R. G. Th~. Since thia was responaible for the consideration of the width of th~ originu curve discuased above, I am much indebted to :Jr. Thomas. It may be pointed out that the original. of the unfolded curve waa obtai.Md with a thicker converter, and that the unfolding procai,,;;1 b ~mmewhcit ineucti so that the width coneiderat1oru1 4 1ven hare &re probabl~;- oore ccnvincing. Table VIII ~ E _f (ke y ) t C d ~ ~ f e = T/c tor cou E (mils ) (mils ) electron 6Dop. t::. Elevel ( kev) (kev) ~ 6li 41J. S ± . 9 .2$ . J,S . 1n .459 -1.2 412. J ± l ·(o) (413.5 .± .9) b .2$ .47 .813 .5).8 -1. 7 - 716. 6 .± . 9 . 2$ 1.03 . 587 . '7J8 0 (- J. 4) 716.6 ± 1 (71J . 2 ± l ) -5.6 1016 . '{ .± 2 (lo'')~"2 3 . I) ' (472) ·- - ····- ..,..., 1022. J ± 1.9 .:~5 1.95 • 9.)~ 10:21. ~ ± 1.9 . 90 1. 95 1016.6 ± 2 . . .741 -4.9 (10~1 . $ .±. 2) 1435.0 ± 3 . 90 ....}_ J~_,, . .960 .au lh28 .l j;, 5 2 . 04 3. J!, .96() . 696 21.51 ~ 16 2.04 6. 8 . 979 . 820 -11 2140 ± 16 2871 ± 15 4-0S 11. 1 . 987 . 812 -15 2856 ± l !> .3380 ± 15 4.os 15 -990 .B~:; -19 .3361 ± 15 3604 ± JO 4.05 16.$ .991 . 866 -20 3584 ±. JO a. b. . o141 ... ,, 9;, (0) • • (.;..j 101'( ± 2 (102);: ± 2 ) (0) 14...·? ; . :,,,., .;i;,.J ;;- . (0) (143$.0 .± J ) 1424 :t 3 (1432 ± 3) -6.5 1421.6 .:t 5 (0 ) (lh25.l .i 5) - 1. $ Bei,t valoos tram all cwtermina t.ions. 'fbe re~.cti on Ba 1(X)Li7* givas 476. 7 ± 0. 9 k ,:-::i17 f or this l ev6l eoor gy. S,ae Eef. 4 .md Secrt i on V r,• . c. Thorium rue·tw. conva~ r d. Sc~tkrin~; L,:n~tb, ~ • a 1.i cucu.l:9ted by Coh.Jtu and Chri~ty ( unpubl h:hed). -.il . From Eq. JS From Eq. J4 The po:5si bility ·~'1.-at anything fl'O~~ no Dop·pl 0r :ilhii't to ·Ui~ i'-ull cclct,la.tr.id $hi i't m:c;y corr~~pond to the ;,:,.ctual ph,:,"~icsl .1,itua:r,ion l;.~.;,; ooen i. S• i gnored in d~t....nninL."l..t, th~ probacl 6 .::1z-ror.s t ,h\:m . -69- interuoiti@u of the variow; y-rays . On~ counts per unit momentum. interval. going from one +-,ray to cmother, the relative inu;;ru.:'1.tieo ot va;-ioutl liuce are given by Eq. (20), -wmich m;.v- oo rewrittian aii,; A (J9) t ooe E • Intsnt}i ties caloulated £r0ili this for the vurioU8 peaks obtained -rl th l l/2J resolution (Fige. 26 to 29) are given in Tabl@ IX. Valma ot cos€ are takmi fre& Tabla VIII, and ~1/',10 is evuuated from the CUM'G$ of Hul.me, et .;u. (;2J) The work at, 3% %'$Solution b not v.wetul tor determinin~ int.ans- ently changed during the courae o:£ ·Ulq, experinwrrt~. :.:iet to gi vo a resolution of l. 9% for vory !iWAll BourC'Clu alld ~ :2. 3% ror too wou.roo E>izes actuuly used. Barylli\'!m ootal toils of irn.ch thicJcmgjs tru.tt tha man square scattering angle i:ras l®oa t.~ ~ .Ol radian2 ~n;, twed ~ targets and as Cou:ir,ton converters. microcoulombs to the target. Count!$ were taken tor a fwd number ot ThEl deuteron bombarding ~nergy, frequently checked !flgainst -WW alaotro,3t<'l\tic anal:rsar, was 1.19 ± .010 Mev 9 the srwa a.a UY.J ed for tha work ~t 1.5% re!9olution. Thli target .:as kept a.·l;, a potiantisl of ❖ 300 V'. with ro;;~pt"iCt t o -th::- r ;;;::,rt. of "i:.h~i ~;ip<..lC'C.l'()ffe't.,_~r J) and ;\i. J/8-inch disioot<,r wlr~ loop { 3 thf.lt.> the deutervn t.mam di£imet0r) a1t -JOO V. ~ac. or Ni!:lidua.l. gas . During all 1"Una, the Vci1.C1.u.m in th@ 1:lpsctrmret,ar ·fii'as bet,t,er ti.-i.ru1 ~ ~ % 10-5 mm o:t Hg. Th.;; curNnt m1:uiauramen·t undo:r tha~s oor..ditionliil to the target with tlrnt w.aaeured in a, staud.ru:-d F(/,,r-;iid.2.y ®g-0 jWst outs idGi th1;, i3~ctroootii:r, the obsGrvad loss of ~ !>% being attribut&ble t,o dei£1ninti av\Flra.ge ~rM!ry-,s l051:i of JS .$ kev calc1.uat-,d froua th.ll i'orncla giv~n by Ha1:tlar (P.,.s.f. 25 i p. 219). * It b noted tl·ud;, hoth peakli- ere ~liehtly a s ~ tric .md ·t:.:.at the one obsiarvad through the beryllium i~ 1.d..dor. Both the window c ~ Too an1~ u.ncler ·thiti ourv111 was incre~ed ~r :&botrc. 10%, which 1!:l f.lbollt ~ pro'tnacl~ error in nessuring it. Thi.:; h~B lnurring on l,he diGicu.,aion o! th0 ·r~riii:.'l',ii>n ot ths photo-peak area with con-~<1rtelr thi.ckm;i:.m gi·tr~n in Siiio. u:r. Here t£'1.eN i ~J no Quast,ion of SD.J' irwrea.:..B in th.a i.otlll. n-ullloor of puo·tcJal ect,roi,w iaj;scted. 'i'hti inc:r,iH:i.'.3~ in ;.1rii!a., it real, ruw.:it the.m oo utt:ribi,t..;id to se3tw:d.nli in thG b13ryllitrill, ..~ predomL~noo of uc~t.toring into th£J ~Jp~ctro::.wwr ~ccep't,anoo cv{]r 1sc~tt-.:;rinf; out 'being indica.tMd. -71loi& are 06tW:sian 1n form, this experiment indicating that too straggling ia a~trio (even excluding the "tail" of lsrge energy loaooa). If it i ltJ asslJlaed U:uit the widths of thaise Oausaians can be ood,Jd aa if t.bey n N complete (i.e.g oe Va2 + b2), t.h6n the atragglin~ in the beryllium foil ia found ·to be +6.9 kev and -U. 1 kev (hill-.·idths at half-ma:id.mm). The primar,r Compton spectrum for this y-ray was calculated .from Eq. (22) nnd a 2.)% wi.48 O&lUGsian windo,r was folded in. The di.s.trlbution in ~nargy . tribution i.;; rou.gbly aqual to th.ti straggling, th~ ~ ~t prohalblz=;: «md @.rrer.:ii--.;,-e bution ia given by coneid~ration~ of convanienC® in folding H, into '{ho Compton apoctrWl4 by numerical integration. Th~ final cuculated Compton distribut.ionll with opti.lnum vall2Sa .for ~ ood the hsightJ ood added to .-an Tha yi.:.;ld of t..ik, 717 k~"l1 rudiat.icn C-!(:".i t<:, obta~d by co~~rinc too Thi~ may be tlons eithar ill ~~ ot ~~ucul~ted and o.xpariloont.al curv:)~. Jt-3rildlai.n~:• it:J incluc:wd in the .final i;,,,,;rm { th~ d ~:) fi:1it -1l in laJgral). in;J in. th~i conv(:lrter distribution., :,">;. In told- t.h~r,;dor-.➔ tuk@ t.h;, ar~;;, a.t, 111qual. to unity :1 and in folding in the window c-u-ve ·,,,3 t.~.kit the h,.;,;ight a._, t»quru. to unity. The .mgla:o 9i_ and e2 u.Jed in -~e c21.ccl~..tion oorr.a.;;pond~d ta 8 = J.58% ot 4,r • As descriood in Sec. II F, 'c.he measurad value of 9 0 for th.is contigura.tion b J.06%.? for€. resolution of 2.05%; the larger source w,ed 1n the present ex_pcrb,ent,c gave a resolutic1n of 2.3%. ing 0 0 accord:i.ng to E,~. ( 24) s ue ga·, ;:;; cor:Ncl'.i.on factor Corniot- -73,3.$8 [J.06 (2.0$/2 ..:3)]-l • ,3.$8/2. n. We note al,t;;o that the 'Wlit momen·t.tml interval (llhioh we no'w taka in momentum unit$) is gi~1n by ·iJ:le units used for µ/o a m0 c • 170).9 g o cm. :md finally ha~~ CO\Ults per millivolt= a/m.V = dlf/d(mV) I/4rr were I i a the total nt',mber of q 1w1tl\ att.ittad into 4,r to give tba thick t®.rget yi®ld, Is o! QU8nt,3 Pf)r d e'Ut.e?"O)l}.o In t.his way, ooo gett;; !'or Uw thick target ;ri~ld ot o. 717 ~v qusmt..;. Tile probable error g1wn is po8sibly 8omewhat ~ f!sittii~tic, &ril is Nquired mnt. mined. The beeyllium metal target-Compton oonvertar heid s m.r~r.i'ici&l deJnsity- of $8.7 mgja,J. (6J.7 wv/oa2 wbandiviood by oosim ot the accapumOQi @xperl.mental.ly by obser11ing th$ photo-peruc frOiitl g 'thorium convarter ano ~ 3.09 i'Nv y-radiation from the roaction cl2(d~)cl3~ both directly .and j thing ~-ore thun meru:.u.N~nt ot the energy losi3 &i, 78 ;t 8 k%lv. The m ~t probable aner gy lost# , af.l given lzy· Cohen and Chrfa·, y • .l;l 1mpubli,3ood t.¼i-.lcI:l.-citions, ia 6h keT, the 4?.Verage onergy los a calcul.Bted i'rom ·Um .fora:rcl-3. giwtJ. Becauee thess three y-rqe from Ba+ Dare quits close together, it vns i'otmd deoir&ble to nm the C~ton elsct.rons trom t hia zingl.e c1 3 y-r;;!y a.nd fit the c.1Uoulated CU!"Ve to theae axperu~nt:.u po:int&:1. A 15 mg/~ · frctn Fig. :5.3 of Rt:Jf. (17)* ,:md thril 2 • .3% insl:.r..~r.rt ~1:i.ndow VJ&!,2 :foldc1d in • • :llightl;;I different vs.lu.~a o:t Pir~ to g~ve th1J:1 r.1oeati~ i'H,t'I, Figs. J4 arid J;, 9 toge·t.n,n: with the a:Jtyeri.rtt9nt&l point~. distribt,tion de!';ignated u <J; 41.N '?how in The cuculattild f 8 agre®r:; wH;.h t.he~e points very eatiaftJCtorily. ,m. t.\1-'1Zl o'biai.nl'J d '..lf;i.ng tbs ~olid curve of thif:, .fif,·o;r.,, ( inr:t,ead of i.h..:1 1 0 d.::!... h::1-.i cm,'""IN; 1 i'or r::,d.iCt>..r: of ::-i:.:r-1~di;~•ncy i.n th.:: llU'i.iSti'X-UJ-al i.."lt,,1gr.:,tion) a @nd I pe&lc i:::i in tn~ right, poaition and o.f the r1.r-)1t ordt:;r of zai,\;nit.udl:: tor these1 pair0). Tbe dist.ribution tiven b.f <.p 10 did not 1 hm;revsr II fit t...ha ~xperimentu From the;;.:0 d&tu, th~ thick t .;arge:·t yL:::td !or J.09 i'ii:rv tru.:J:l-ti!'?. pro&.. o i; d in t.h~ d µ) r<f.,,.ic·i;Io~ by ;,2 ± . 0'.2 )t,;-11 ck;,u·t;.i;:rott:- h e;::;J.c1J.2JA:d ,,,~ .; .Jj ~ 1oi' y/µ. coul.01.ab Qr 5.i~ x 10-6 ·Jt. c l 2 ( c l. ; ~ l • -7$of Pmu for the J.)8 Me• line would give a slightly better fit. Th• over- all discrepancy is, however, definitely larger in the case o£ tbe J,J8 MeY line than can be accounted tor by experimental errors or by the approximate nature of the calculations. The 3.60 Mctv line is not well enough resolved to allow any definite conclusions to be drawn. EJq>erimental error is definitely ruled out aa a cause of this diecrep- . ancy, since the Compto113 from the 2.87 Kev line were obtained 1n the same • series of runs, without any changes in the experimental set-up, mm7 points on this curve being obtained both before end r4ter the higher energy curves were obtained, If one assumes approximate isotropy ot the ;-radiation ·anc:1 approx!• mately random correlation between the direction ot motion of an excited nucleus and that of t.ne y-ray it emits, Doppler broadening u.,- also be ruled out as & cause , This broadening would be largest for tbe J.4 lle,r y-ray, and even then is only 1.4% (total width.} , which 1a mall compared ·to the width of the Compton distribution from other causes . Its effect is thua onl.7 to smooth out the sharpest curvatures, and is almost imperceptible, as oan be shown by .folding in a rectangle 1.4i wide. Fig. J6b, furthermore, shows how the converter energy loss distribution is changed if rectangles 1% and 2J to represent t.he Doppler broadening, are f'olded in-1t is c~ar trom wide, this, also, that the effsot of the broadening will be apparent only in quite fine detail. A strong !ormmi and backward distribution of either the residual nuclei wi. th respect to the de~teron beam or the y-radia:t.1on with respect to the direction of motion of the residual nucleus would, on the other hand, give a distribution in energy of they-radiation strongly peaked at the ex- treme values of the Doppler broadening and would account for the observed curve . A third post:;ible &Ji:Planation, and pt.; rbapt:i the one to oo ccnuiderod most i'avorislbl.y, itS tb,l;).t thertii arc uctual.ly two ·-r-rays, of rougb]J' equal int.inaity and lieparated b,, l:le>mething like 20 to 40 kov, in the neighborhood of 3.4 JMv. It io then appropriate to c:,.u.culata a theoretical diatribut,ion that will -77- • ~E10wl t a Xm (~-v) d C g y h da-(11'/2) t I'... P'no·to-psak ¢ic b I ~, Iy i a.rea do-- ( w ) J;; 2.42 0 ( a rb.unit.a ) X ~ -1/ Dxlo6 y/D :ttl0 6 1$.,';, j 0.4123 730 73 2.8 .0538 l •"".' .;.; l ") (0.472) .S3 490 so .3.3 .O)liJ. 1.6 1.6 .24 860 20 19.6 .0111 1.3.7 13.1 .1.3 78 9.5 4.J 0.1166 {O.?13) 1.017 (l.022) .46 370 d. f. g. 9$ .61 200 2.140 .3() 58 J .O 1. 2 .0049 J.S 3.9 .. 4 "l 2. s 2 . :., ,:' 2.8 1~ 2 2.856 .. );, 170 2. 2 2.1,2 t·'.,..,; . ~ ''.l ,._, 3.361 . ;?7 uo 1. 6 f .OG 2.07e ~?: .l ~84 .2;:; 28 1.6 o.6 o.e9 0.9 ¾- , ,.., _ 2.4 . OO"J4J t A rJi; = relative inteooity from pboto-~aks-: . 2111 ~ • '.')9 " -.4 I~otropy of · y-radi&tion a:sst!mi;ld . ~o F1"Qll Compton second&rie@. I 1<1otropy ass\m!Gd. I! there are really two y- -r:;.ye here., the inten01ty- f:'. ivan will be eWl®what less than the sum of th.e 'l:;1ro inw~U,iea. From Sauter 1 5 photo crosll f,~ction (Eq. l). I I' y h. ;;. 3 .21 coo€ a. 13. 7 5.0 1.424 (l.432) ~ .)•-;) c. . (0.413$) • 70 = y l+bcos'"£ "Best"va.lues. do-('rr/ 2 ), b determined to match I 1 and Yy for the do- (wo) • 717. Mev line . The clisagr-~emcant °betW'Oen r..il~tive intensities raeasm"Od i:r,r the photo- el~ctric effect and the Compton eff~ct for the .717 and 2.86 lines is believ.z:d to be mor~ than the; po@oibla a:;q,i:1rlmcntal Grrors, although too tho contribution ot L- and M-photo-Jl c ctron,".. * A co~ction for pbotoeleo- energy line& in the forill s~eated in Eq. (21). Tho ,!;\J'bitrary conata.nt b was determined for the • 717 Uev line, and the r usul t.?. ue given in ·the column h<-!,adsd "I' is too large. y l'l in T/1.bla n." It may -2ar;ily b<.i th at th.ia correction Howe·ver., these value :£! are used ,for tha l'lb$st 111 valivMi in ·the they are prob.ably reliable t.o ± 25% in ab~olute val~ Md± 15i in relati"f'e 11uue . Where they i:lN obtc.iood froo pno~le otron :pn3lc;~ tbisy are prob1ably fl;!.llittblt. t.o ± 40,: for energit:i:B sbova 1 Me v. &low ·i:..i.,,ii:;1 value, e rroru u:p to linm, cl'iani'!cd with bombarding voltage, oortain relative yield!~ wen obti.s.1.nad It may also be notad th.at the calculs·,ed !i:icattering l~tht!, 711, ma:r oo oonsioor@ly in error. Th.is ahould not be import.ant unless thsiJ" varia- tion with energy is also incornict, since comparoole valuel:i ot t/x. nNl !ound !or theBe two 11.neo. H Bocauae ot the .finite thiclmeae of the:&:? target, t.ha ~ ~th l~m~"tb o:t a y-ray in the 0.0002.5-inch thorium converter WlW ~ 0.025 inobes. Attanus.tion ot the y-mdiation is therefore negligible. -19- at tour different volt.agee. The total y-ray yield wu muu.red at the s&me t:1.m with a 1-r&y counter at 21. 7 1.nchea :Crom thlil t ,a r.get. Tb.is counter w~s ~hiolciod by l.4$ =i o! aluminum oomp~tely ~urroubding it., and by ).8 cm or lero except 1n the direction 0£ the 'U\rt:~t. The g00:ootri0 factor i"o:r thia arrangei.'Wnt -, as deten-1ilwd by obmiirving th~ cov.nting r att:J w1 th ~ eo60 so1.u-ce of !mom activity* 1n tll0 speotrometer source poai't,ion. oounting et!icienc1 An tief.fective!I' e • for both the cof:1:J ~1-nys (1.1'1 and 1.33 ~v) :mtl the &i + D y-rqs wu calculated bf tu!ng w product 0£ t,.i,,e .a.ttenii..'\tioo ot a particuJ..u- ~,-ra, 1n (l.4S-R0 ) ow of &luainua tiw" ·Uw cowter e.f.f1cien07 €. tor the y-ra-, timsa the roativs intensity of tha y-r,y (as oompared to the whole spectrum). The t1ttenua.tion 1t1atJ ca.lculated from cUl"ffo given by Beitler (Ref. 2$, P• 216). R0 , t.lw aa:dm1a range ot aeoondaey electronsg md E Ii t.he counter efficiency, were takGn from curYel'.:i giwen by fowler, et aiC.37). Thii:S correction is wry approod.me.te (lkliilir•e1 curv~·H ,, tor example, give only the number or primacy- quanta ronw.hlillg after tra"9rse.l of a given thiclmeaa 0£ &ltmdnum, .1t1lld mako xw corNction for tl1ti aeccndar-3 quanta that may appem-. Attem;u.1.ticm in the .145-incb. will of .t h,e tied by the observat,ion that the total yiold o! the Be + D _-, ,-r#.\db.tion w- cula·ted 1n this nwnner is not changed if t.,he attenUli>tion col"roct ioo. 1m n®glected entirely. Another source of error in this dete:nru.natioo is lliat ~1.e trr.rooo 11 as ·o oll as y-rays:, may be counted. Olaa&-lrail counters ffi1ch ~ t.;,1o~ e ti..fKJd. will count ulow neutrons by the B1,0(n a)Li 7-• raaction; and rwmtron o.:.p'l',v.ra or ir.1~l;.9.~·1:,1c,.... al scatt,ering by matter- around tbe targiat-princip-,\lly th<@ speotromet.sr * Comp&Nd wi.th a calibrated eo60 uotll"oo obtained frc,m t..ha B~.a-etau of Stm~. -80- r~mtron gro-up •th.st ,&\ppe~r s ~t .;,. thr;Jshold en~ru;y ot En m 900 kev, ~"s dis- coveNd by Evo..116 , Malich.11 and Risser< 60 ) ooews to oo 1;;1,';pecially ef.fccti"fl3 u.-uch clo~~r ·c.o tlwir target, so t.h.at thare is nc reason for qt;.,Hrt.ioning . tlw1r assumption ·t hat they did not count neutrons to any ®:d,ent .. The N$ulta arei given in Table X, wher,3 the third column giveia the result of integrating the "t,hin target y-ray yields of E:vruw, •t d. C.!luse of the long bolrlbe.rdment..s necessary 1n e.ome Cti.1;Je s , gmri'ac.» Be- b.yers c,f C-U°bon Otiuaing an error . of ~ l~ 1n yield is po,.;~ible. Table I Bo9 + D Thick tQl"ty;t yields a ED Mon. co~tu p;sar Totru. b & a f\mct,ion of ED Rel. yield 2 .9 ~ 'f ·'{- :rhild ;;. oorJJ.omb ix-:r {kcv) ( ::u-b . s ciu<J) ( i:...rb. sc.ru.e) µ.coulomb 1,; · ' per tot.f.-'.l y-yi:;;ld Rel. yi-ald O. '72 ~.:rv { p t.1r ~,r t otal JJ-Coul<>i2b y-yield 45.$ 9'-} 9h 102 802 46 46 16.9 lOOli 95 92 39 J6. 8 4d..·";.:, 1188° 161 151 65 43 165 109 140.3 264 220 99 44.9 234 106 ~ a. Raterred to elactroet",:tic snalyzer. b. Integrliii.ted t hin t ,;;r ge t yield o! .Evc'm5 11 Malich~ and Ris:00r, (60) ac.muming ow moni·tor counta only E, at 802 lc:eT. o. At:~uming 10/161 of our monitor counts are dua to ne:u;.rona, the cc60 calibr a tion of tha monitor d~.-,cr1ood above gh·e;.-; Y 32. 2 :< 1o-6 y/D for ths tot.ru. ·thick targ~t yi eld of y-rHdit~tion -srt ED = 1.19 M~T. r' = mw. -81- AG not.ed above, E'Vruw j et al, in Ref. ( 60), Nport finding a n;.,""d oout"On ~oup, correeponding to a Q of -0. 74 iev, from the :Em9(d n):elO reaction. A ~&arch waa made for the uound $ fiev. ,-radiation, which wae e:a.-pectsd at, TM target consisted of sevsrel. berylli-wn toils, agregating ~ 300 kev enorgy loss for the l.4JS Afev deuteron@ Wileds, SO ·mgJom2 ot thorium toil to stop the &rl.lterons,1 and 1.6 v;n/cm.2 of copper to ~rve ;a.~ a sour~ of Compton e:lootrons. The Nsults are shown in Fig. 40. TM moat notioa- able point is that th@ high energy rcldi.ation is very weak.11 althc-ugh :Evans, indicat.t;.id, and tharo m--e ·t-.tro low point~ just abov~ th~ Corupton.o from tm~ J.6 l\lltJV y-ray tllcit ':R®N later .found to Nisvl.t :trom .a t,hird rww y-r;~y. * Too principl~ dif'ficulty in obtaining the ci.-...n\.;.:; of Fig . 40 nf: Ule highs2t eoorlflY line (at a potiantiomet.er reading of 47 mV) '<39.S about ·t.J.m_ tiroo!iil the counting rate d\w to that 11.m, and fluctutiona in this back- ground were au.ch that each point in thiu Ngion hsd to be takan 8 to 10 ti.ma~ belora they NN well averRged out. Too converter was ~tilO ll'tlob too thick compared to the .teptar£ition of the lines. An attempt vas made to reduce this nautron background by oodition&l. shielding. A reduction of approxifilately a factor of two was attained by adding lilheet cadardum and 3 1.nche.l} ot paraffin oonteini.nig boric acid to thG 3.5 il.u::h~c of li'.:Jad ~i!.l.dy ground t.he spectrometer· oountor (ou:t.sidG of th~ * Too sltlpo of too cr-u.rv?i:-i at:xrvc, S »aw h, at tri·u\.itti:cl tC1 ,:.111 undi.,ros·r..u,&.ttt o.f the tiold-1.ndept,ndmlt backo-ound ,W.id ·~o scatt0rin:s'. ~1d inmdc;q..w:t..-1 nhiolcling !r. U1c ~ptHrtN~t.ar. -82mater ~nit could be uhielded from the counter by at least 2 inchos of l1M1.d, &ld bf putting a plats ot pyrex gl.aww (1;ctni~ contairw a fsw per cent of boron) against the i')pectrometer end pll.iik whi£1ro ~ru.ch l~.a.d shialdtn~ wac not f@asibl©. * Similar shielding wa.-. &1h,o put ;~o·ooa t.h~ mom tor coun~;r. iatat1dly .30% im.,reafule in are.;;,). The net ~~ult of tlloi;i<S chzmg-~~ VH,,lh ,J;I. F,;aiu. ol &bout a factor of t.bnie in 'th€: r~tio oi: Com:ptoi1 t~Lectroo.$ ·oo baclq,,l"Olm an.t 47 mV (5 •v ·,-ray). The tuget used in tbeae later G;;::perbh.7Xit.a! coo;;.d..~.,wd 0£ ~ 300 k~v o:t Be foil, 2S 'l!Y/lcm.2 of Th loll and 2$0 mp.Jom2 of Be. TM b@qlli~ con- ve:rrter wa5 snbstituted for the copp,ar because ot ·toe posaibili ty that. a<Xll'tl of the -r-ra,-s observed might be :resulting .t':ro~ neutron cciptUl"le ( or 1.n@la~tio a;c.atterlng) in t.h.s copper. With thia oomrerterlf the ratio of al~cirorw trom the· 5 Mev 11.oo to ba.ckground w&s .lbout 1/6. Th$ ira.rioiM,, 'r-ray:;;. ii-11'(') 1 ho~~v0r, nm.oh ootwr dis.tined, a.i:J hi :1tpp,ar~nt i"ro~1 Fig. 4).. Th.u ~i;.nart-;i(~.;;, of ·i;,oo val?'i- tion ot 0.5% to 0.1%, i'or thi.~ qli::.ntity .for ocri;h .3.1 Mf.JV (cl}1~') c:.:ud 6.1 ~C'V (ol~) y•radi.LLtion, provid0d ouly that. th.;;, c,m.vertor thick.n:3:JC i;;-; ;3{~~1.63;. n. ~uld ~eGm from -the attempts th&t w\fil:.--e 1r;oo.e to reo\.H::0 too b.::-1ckgrouoo th@,t the count.er w~s responding both to ;slo-w at2:u.trons that. actW'llly re~cbed it., and to capture rad:l.&t,:ion from ot,her part~, o.f th:dl ~.:1,~ctro- mter. mex1·~um interval v::.i. r.oomantum plot) U) proportional to the total COmpton ~dul"llil is justified by the lollorlng 00,.'"lsiderationi:,. • Fir~:it, th.® cli1J1tribu·ttooo dUii to the several lines overlap so badly that it is 'fiery di:t'ftoult ·i:,o d:aterw.im the height of a p.articul.mr distribution-the dau.1 obvioumly do not ju~tity tha L.1bor or trying to tit ~ach of tbeiae di~Jtributions with * Thit-.; can b~.i1 @:qJlainod, in i0ner a.l term.r,, ~, tollowt::: It, c~.n hi; iiJ.&.ai l11 :,1ho~m :that if & iv.net.ion that ri~<cii;,., ee li5~ntially lins~rl..v irom ~1oro i s 0000rved ·rl th ~ ";yu.aetric wind~ ~ro'W ~aroo\ t,o the lengt.h .of tlw linQJ &r portion or t a0 curve11 the :aero in·t.arc~pt and th(;;, slope of too 11.nti ~l;l e.xtr!!.polat.R&d edge are not, changed. For ·Ul@ C~ton dili.rc.rlbution, the extrtt.polated sdg® in•wrcwP'l; ii0 doter.ni.nsd, for sm,;sll window width.I,) by the fold of tJ.te conTert,er dii.rt.ribut,ion into th@ primary d!etribution andjl for oonve.d:,Bri:~ thicker than a certain minimum, tl:w front. G~8 will not ch~ with comrerter -t.hickness (see.11 for @~le, fig. 54 of Ret. 17). It is r~l so .f-:.n.md, for r-asolu-tions of 2 to 3% and con~rt.en:i 3 t..o $% thickg t?rnt thia 0xtr~pol&ted end po.int does not ch~nge much ·with euerf;_Y f:r<>fll O. 7 to 7 Yev o On the oth4tlr handj the e;~lr'WOl.ated iadge i@ not well enough defined for ~1:ther ~xp,arlmantal or calculated distributioru; to gi ~ erieirgy dll'J"t.enu:tn~tiorw of tru.i ma1d.mum accuracy. imaticn, then, one is counting a coruetant fraction of th~ to·tml. nmnbar ot, Compton elactrOM, the total nttmbar b-f,J:ing given b,r the in:l:Algraud. llein- Interu;i ty 2.89 % .04 & 2.9 - 3•.;s .t .OS a 1.a "- 3.,6 .t .06 t;1 1.0 - .3.97 .t .08 0.1 3.94 4.47 .t .01 O.l.4 '1i4 4.,. 5.20 :J; .l o.04 ;;.16 (Mev) ~o iel.utive ~ From this ~Jq>eri.~nt only. T&blvl} VIII. 611,nn.-:l (~v) Compar,z;, nth complete investigation of the vuious groups of charged particles resulting from the bombardment ot beryllium with deuterorw. They find two grcupe ot ~diate int.ere.e t-a proton group corresponding to a level in BelO at :,.:,1s .t .010 Mev and an a.-puticle group lal\'rlng t17 0xoited b1 o.482 ± .003 Mev. They alaso c,t.lte v.1 th oom c~rtni:uty th.i.t theN AN no 0th.er e:'!Ci t,..;."Ci le'felo in these tlro nuclei bot"an O and J .4 x~'::v that aro re achad by h<taV"J' particle groups at the deutGron siMrgi~::: o! 1 to 2 Mev ti."lat •re ~ed. Too ·. 3.36 .t .OlS Mav y-rq can tht\:. clearly be ae3:l.gnad to BelO. ~ tb..1 y-ray at ~ 47S kev ·to Li 1*. tollowing section. Thia l.atwr -~~ray is dtsc U£aed in detail 1n th-a At 90° to a l.J8 )J@v dauteron beam and 'W'31n16 a thin target, Bueohnar et.ates 1n a pr1Tate oormnunioation tha·t. oo would inter from tbe curves of Re!. ( 61) a ratio ot B@10./Lt 7* • O.S(>. corresponding y-ray intensiti•s (Table IX) 1e 1.3. Tho ratio of the Tm dii'l n~eent ~ result, in part, from the differences in bombarding enargy and tar~-et thick- nes•, or it ma;y indicate errors 1n th11 procedure used to calculate the ,-ray intensities. It. aeeme quit0 cert:lin that it is not the reault of .an1.~otrop7 1n the proton or a-particle distributions, sine© R~snick uid ilarw~< 62 ) N port that the proton group 1a sph.arically sym;~-atric and (in .::. priva·t;a communication ruuplif'ying their published report) th.~t although t h:"y could not adequately- separate th@ a.-Groups to ·i:J18 grou.r!d .md th~ u;(t:i t®d ;.rt ~t.e1,1 of Li 7, the combined groups are rour~ily ~phi.ir-l~all:;- :~1 j11111:.<>1; tric» n,".ld ;JA p~r-ti1ll tb.~ir dir,tribution is giv,;;;,n by (1 - c91,; 8) ll ~'>o tti.,.(e, s1sl rui m(:&iJ'Ul\'.,d a.t 90° to the deuteron b®e1m would l;Yi, M av,~r-~ge -value . This diaagreemcstrl:. in relat hrs intaln6i t i -:; u ru3Y, on ·;;hs oth'°,r h&1d, r-:.::i= s ul.t from anuotropy of eithar -1-rayj or H, may ali-tc indioats t.h~tt. t,h,srQ! are two y-rays in ·Ula Dfliif.lborbood ot 3.36 JfeY, as mentioned in Sea. V c. In thia latter case, the secoud y-ray may al.so belong to 13elO, since the corresponding proton group miiy have bean obooured by protons from tl'lG ol6(d,p)o1 7* r eaction ui the work of Boochn,3r and Strait. The third reaction* that yields charged p&\rticlea is :se9(d.,t.):se8. Bennett, et a1C 6J) !'ind a y-~ay or 4.9 ;t 0.3 Nev !rom the L17(d.,n)Be8* n-~ction. Thie level is energetically e.cce~sible in the present ca.M.~ On€J can calculate that it the trus level energy io 4.44 iiiev, Buecluwr, et al, should be able to observe the corresponding triton group. I! the le-vel 1'11 at 4.9 or S.2 Mev1 the triton group would b$ obscured by elastically 3Cat- ured deutorona . .At our requost, Pro.f'esaor Buechnctr kindly re◄xami.nod some of their photographic plataa and .found a short range group th&t could be t,ritoi.W from. thb reaction. TM leYel 1n 9oS col"r6sponding to this gro".tp would ~ at 4.6J 'Kev., and av-years to be about 70 kev wide, indicat.ina . t..'1nt. the stat4\:l decays by a.-p.:::.rticle emiasi.on rather than y-rad.iation • The remaining reaction i@ ~9(4,n)BlO. The energy spectrtim ol tb9 neutroru.i from this niaotion bas been 1nveatiga.ted 1n SOlllt:t detail (ae sumnuAri~sd in Ref. 5, P• 202) althotJ.gb unfortunately the methods used have poor resolving l)()l'ler• Thi! earlier re.eulte give neutron groups corresponding to \ levelsi in B10 at O.$S, 2.1.$, and 3.45 Jirov. The group corresponding to th0 sl0'11 neutron threshold of Evane, et al.(60) hu been verified by Whitehead *· boitation or Be9 by 1nelaet1o scattering of deuteron. 18 neglected not only because it ie expected to be improbable compared to the other modes of decay of the compound all nuclaus-n&utron or fast charged particle emission-but also because no energeticuly acoe$aible leYels in :se? are known and because the observed low energy 1~radiation can be eaaU7 accounted %or 1n other ways. • " .Although 806 is energetically unstable to o.-partiole d.!toq, such deo&7 ~Y be forb1daia1n by strict sel~ction rule3 and too otherdoo improbable decay by y-radiation will be obHrYed, ~ in the wll k:now 17 -.,.,. capture rooiation £r(»j Li'+ p. -87and Illanderllle(64) who obtain., at a bombarding 0nergy of l.62 Mev, a neu- tron spectrum corre3ponding t.o lewlss in BlO at. O.69 ± .10, 2.20 ± .10, J.66 ± .10 e.nd 5.13 .;t .oa xev. In no detera1111ation ot this- neutron speo- tnm ao .far published .u-e fairly strona groups to lavola at 0.4 and 1.02 l\fev or ftak groupei to level• at 1.4, 2.8., 3.9 and 4.4 Mev ruled out. The work ot Ha.xel and StuhlingerC 6.5) on the L17(a.,n)n1° reaotion (Q • -2.78a.v) g1wa erldance for a level at 1.4 hv. In a recent abstract., Bonner., Butler, end Risaer< 66 ) report five threshold• for slow neutron production troa. 920 to 1070 av deuteron eners:,, correspondina to tiw lewls in s1O at ~$.1 lleY and within 120 kev o! each other. Certain relations betrmen the ianer~ias ot these y-rar,, ( eee Table VIIL ) } P• 68) that are lett mq be noted. Tho moat _striking is, as first notioed b7 Ho~alc, (56 ) that ee'"'ral ot them are integral multiples of 717 kev to It was noted in Sec. V B that it. ra@@med very probable that no with.in O.$j. Doppler co1Tit,ction should be ~ !or tbio -i-rq., so that tht;l laW:11 soo:rgi&e should alao ba oompared with multiples of 717 kuv. Suioe it i s not pos11ible,- in the other cues, to ~y definitely whet.her or not thti Doppler correotion, o! ~ o.SJ, should ha ~ , the present data can only be used to conclude that the interval rule hcld:l t,0 at leaat thi2 accuracy and ma,. hold exactly. It lH\Y' alao be noted that the sum of the ';-ray energies., 41.3 kav plua 1022 kev equal.a 1435 kev, which compares closely vi.th th9 14)2 ksv observed tor a third y•ray. U we make the Doppler correction tor all three ·r•niya, we get 412 kev plus 1017 kev equal11 1429 kev which d1ttera from 1424 kev by slightly more than i e consistent vi th the probabl@ errors gi'Yen. Since, as discW!Ji:,ed in Sec. V B, there are ot."'.iar expGrlmtantal ob- servations that imply that these Doppler cor:recticns should not be made, we assuoo that this is the case -tor a.11 three of th0 ~e lirws. Evidence from the neutron .groups and y-radiation can be combined to giva an energy level di&{~ram as shown in Fig. 42 where .t he Vl!lrtical oee.a 1a proportional to the level energy. Levels de:manded primarily b7 y-r;,J.ye. , whose existence is also allowed by the low nusolution of the neutron work are s holm dashed, and a level a t 2.86 ~ v ti"vat i s indi cated solely by- too 717 kev interval rule is shown lizhtly dashed. Other l ~vel a ma;r al.so oecur-- the y-ray and ru.mtron reletiYe intensi t i es are not.ad. The 1::att,a r :;a'(~ t.&1..~·:m. , as noted, f rom the calculat:tone of Evans, -a t al ( 60 ) bass d on the exp~riment al work of Bonner and Brubaker< 67 ) (900 k~v p-,,iak A..C. deu:ter ons , thick target., obserTatioo at 90° t,o the d®ut.eron ~ om) an.d .frc.,J!i the ras ult.s of Whitet:wad and 1tandsville( 64 ) (u.,o kev deuterons, 100 k <2·1r target, ob~¾:lt•va~ tion iat o0 to the deuteron beam). In neither ease a.rs the tl:!Cpe rimental oondH,ions as close to those under which the y-r;jy intenv;itietJ •ra 1lll'H\5-Ured coos1on of intensities, eince they iu-e at l!lOei 2% of t h-o t.otal interu;it;r. F'urtl!~r, it may be noted that tha fast neut ron and total y-ray yield$ of Evans., e t. al» i!lre parellel up to ~1.4 lfev-i.e., the y-ny yi~ld doo a not r eflect the. production of SJlow neutron.is corre15r,onding to th.a 5 MeT states, r.&egl i gible • ,. * . The ne t countinf, aftioiency oi' a y-ray conn.tar w.rnld D\:.\ r cnir,h l ;r the e~ for ooo S ilfev quantum <'ls !'or any combinations of quanta ( of .~t lli3.'ll6t ssvaral hundred k®v aoorgy) t,he:t. ood up to 5 Mev . Thu.2 decay ot the 5 MGv st&te s by cascad~ tran~i tions would not expl:dn thes@ exoitation curves . Th® argwoonts uaed to construct this level scheme m&y oo outlinsd Tht:i O. 7 Mev level 9 <imtabliahed both by toe ooutrcm group and iH 10 by obee:rv&tion of the Be (p,y )B c~~, roaction. >.-J mld 5.04 to $.16 ~v ~ required by the Obi$er-v~~d ooutron grov.pa . A li;;)'ffll -:\'i:. l.43 Uev, indioated b;/ ti1® Li 7(a.,ri)a1° rt)~'t,l ou i s also L'lclic:!ts-d ao In r~i'eNnoe (53).P the 0.42 ttav r&diation obser'V19d ·•hen 13lO i !l bom.b:a.rded with protons is attribuvad t::, axci·t~tion of the .4).2 Mev h ·vol t ,y inelastic :;,,o~t·t.aring. Reoai,t wo:dc by Brol>m.:1 Chao, Fowlar» ~nd T..au..ritsen(6B) 6tlld Uiuri ts-.'5n and Thon1a~(o9 ) has sho»-n Un,'t the r eaction fa, BlO(p,a.)~1* 1 ·u-ie rsdi:ation corresponding to a mtate in :&si 7 a-t o.4JO r~v. The 5.16 MGv •1-re;y is clearly to be s.ewoci.swd with the sl<ffl' neutron threshold of Evsns, et al. Sinco 0.72 + 4.44 • $.16 and 1.02 + ).94 • 4.96., ooo 0&1 uae ·the reaulte of Bonri.sr, et al, (6!4 to m1n1ooH discrepancies ( the ri"Jaxi.mura aetLl!atecl erl"Ol'l1 muat, be t,&ken, ruxi in opposite directions) by atH:Jmltlng one level at ,.1 fAev that can decay to both the ground etats and too O. r'l'l Mev eU!te mid ai.1.other e.t $.O Mev that de~ to th"' state at -· 1.022 r~v. * Tber.3 lei,. or couroo., no over-riding re~on for doing thti-. ;:::aot1..wly':I the ,~. 44 and J. 94 y-ray,8 may belong t.o Be10 or \:llvan to BG8., tm ·triton grot'!p in t.h,z.i l:3.tur <U:lfH~ <9;:;;capinif notiO(-, in Buec}:mqjr' o work ~oa.1W@ of ik., low inten:.;iity. At thfo excitation., Li 7* b uiurtabhl to oo~v;r pm-t- ~ 1\f3ndeville get 15% at_1.62 1'1:Jv), their tot.al y-rr;q yield doos not re- .f'leict t.h.e presence o.f th.is group. ThiB behavior 1e reasc,~bla 1 QB C£n be sin.am by oalc:-ulating the li'idths., r a :and r 'f., tor a.-emisf,ion and 'f-8miss:ton respecti.vel3. Using &the 1 e formulas for e-wave a'$ (Re.t. 35, p. 166), OWSt ~~-----------------------------------* Only prelimin&r"'/ results of the worlc of Bonner, et al, in wb.ich tlw :num.bor o! 1'8-velt:5 llli::ar 5.l Mev was unctl.l?'Uiin, l7\3?"<t) .!!.V3?.ilabl~ wban Fig. 42 -~af; p~p:a.ntd, so that ohly three of t.he £iv~ lewlt1 an :;.;hovm.o -91- 1 kev to 100 l.te-v. This givee r a. = 76 to 76oo ev. For ry, one nv.q usw too i'ormulru, oi' Fo;rlar, ~t.ru. (Ref. 37, p. 2·14), vtiich giv0 for i@lectric dipola radi4tion Hsre r/r0 represents a nuclear matrix alement that can have values from., ~s.;sr, 1/16 to l/2. This gives r"( ~ l to 60 GV. Thus evsin w.t th the amall ~unt of energy available, a.-deeow can ea~ily bi t.;;in times m<>N probable than stat.a d~ca;vs primarily- by a.-eaisaion. r -deOc11:1, and we assume that this * by BUldohoor. Spina may 'be &seigned to oeri.ain of the l@veli) ill 1:110 • the ground staul hu been ~hovm to be 3, ( 70) t.alcen as even. Thia tipin ol a.oo the parity ia u.sually , Cohen(?l) has t.hon sh01m th&t ~xporirit:m'te on the s~ttering * This ii:,, o:f course, .a 21:tmpls order of ruagnituda diacuordon of a si-l:.'<1Btion that is undoubtedly qui ta complexJ> especially i• view of the posf.libl(l) m~J.ltipl@t ~tructure of tha level. of' proton" by Be 9 le;e.d to an aa~:tg:nment of ~oro i.:,pin itnd evon part t.y to tho state et 7.47 Mev and a apin of two and odd parity to t,he state a.t 7 .J8 M~Y. I t hae a.lso been ~hown(SJ) that the 7.47 Mt:1v 1;~te decays by ce..sc.,;v.iei tbrot15l-, U18 state st o. 72 Mev while the 7.36 Mev s t.ate goes primarily- to the ground state. These observnt,icne are in agre~11ent w1 th mi a2sigXJrOOnt o! spin one and evon parity to the o. ·72 :.:£.ev state, prr>vidtad one !Dake~ vary plausible assumptions ·as to tbs relative dipole momsnt,:il for th.a 7 .38 l\iev to ground and 7 • .)8 ) Mev to O. 72 1Jev tranaitioniti. l'l; ia :not poa!aibla to make definite •i$pin a.adgmoonts to an-.7 of the other lavels in B10 • H01mver, ooo Tb.is iQ thE:t tho 413 md 1022 k\'!v radiation appear onl:r in combinati.on out. that at 1022 (or 413) kev. F. The first 8AC.ited l:i'ta.W of t1?. peak !rom tha radiation at 475 kev i:::. Nost notic@able (Fib• ~ ~6). Thi.., ra.distion iG ass:l.gn~d to the Be9 ( d,a. )Li7* Naction both on thl<l bat.d;:; of Buechner• s investigation of the a.-g;rou.pctSl) a.ud oocstme oi' +.,he bro£d.<drii.ll!J;; (d,a.) r-eaction than i'or the ether possible roa.ctiou.B (bec&UIJ.S of the large Q and the large mass of the eid ttad o.-p.u-ticle). In order to comp.are thla obaerv\3d :iShape ~it,h Uliit. of the -:.:mbro~aood lina» and to Si>tablish the l eveil -Jner f:%, the p!ioto-pe~k ;1;.~ie ob-t.<1.irMd "1Jhen th~ st&'i;.e in 1..(( -.if@B <:l:toited 1n t;no oth~r w:.,,ysi b;y' the ck: cc1y oi' Bt; 7, -93Be 7{K)Li7* (r} Li'( (p,p' )Li7 ~. and by the inelastic soatterins of protons in lithitIDi, The wame thorium. metal photoeleotron converter (7 .o t"!g/crrl·) and saa.itnt:1.ally idantioal convarter-aource geometr-J were ueed throughout. Too t :n.ree l: photoelectron peakas normalized to equal ar~ss , are shown in · Fig. 4,4. 'l'he p.,ak !roru 13e7 decay is 2.1 .i; O.lj wide (tb.e increase over the instrument resolution of 1.47 ± .OS% being completely attributable to l!!mar(;Y loss in the convert.er), tha:t, from inelastic s cattaring i s 2.2 ± 0.1,; wide, and. that f'NiB thG B09(d,a.)Li 7* reaction i il 4.1 ± 0.1% wids. Th® pee1.k trom thi.3 inolastio scattering iG 1.6 : 0.5 k<2"'f higher 'i',han that .from Be 1, .f16uroiJ g iv0::.; tha limi i,i; of thij Doppler broadenin;:; for t~i6 ( d.,a.) l"€1';i!,C'ticn1 aG obto.in('?;d .frcna the loca-t,i. on oi' t,he Bia 1 curv..- and from Teblo XII bslo·~. ~"Mn Li 7* is .for.red b-J Be 7 X-c.gpture, th.~ ma..-d.mtn.1 Ncc:l.l {JntJr ~r of the 11 7 is 67 @v (n~utrino and 1-ray in t.'·w ~ame di~ction), end Dor.,pl~~ for tho h0av.1 particle reaotion.s , and in pa.rticulr:.r it, fa eesn t.uB.t Doppler bro~dening is quite large for the ( d!lct) react,ion. r I am greatly- indebted to Profo s~;or J. a. Richards on ot th·>!i lJni ~rsi t:, of Calif'orn.i a at Los Angeles for making thr, Be 7, s.nd to Prcft;stmr D. u. to2't. of t.hf.l C&liiornira. Dwtitut.a !or performing th<G ch'<;lKt1. ool zoparation~ invol-ved. Table XII ED (Mev) "cm u7(p,p' )t17* 1.05 :aia9(d,a)ti7* 1.19 Reaction t 6.cm t (kOlV) 't17 (in om coord.) 6. (k~T) 0.00$9c 2.8 0.0041.c 2.0 o.006.,c .3.1 0.029c 13.a o• 'l'l:Mi obrJen.ed paak shi.n:. ;." ill 'oo t:i ven by 6.0 m oof•, E • Froll!. Table VIII., "cos E = 0.548 ior this redi.at:l.on !il.nd conv~rt.,crj) f;i wing r.= l.S o k 1.1Vo four aepuatod coil arrangement. Too instrumr.mt ~eolutiou l-'f~~ kept tlw ~.wie { ~ 1.47%) and the same 7 .o -,/cw.2 thorium photo-conv-0~r wwi ~ed. The targ®t was an ,.._, O.14 mg/am.2 beryllium metal .loll ( deuteron3 us~id) j ssparated .from the thorium b:, ~40 kev tor tile ~O.Ol to 0.02 inch. ~ I photo-pofllks obt!11ned for the 717 and 41.J kev y'o are sho1t1!1 in Fig. 45. 'l'h@y &re e~raentially identical with the correspondi~ curves fro» the earlier work. Tho 47S kev lins wst. run with thie sour~ at, doutoron (,margies of USO and lh8$ k~v ( curva1;1 III tmd IV ot Fig. 46). foll was replac~d by one 0£ Th~ ooryllium a.9 mg/om2 and t.he curv~ run at, 1210 and 510 There W°"d four poss iblo reasons for t he aeym;natry of th1.a lioo. ·i:Jlan only or1e, may be involir~. Thi0 additional radi ation woulcl have to be both lowe r 1n ener gy and considerably more iti-tt:nse than that attr ibuted -to Li 7*. Consideration o! the relati v~ intenui·t iee of th.l!il y-r&iiation and too oorre liSponding a-particlas ( ~@ Se c. V E) and of this ob818rvation that t,Jlli) f.'!h§pe 0£ the line doem not crumg-e with bomb.grding voU,age both make t,hie an 'tJ..TU.ikely expl anation. A weoond possibilit7 1a that the lifetime of the st.a'e,e is sl ightly longrar than the atopping time for the recoil nucleus. ' . Th0 nuclei in the !'orward direct ion are then mostly stopped in iJ1e target nwterisl before t hey rlldiat.e, those in the backward di rect ion, on tho other hand:; eacape from the tm'i8t ~fore th0y lose much velocity ( the 1c1xponantL.-u 1ra.ri1,rt,i0n or the reaction yield with d9uteron energy i a s ignif icant heN), th~ not reault being a i; Nd sh1lt19 al the radiation • .As ide fros the .tact that this ll".achanism oaim.ot quantitat,i'IJQ?l y account f or our obcEn1·ations , it i s rJlsd out by Elliott mid .Bell ' E mea~un;ment<72 ) of the lifatime of th~ ntat-c~ •M-' o. 75 ;1;. 0.25 x 10-1 3 :c.~ec-the stopping ti100 f or the u7* in Be me·U!J. wit.\:, a th in t.argot i:l{;lpt'.r'ated from the conver ter. A third possibility i s that ~~e r ecoil t17* 1 e ,'lre primarily in th.0 backward direction, the radiation being i s otropic, ai:id a fourth b that the radiat ion i s primarily ba.ok:wa1·-dr, with Nspect to the u7* velocity, t.he r.1'7* 1 i.:l ooing distribuwd i s ot,ropicall;r. With eome simplifying u el.llllptions, the at.fact of ani aotropy in the Li7* distribution or they-ray distribution~ ~ calculated (both may oo contrlbutinr simultaneously to the obaened re~ult, of course). 'fhaa0 aasump- center of mass s;ystem to the laboratory eystem on the angular distributions and that n observe only that y-radiation at a mean angle E O with the spectrometer axis. Vis note that tho deuteron bemn is along tho spectrometer e::d.a and define angld as follcnra, Q • E a angle between tlW ,,-quantum and the sp;~ctrorooter rude, ~ = Qngle bet1ftten tllS y-quantum and th~ 117* velocity, "P - angle between tne Li7* v,,2looity and too spect.rotM,ter rude, V e = angle between Q and a., in spher-loal triai1gle. Than U @(0) is the number of radia,ting 117* 1 s par unit ti.me per unit solid angle and 4>(a) is t.he y-diatribution A~ in Eq. (6) we have •f · d'f'-= sin E dE l[coa {E - a.) - cos e][cou 0 - oos (€+a.)] Putting X 1111 CO& 9 and 008 {E: + a.) a b, COE (E - a.) z a }-l./2 • :iinci noting that the limita on 9 are giTen by (E + a.) and IE - a I, we can write b dli 1 • 21r<f?(a) sin 11 da. sin E dE (-2j a which ia inw~rable by s tandard fomulas if ® (,-::) is a polynominl. As shown in Sec. III B, U lira t&k0 th~, phot-O a l0c·trc;n dir.rt.rlbution ~.5 & 0-.function at w 0 = -coe-1 ~, then cos E = 008 ' . E O is a;-1.vei.: by (11) -97whe:r-e 8 0 b the x:iean accaptanc0 angle of the spectrometer. If w,.;1 incluoo the effect of scattering in the converter (Swo. III B) (JB) tion over E: than giveill If V ia the. velocity of the radiating nucleus 1n tbe canter of ma.al'J uystam, in units of th.a velocity of light, the Doppler sh'lft b t;iv+im by or dEY • dEe- = -Enx. V sin a. cia.. (40) tribution o.t' the form (A - oo@ a.) or (ii - cos 6) 11:J required. Tald..tl(I; the Ta.king the Li7* distribution a.s isotropic, lUld the y-distribu.tion A8 {A - 00~ a.) giVC31$ 'r aking the acceptance Mgls of t he spectrometer as 13°, we have . coij E 0 = 0.796 or, if we use Eq. (38) to alloii for scatterini, w have co~ EO :: O. $48. The calculated pri:ruru:-y distributioM u,,;1 shmm in the loer pM"t of fig. 47 ~ in the conv-~rter. 'fae !-photo-peak from Be 7 decay (Fit;. 44) g1Yaa {:i The re:.,ul t o:f .folding thi~ "'wil1doo11 into two of the pri- dashed curve corro$ponding tc th~ da~hed prh.acy diatribution. 'l'h& anerror :.,hi.ft due to th"' center of roass ootion h&s been tak1Sn as wh ich woul.d il;iprove the .fit to t.,'.:ta e:Y.V'_.;eriloontal. point~ on the high energy :.:.ide.11 but ::•ake i t definitely poo~r for lower ener;;ies. Actually, euch de- 9 (8) - (1 - cos 8) or a y•rrq diatribution sP (n) ~ (l - o.8 cos a.). A more~ detail@d e;,,;£:u>zd.nation of the distribution is po.esibl@, but would not bee.awe of the approximation@ in thci thso:reti cal t.reat.ror;1nt. Th~ principal. generml di .:H~l1Htsion of Devona and Hin~ ( $9)) in e i th.er t.lw cc1t1p1.nind n.ucl on;::J, a11 , which could i,i;i.ve tho nquirad distribut,:!..on of th-., 1,17~ nuclei, or in ·~he re,i;J.dual :nucleus, Li 7, which could give the required. distribution of the y-rt,.di&tion. In neither Clise are direct mear:mrewents of 'i',;1,sse diEJtri- but.ion5l <'Available. The work of Resnick and Hanna on the Li 7~~ distribution thH't the g~ner al cha:r·acter of t.he at.:iJ:.:V.otry dOi"B r~t c:,,-1'"1~;~ notio'i;iiably in goin1; f ro:m 16.15 to 16. 95 ~ll~V e.;..citation in B11 (ED = 5).0 't,G 1485 k~i'!f). On t,oo ot,h,~r hand, ·t oo lov.;)l ,, in 1!'7, s ine,;;.: ili~y CfUl dec t,t only b;/ y-radi.atiori, on® be a.cc~n;si.ble in the :a1 0(n,a.)Li'l* roa.ctioui for which Ellic,ti mid Bell (.58 '72) 1 ' observed a s~tric Doppl@r bro~d®nini• -100- ~CES - l. • Buechner, Strait, Stergiopoulos, and Sperduto, ?hys. Rev. 74, 1569 (1948). 2. c. w. Snyder, 'f'heaia, California Inerl:.ituto ot T~chnology, 1948. J. Ro L. Willer and Bo D. McD.cmi;al, Phys. Rav. _:&., 315 (1948). 4. Horlly~, taurit3sn, and Rililsmussian, Pl-.cy·s. Rev. 76 731 (1949). ·-9 Preliminary Repor'c. #5. 7. Deutsch, Elliott, &.'l'ld Evant@, Rev. Sci. Inst. ,2, 178 (l9h4). 8. C. M. Witcher, Phy~. Rev • .§2, 32 (1941). 9. I{. Siegbrum, Phil. Mag. Jl, 162 (1946). !!±, 974 (1926), Arch. Elektrot,ecll. 10. a. Busch, Ann. Pbyeik ll. '!'. Lauriteen and R. F. Christy-, Phyel. R@v. ]1, 536 (1948). 12. s. Frankel, Phye. Rav. ll:1 804 (l9L~8). 1,3., E. Persico, Rev. Sci. Inet. 14. J. w. U. Duifond, Rev. Sci. Inste ~, 160 (1949). 1$. Rutherford, Chadwick:, snd Elli!S, 11 Rilidi.ations from R-ldioactive ~JI 583 (192?). I Substance:J" ~j) 191 (1949). Cambridge University Press, London (19.30). 16. C. D. Ellis, Proc. Roy. $00. !!}_!, 318 (1932). 18. H. Sl.ltifl and X. Siegbahn, Phys. R\:!Vo J.?.» 1955 (1'949) i Ark. :i.'. F';;·s. _!~ ifr. 17, 339 (1949). 19. Lauritaen, Lauritsen, and Fowlsr, Phys. Rav. 22,, 241 (1941). 20. Fowler, Lauritsen, and Lauritsen, Rev. Sci. In::it,. ~., 818 {1947). 21. N. Bohr., "D. Kgl. Dan£ike Vid. S~l. :&iath-. fy~" • M:edd. rr XVIII., 8, 1-ll"h (1948). -101- 2:;. ' Hulme, McDougall.!/ Buckingham, and Fowler.? Proc. Roy . Soc • .±~.211 131~ (1935). 24. a. Hall, P~s . Rev. J:.2.P 620 (1934) . 2$ . w. Heitl~r,il 0 T'ne Quantum Theor,f cf ~dia t,ion~1 (Oxford University Press, London, 1944). ~'7 GI• Bethe, Ros-a , and Smith, Proc. A:tsi. . Phil . Soc . 78, 513 (1938). 28 . Ri!?Jjmuseen, Homym<, Lauritsen., and Lauritsen, Phys . Rev. ]1, 617 (1950). 29. R. 1.. • Walirer, Phya . F~v . 'J2. l iJ.40 ( 1949) . fl JOo M. i. Ros@, Phys. Rev . 12,, 678 (1949 ). 31. Dougherty, Homyruc., Lauritsen, and Rasmu:se@ll, Phya . Rsv. J,b, 712 (1948) . J2. Ellis and Aston, Proc. Roy. Soc.!~, 180 (1930) . 3). •~ n antl Primako.f.f', Phy~. F.sv. ]±» 1406 (1948) . 34. Bethe and Bacher, Rev. ~od. Phys .~» 82 (1936). 35. H. A. Bethe, R®v. Mod. Phya. 2, 69 (1937). z, 245 (1937 ) . 36. Livingston nnd Bethe» R0v. Mod. Phys . J7 . Fowler, Lauritsen, and L:.\11.ll'i t.e.en, Re-v . tiod. Phys . 20, 236 (1948). J8. Dt1 wlli~ 39. Stre1bi, Fowl e r., and Lsuritsenll Phys . Rev . z2ll 253 {1941;. 41. S. Kojima ., Proc . Totp . tcad. Tol{;/O }2:1 282 {194.J). 4 2. Oppenheimvr and Sc..riv.r".,.nger.i Phys~ R~-=v. ~., 1066 (19'39). LJ. E. P. Tomlinson, Phy,;; . Risv. ~ l l 159A (1941h t he,::is , C:slif cir n ia and Hor eward:, Nst. ~ " 3.31 (1948). Instituw of Tachnoloa (1941.) o 44. D3vons a'lld Linw~ay, Nat . _!.§.» .539 (19!~9) . l~5. Devonsll Here-wards &"1.d Lindsay., Nat . 164» 586 (1949) . - 102Buroha.rtJ. end Freeman, Phys . Rev . 7$ , 1756 ( 19h9) . Chao, Tollestrup, Fmvler, and Lauritsen (to ti© published in Phys . Rav.) . Herb, Snowden, a.i."'lcl SJ:l.la, Phys . Rev . 15, 246 (1949) o - J . R. Oppenhe inY3r, PhyE:1. Rt<;v. ~, 164A (1941). 50. RooE.J ro1d Uhlenbuck, Peys . Rev . ~, ~~11 (19JS) . .51. Bonn0r and EV&"W.11 Phys . Rev . ]1, 666 (1948 ) . F'owler and Lauritsen, Phys. Rev. J.2., 314 (1949) . Lauri tsen; Fowler, L!\uritaen, and R&smussen, Phy~. R~v. ]l, 636 (1948). l.&uritsen, Dougherty, and Rasmussen, Phys. P..av. ~ i ; 1566A (1948). Ra5lmUBsen, Lauritsenjl a.112d Lauritsen,. Phys . Rev . lz, 199 (1949) . Ra.smru.ssn, Hornyak, and Lauritsen,· Phys . Rev. J!:., 581 (1949) . Chao, La:u.ritsen., •and P..as,m.1ssan, Phys. Rev . 76:9 582 (1949) . 58. Elliott and Bf.Ill, Phys. P.av. ~» 168A (1949). f)l.!)vons sud Hills, Proc . Roy. Soc . A.199, S6 (1949) • '75, 1161 (19l\9) . 60. .E·v.sr>.s , Malich, and Risser, Ph,ye . Rev. 61. Booe.hoer aud Stra i'l;1 PhyF~ . Rev . ~, 1547 (1949) . 62. Ro.:lnick and Ha,.~, Phys . Rev . 76, 16BA (1949). 6J. 6;5. Ha:.':l:liz)l ,:ind Stul1llnuer» Zeitz . f . Physik 114, 178 (1939) . 66. Bot111E,r.:1 :Sutl e r, .;i.nd Rii;;oo:;.. , Bw. . Ml. Phys . Soc . _2, I:fo . 3, p . 49 (19.50) . 67. Bo~r and_Brubaker .:1 Phy'.19 . Rev. 50» .308 {1936). 68 . :e.ro~n» C.i:.61.o, Fowler/) &!J.d Lau.ritsan, Phy·13 . Rav . ~, 88A (1950). I...aurltsen and '!homas .9 Phy9 . Rev . ~.:1 88.A (19.50) . 72 . Elliott _;ind Bell, Phys . Rav . .Jli, 1869 (1948) . -103APPENDIX I Thra experiment,al. procedure used in sErttiD.g up th@ ring .fociw for t he four l'ii®pte.retsd coil confi~uration (Sec. II F) fa out,lined M TS 3 S a »w.tt er of possible intere!:lt to oth~r i3~'q>'ilrilnent.$ra . counwr. The sou.re~ wa.e a Th B deposit ,.,_, 0.06 inch in diameter, and th@ counter opening used. 'l>'Iaiw 0.078 inch in diameter. Under t,ha~e conditions , a single internal conwrsion line appeared ~B 'three digtinct pes.ks , each One of these was a plug of 1.:22 inoh~ o outside radius , and tha o·t her wra.s ~ ring of 2.2$-inch inside rsdius. By moving these st.ops along the spe ct:1:-0- meter ad.s until the warioun peaks -wen reduced to half intensity , t,wo points on the corresponding ray~ were located. gave a third point. The counter C};'.;'-:ming t.hoo By moving the counter 0.75 inches out ruong the z-tt!Xis , 6 I/ 6. z wa.s determined for the thl"8e zones . Ii' one then .ass1JID@6 that 6. I/6. zt is constant over thie range of t:. z» and that the eilectron p~.ths 8\N displaced parallel to thei,.JSelves, the positions of the thrae raya at a. g:tven magnetic field can be calculated, and· the location of the ring fo cus b~cozrM!ls ~ppoil"ant o The reirults are shown in Fig. 48, where i3xparimenW point$ for th® middle and outar p.athe are S1how. Simil~ c ~ s , obtained ·nth the two m,.rpar at ed coil oonfigt:1.rr:;/l'.ion, ~) shown in Fig.!,. -104Although one may get m.orGJ accurate data from the obvious sacond approximationj the s imple $Wp~ outlined above served in our caae to locate -c.he ring focus with suffic.ient accuracy. Appropriate thick conical stops, suitable for UJSe 'Nith high energy electronw, were than inetallad in the apeotroinetisr, as ahow in Fig. 2e At first, both of th.Gae nre made movable from out~ide the spectroo:.eter bscau!:36 of anticipated dii'ficultiee in ~tting both ths axtreme r3Ys into the counter. Once & auH,able location for the hollow cone was f ound, it w2s li!!.ft .fixedo Att.sr 'llie spectrometer solid angl(1 desired had been selected by the, ring s t op on the source and, the ' • approprl.&.te ring foous aperture could be obtained by moving the conical plug. It mey oo noted that al though a mean diam,r.fl:.er of 2. 25 inches was se- lected for ·t..~e ring focu® aperture, it was found experimantally that any diameter b®tween 2 and 2 • .5 inches gave allr.-0st ae good resolution. As was previously- noted, this w~ ®xpected since the ring focus is, in reality, only a re:t.ner poorly-defined interfilGtltion o.f ray,-, with a small divargence . SoD119what more dUficul ty waa amcounte:rad 1n locating "Ghe ring locus for the two separated coil configuration (Sec. II E) »tn:ce the desired trmnsmission zone corresponded to an &1nulus of four to five inches radius at the center of the sp®ctrometer . It did not seem possible to ga-t three well- d@.fi.ned peaks corresponding to the ial'ler, w.ddle, tmd outer parts of this r&ooo . The following l ess ss·tisfactory and uruch more tedioU£ prooodur<iil wu thsn1foro us®d. A.tier -the four to five inch r adius transmis sion zone was defined-» the oount.0r end of th& :1pectromoter was completely closed by a movabl® .U\.illiinmn disk . J, 1/8--in ch ~d.-Ok-.) raditl s lot in the disk ~ s covered by a ahocrt of al00l...i.n1.m., L"l which was cut a 3/16-inch wide diagonal slot . The dia&;onel slot could oo r,ioved a.cross th@ r ad5-al. one, th us l e~ving Q small -10,opening at any desired radius between two end four inches. Thtu:1 it was possible to determine, in a roundabout w3::1, the width and location ot the transmitted electron oo.wn, and consequently the appropri~ts location for the ring focw, apertun. ACCELERATOR BEAM HELICAL BAFFLE LOCK r. ~ -------------------- ffl vI =#\V rrf- I -=~ \ JrJ 222 -flt FOCUS m -ll v v v " -=------ ,;; v v v v• I I-' f ------------SOURCE --FIELD COILS '-2• OIL DIFFUSION PUMP 0 I l 1 It I e I e I INCHES FI G. -107- --::;f.t::==-===:zti ,', I , I , / , I I I Cl) Cl) .c 0 C 7 Cl) :: _ Ji [ .0 a.. C\J . V -' <.!) 1 IJ.. (\J ~ Cl) Q J 0 ::s _J r I X .... ~ ~R t-~~ ~ R l__ r1 S1~' 2 ► t 7~zr - B z A' SOURCE RING FOCUS APERTURE FIG.3 ' ELECTRON PATHS ( ROTATION NEGLECTED) rl IMAGE I I-' 0 0:, I FIG.4b Th B F-LINE FI G.4a Th B F - LINE Two separated coi Is o Source diameter and 1 counter · opening 51r Two separated coils ?~\ \ Ring focus ~140 outside coils 6 Tronsmiss ion zone 1 1 2 ~5 -5'. 0 radius Source and counter 1 opening both 2 l/1s .0 Transmission zone 1 1 4 .'0- 5 .b radius Source at I V,s' 1 "' Source at 2 1/4 • Source at 31/16 1 • ~'.04 source diam. I I I I ll l \ 120 I 100 11 • oz. 12 source diam. 200 I <D 2.1% U) 5 1.2% 80 X -' X (/) (/) I- ..... z z ::> 60 g 0 (.) 0 40 20 40 0 16 17 18 POTENTIOMETER READING (MV) 19 20 .....__.______..___.__ ___.__....._______._ ___.__~o 16 17 POTENTIOMETER READING (MV) I f--' 0 '-0 I FIG. 5 TWO SEPARATED COILS o/64 DIA . SOURCE AND COUNTER OPEN I NG 1/ + 240 SOU RGE AND COUNTER OPENING BOTH 2 1/1s OUTSIDE COILS 200 <D • 5 (/) ._.. z => 11 , 1 11 3 7/ 8 ; 4 7/ 8 R. tr-OUTER ZONE OF MIDDLE ZONE :+.- I 1/is" I I-' I-' ? 160 X SOURCE 1 4 WIDE TRANSMISSION ZONES AT 2 5/ 8 0 SOURCE 2 9/ 1~' ZONE I 120 + 0 a 80 )+ +_/"1"" /+ \_+ 40 Q.....__ _~_ _ _......____ ____.___ _ _,_____ _ _ _ _ _ _____.,_ _ _~_ ____.__ _____, 16 17 18 POTENTIOMETER READING (MV) 19 20 ~-RAY SPECTROMETER END PLATE 0 :0. +I 0 0 LO .:1 • 0 0 =• ~ 5;~' , 251~·1 -H 0 ~ =~ -Et -1 I I-' I-' I-' I SOURCE 1 CENTERED TO WITHIN ~ '.002 FIG.6 ANNULAR SLIT FOR SOLID ANGLE MEASUREMENT -112- FIG. 7 Th B F- LINE SOLID ANGLE MEASUREMENT SOURCE TO SLIT • 475 O INCH 9 .500 II • .625 + .800 II II .., .925 0 .950 II 0 160 II .9QQ A 0 II SLIT OUT 120 (!) - ~p X 7,= 2.04% (/) 80 ..... z :) 0 0 28 29 POTENTIOMETER READING ( MV) -113- AN NULUS ANNULUS OFF CENTE R ON CENTER TRANSMISSION ZONE AT •~475 FROM SOURCE SHADING SHOWS EFFECTIVE APERTURE FIG.Sb EFFECT OF MALALIGNMENT r-, I I II 1 21°50 r 1 \ II II I: I I I I SOURCE I I '~020 DIA . I II - - ~ ~ - - 1~'- 11 ".030~ I◄ 'fl-75 -◄,-------':625------ ~----------'~950-------.i FIG.Sa POSITIONS OF ANNULUS SOLID ANGLE MEASUREMENT FIG. 9 ThB ,-.... 0 F- LI NE 0 U/ SOURCE CENTERED • 'l,s' OFF CENTER \ EFFECT OF RADIAL MOTION 2001- I <D -' Jo OF SOURCE \ 11 SOURCE DIA.~ 1;16 X II II 3/16II II II £ I I-' I-' • (/) ~ llp :) ~ = 1.92% z ~ 1/e" ~ I 0 o 100 O..___.__ _ _ _ _ _ _ _ _ _ _ _ _ ___.__ 27 __.____ _ ___.__ 28 POTENTIOMETER __.__.._____,__ _ _ _ _ __...__ 29 READING ( MV) __.__~ 30 >-< (/) d tr w ,LL) ,z w :E 0 tr ,-w 0 0 0 z a. (/) -_C) >- 0:: I- w ~ 0 w (D w 0 0:: ::) 0:: 0 .,_w (f) w ~ 0 0:: X .,_ <! (j (.) LL QC/) w 0:: a.. Cl) .,_w 0:: _l w z> .,_ 0 0 t w 0 0:: => 0 Cl) -0 8 = I STERADIAN FIG. 11 z z 0"=2 .3% fl'Pir = 0 .0252 >-0 0:: .,_ <! :::> ~ CD -0:: 0:: 0 CJ.,_ w=> OCD _J - PRIMARY DISTRIBUTION (PER STERADIAN) a.. .,_ (/) oa:: LL.,_ en FOLDED DISTRIBUTION 0 0 10 400 300~ I / WINDOW I 200 I \I I \I I/ 1 \I l I 'f ~ 8 I I/ \I I 1.21 I/ \I 16 =~ .ai-- /I I\ 14 I \ ~2 I \ 0 0 1001- ol L .10 I / I I .14 , .18 / , .22 z - 41- I\ \ \J. .26 ,I .30 ~ \.. , .34 I + tn p 01 , --I .88 / I IJ .92 I \ , .96 \,,,, I 1.00 '==--- 10 1.04 I ~ ~ ?' 0-= 2.3 % AV"ir = 0.0252 FOLDED DISTRIBUTION J I 4001- 9 = I STERADIAN FIG.12 PRIMARY DISTRIBUTION ( PER STE RADIAN) . ~10 z 0 - 8z I- .0-_ :::, 300 CD a:: :::, CD WINDOW IU) a:: I- I - Cl ~ 200 6 CJ) r, I\ <l: I I\ I I I \ ~ a:: a.. I I I \ I \ I \ I I I / \ 0 40 44 Cl w \ ,' \ I \ /I IOOl- Cl I 48 .50 p .90 I .94 4 :3 0 LL \ \ \ \ \ \ I \ ~2 \ .98 0 1.02 I I-' I-' -.J I -118- 0 I{) 0 - 0(/) - 0 .... ujz z 0 0 0 rt) .Q. (!) a, - + -LL -LL ·, ~ I- ¥' <! - \ <! ~~ m _,,- r m ~ ..- +. -- r--- ~ -- 0 a:: a:: -I- ~(.) w _J w / w a:: a:: o=> oo tri a:: v=e,J -w N >_J ........ \ ~ V z <! (.) 1- +\ ......... ~ w z (!) 1 0~<! 0 ~ \ . I'. <! " 1---- r-;-...._.. z <X) r---:,+. + (/) ..... z L.~ I <X) 0 0 - "~ y ~- 0 I{) (D a:: <! ~+- -;~/ ..... -& -&~ 0 0 ,__T ...... .-L---,---" I 0 I{) ~+--1 >- a:: <! a:: • ► 0 0 - ::> I/+ . ...-- -119MEV 0 0./ 0.2 0.4 0 .6 0.8 /.5 1.0 2 .0 2 .5 3.0 3.5 4 .5 4 .0 /!~ ~~ 5.0 F 19 (1,aJ"o ~--t 11 Et, =1236 KEV ELECTRONS I tt 0 4,000 8,000 12,000 Bp IN GAUSS 16,000 CM FIG . 14 b MEV 0 0.4 0 .1 0 .2 0.6 0.8 1.0 1.5 2.0 3.0 t / / / --- - ---r-- / Q: ..... , POSITRONS I \ \ / ~ I ~ I :::, .... I ~ I I l,J I :!:: I ~ I 0 ~ :::, I I If) I ~ / 0 (.) I 0 \ I \ I I '' I I I I I I \ I .... \ ~ I Q: l,J Q. \ \* I I I .... \ \ *\ I :!:: 5.0 ~ ' ''\ \ / ..J -- 4.5 1 F 1t,a.) "'0 16 Ep=/236 KEV '' / / § 4.0 3.5 J ________ ) \ I I I I I t'{_ \1 // ,1 .._,1 4,000 12,000 8,000 Bp IN GAUSS CM 16,000 ~ FIG. 14 a ELECTRON ENERGY IN t,tEV 4 J ~ \ *\ F'9 (t, a, JTT 016 E11 z:1236 KEV ELECTRONS- END POINT ELECTRON ENERGY IN MEV 5 .0 4.5 4.0 5.5 I . I F'9(t,a,}rr 016 E11=1236 KEV E!OSITRONS - END POINT \ ..J \h § ct: Lu I- - C: ~ :::> \ I- C: Lu ~ C) ~ I- ~ :::> ..J ~ ct: ~ ~ ~ t, I- C: Lu \ ~ C: :::> C) <.:) 0 I I- C: :::> ct: Lu Q. \ \ L 18,000 16,000 ELECTRON MOMENTUM IN GAUSS-CM. F IG. 15 b !\) \ ~ *\ Q. ....I \ ~ C) ct: Lu 14,000 +\ \ \ ~ Through 250 mg/cm 2 Be C: \ \\ :::> C) -ti "\ \ <.:) \-,_,~+-•h~-+ 14,000 16,000 18,000 ELECTRON MOMENTUM IN GAUSS- CM. FIG . 15 a 20,000 F'9 ( p,a.) 0'6* FIG. 16 Ep= 939 KEV INTERNAL CONVERSION PAIRS + NUCLEAR PAIRS ~ POSITRONS FROM 50 KEV Ca F2 + 23 MG/CM 2 Cu IJJ PER 62 µ. COULOMBS ..J 0:: rz r- :Ii! z r- ~ z IJJ z~ or- ::) z Co :Ii! IJJ C) 0 a::z :Ii! <t IJJ rz ::) ~ a:: ~~ IJJ ASSUMED INTERNAL CONVERSION PAIRS (/) I I 30 I I ~ LAB BACKGROUND I n # I I f-' Oo:: 0 0I + ::) I rz ::) 0 ~coSMIC RAY ~~ 0:: ~ t I I 40 50 POTENTIOMETER I I I l;:f: 60 READING ( MV) :! - ELECTRON ENERGY IN MEV 5.0 6;0 .. \[ + 7,p I F 19 (pa.) .,.0 16 I FiG .1 7 Et, =873.5 KEV ..J r § a: ~ SECONDARY ELECTRONS FROM 23 mg/emf! Cu + 250 mg/emf! Be - ~ ~ :e I ~~ . 2 ~ I ~ ~ ~ 0 l\l (.) <.!) I " "" Q.e ~ .... (/) (I) II) - ::> q: ~ <.!) ::, a: + f/H lu ~ ~ l\l -. Q) ~ l\l "If § Q.e i 0 (.) t 18,000 20,000 22,000 ELECTRON MOMENTUM IN GAUSS-CM. 24,000 I-' I'\) I'\) I -123ELECTRON ENERGY IN MEV 60 7. SECONDARY ELECTRONS FROM 23 mg/cm' Cu ..J ~ 15 I- + 250 mg/cm' Be t ~ ~ ~ l.u :e ~ I- ~ It ~ r ~ :::, 0 0 18,000 20,000 22,000 ELECTRON MOMENTUM IN GAUSS-CM. 24,000 FIG . !So ELECTRON ENERGY IN MEV 7. I !+ t ( ~ :e 0 :e f ~a, a.J -ro" Et,=1381 KEV SECONDARY ELECTRONS FROM 23mg/cmllcu + 250mg/cm' Be ~ 0 I (/') ~ ~ IC') I<') I<') I- ~ :::, It ~ r ~ :::, 81---------------~ "~ +--..$t r---------- 18,000 20,000 22,000 ELECTRON MOMENTUM IN GAUSS-CM. 0.E + ½ T----- 24,000 FlG . 18 b - - ---- - ~----~-=- FIG. 19 F'9+p __J <( I SECONDARY ELECTRONS I PER 77 µ. COUL. 0:: w rz - + II.001 Cu + II.005 T h 50KEV Ca F.2 I > Et:>= 939 KEV ~ :::> • rz w •• ••• • + ~ ••• • t • • • •••• • • • • • • + I f-J N 1 0 ~ ~01,2 'I I I I 14 16 18 20 I I 26 I 22 24 100 MV= 75 A I I 28 30 w a.. hv = .95 MEV hv = .75 MEV (/) rz 0 ::) 0 (.) 0 O t 44 O O O 0 O O 0 0 0 0 t 0 52 0 60 t 0 0 0 0 + 0 0 0 68 76 IOOMV=IOA -0 84 0 O O 0 0 0 92 t 100 -125ENERGY 0 .2 0 .3 0 .4 0 .5 0 .7 0 .6 MEV 0 .8 0.9 1.0 I. I 1.2 / .3 / .4 /.5 0 <o '<t 0 IO ;:: l\j '<t 9 Be + d )c 7-RADIATION t ..J ~ ,., 0 0:: ... ~ i.i ~ 0 ~ '<t ... 27 mg/cm 2 8t1 +29 mg /cm 2 Th ( Ordinate K 5) +-+- <o _j :) ~ i.i ,., 0 ~ 0 ~ ... ~ / :) / / ~ I ~ 180 mg/cm 1 Be 29 mg/cm 1 Pb ...4!: 180 mg /cm 0:: 0 !"' II) :) 1 ~ '71- Bt1 C (n• (.) --~ 27mg/cm 2 Bt1 ( Ordinott1 x 9.6) /500 2000 2500 3000 3500 • 2000 2500 JOOO 4000 4500 5000 5500 6000 6500 Bp GAUSS CM FIG . 20 3500 Bp GAUSS CM F I G. 21 4 0 00 4500 sooo -1260 0 ./ 0.2 --,:---- ELECTRON EN 0 .6 (ME V) 0 .4 ER'JY - 1.0 Q) ;:: Be9 + d ci le 1-Radiation t Se Edz/ . lMEV condorY Electrons TllP = 3 ~ 28 mg/cm2 8 +23 mg/cmz The (\j (\j 0 .;;(\j 0 ..: 145 mg/cmz B x.1 e 2 C,0.7l8J ,ooo 2000 0 4000 0 P (GAUSS C,.,) FI G. 22 ELECTRON ENERGY (MEV) 0 ,6 0 .5 0 .8 0 .7 Be9 + d ;-Radiation Edz/ . i MEV Se condor llp Y . Electrons T =3 i 28 mg/cm2 Be + 23 mg/cm2 Th 3000 3500,Bp (GAUSS - -CM) FIG.2 3 --- 1.2 -127ELECTRON ENERGYiMEW USO Z ,0 Z.5 3,0 Be 9 + d 7-Radiation Ed :>: /. I MEV Secondary Electrons 11 p .., p= 3 'f, ,t ..: 28 mg/cm 2 Be + 79 mg/ crn 2 Th IC IC I')..; 145 mg/cm 2 Be X 1.25 t.," c,Z.9 7000 6000 8000 9000 10000 Bp (GAUSS 11000 IZ000 13000 CM) FIG . 24 Bt> + D 1 -RADIATION E0 = 1120 Kt>v SECONDARY ELECTRONS FROM ........ +-- B.9 mg/cm2 Be+ 113 mg/cm 2 Th .Q. ~ "' *-- 69 mg/cm 2 Be 0 IC 0 IC I<) 2 I 113 mg/cm Th -z.._-.\ ..J i 70 80 POTENTIOMETER READING FI G. 25 (M.V.) - 128ELECTRON 360 -,300 T- ENERGY IN KEV 480 -420 ,---, - - - 540 1·-- Be 9 + D .,-RADIATION SECONDARY 8000 ELECTRONS 6400 /6ool1--I---------N-eu- ,-, o-n- Bo_c_k_g,-o-un_d_J~- - _J__ O 1800 - 2000- __,___ _I_ _ _ J _J_ ___..__ 2200 2400 ELECTRON 2600 2800 __ __l - _L _J 3000 3200 3400 MOMENTUM IN GAUSS CM FIG . 26 ..J I Be+ D 'Y-RADIATION .... ;:: 2 Secondary electrons from 8 .9 mg/cm Be and converters as noted • Ed=/./9MEV ~,, p • l. 47S - - --z:....-24.9 mg/cm 2 Th ~ I 1\1 1\1 ~ 57 mg;cm 2 Th ..J I 1\1 1\1 1/) ..... .:: ..J ~ :::i 0 I 1\1 (.) /\I • 7.0 mg/cm 2 Th----• 9 10 II I<) '<t- I A / \_ ___________•....__..,,_., 12 14 13 POTENTIOMETER 15 READING (M V) FIG. 27 /6 17 18 -1299 Be • • +D Ed= 1.19 MEV 350 A/= 1.47% 300 -I«> 113 mg/cm 2 Th - I'- r<) Cl) oo 250 01> O:E - • t\l I (.) • " ~ • 200 -- • _J 150 IOQ...___ ____.__ _ _......__.;.....____.,_ _ ___.___ ____. 28 29 30 31 32 POTENTIOMETER READING (MV) FIG.28b 9 Be + D 57mg/cm 2 Th • Ed=l.19MEV ~pp=l.47% -1«> • r <) (X) I 200 - (.) 01> 0~ • > w ~ lO - t\l " ~ • --t _J • • • • I 00 L - - - - - . J . . . - - - - L - - - - - - - - ' 25 21 22 23 24 POTENTIOMETER READING ( MV) FIG . 28o -130- ,___________:_______7~ m C\J C!) u. :::::.. ~ C ~ + -. CJ\ O)Q) co .c: ..... "'E ~ -., ' "-. - ;1~ . (.) ~ t:J\ E ~ II N) ~ l\3W 09'£ N) N) l\J o, c______~------~00~ o L__ _ _ _ _ ~ 0 t\J 9/ ) /\W T (£S-o 001 4\ 9 Be +D & ...J <{ > 717KEVY FIG. 30 K PHOTOELETRONS FROM 7.0 mg/cm 2 Th • SAME, OBSERVED THROUGH 19.2 mg/cm 2 Be (20 .8 EFFECTIVE) a:: w 1- z ~ :) 1- z w ~ 0 ~ I . f-' 1- \.A) z ::> a:: w a.. CJ) 1- z ::> 0 (.) Q.....__ _ _ _ _ __.___ _ _ _ _ _..,___ _ _ _ _ __.___ _ _ _ _ __ _ . _ _ _ _ - - - J 15 16 17 18 POTENTIOMETER READING (MV) 19 Be + d Y- RADIATION FIG . 31 hv0 = 0.72 MEV ELECTRONS FROM 19 M G/CM 2 Be _J ~ a::: w 1-z ~ :::> 1-- z w + + +++,..., r+--r + t + +r + + \ + +++ + '+ ~ \ \ 0 ~ 1-- z :::) a::: w ; ~ I I-' \.J.J 'i' +.\ ':.'~ .o.E ~ ~ +i 0... (/) 1-- z :::) t,+. . .+ 0 0 --+- Q._____._ _ _ _ _ _ _ _ __....__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ 13 14 15 16 POTENTIOMETER READING (MV ) 17 3.1 MEV Y-RAY FROM c' 2(dp)C 13* A- SECONDARY ELECTRONS FROM 1 0'.'010 C + 0~ 003 Th _J <! > 0:: \ w r z ,---c '\. '- - ~ ' '- 8- SAME, OBSERVED THROUGH 58.7mg/cm 2 Be (63.7mg/cm 2 EFFECTIVE) C-8,SHIFTED UP 79 KEV ::> r z I t-,J w \.,.) \.,.) FIG . 32 ~ I 0 ~ r z- ::> 0:: w a.. (/) r z ::> 0 0 0 27 28 29 30 31 32 33 POTENTIOMETER READING (MV) 34 35 -1348 > w <( 6 "'8 <] 4 ! 2 0 2 4 3 5 fl p (%) 5 p 4 3 "'7 2 0 2 4 3 fl p (%) p 4 3 t/13 2 0 2 4 3 fl p (%) p 4 3 ~ 2 0 2 3 fl p (%) p FIG.33 MOMEMTUM LOSS IN CONVERTER USED IN CALCULATING COMPTON DISTRIBUTIONS NOTED c12 (d p) c' 3* _J ~~ r t~+ ~ 1/ <{ > a:: w .._ \ z ~ ~ ::::, .._ + / z w t// ~ 0 ~ .._ z Ed= 1.5 MEV t t +// ::::, 0:: w a. (/) .._ 2 2 15mg/cm .C + 59mg/cm Be \ FIG . 34 \ \ I I-' l..,J VI. I ~ z \ ::::, 0 +'~~ \, (.) \, 0 26 27 28 29 POTENTIOMETER ~-t 30 31 READING (MV) +-------'----- + 32 33 34 c12 (dp) c13 * ..J ,,:f?-+~~ ~ w t- z /f(f :::::> t- w :E z- + 2 2 C + 59 mg/cm Be F IG. 3 5 \ \ t/ + +/ \ / 0 t- ~, -f z 15 m g/cm 1 /.p ~ ~ Ed= I. 5 MEV ,A \ 0::: ~ I I-' w ~~ 1 :::::> 0::: w a.. ?' \\ CJ) t- z :::::> 0 0 :i\ \ 0 f~ ' 26 27 28 29 30 31 POTENTIOMETER READING (MV) + 32 33 + 34 -137- FOR 4 lp,10 3 ~ooP. = I% TOTAL 2 2% -I 0 2 4 3 II AP -(%) p RECTANGULAR DOPPLER BROADING FOLDED INTO DISTRIBUTION BELOW FIG . 36b 8 6 4 " ~ 2 0 ~o ~ ~ 2 3 4 ~p (%) p CONVERTER MOMENTUM DISTRIBUTION USED TO CALCULATE COMPTON DISTRIBUTION \P, 10 DASHED LINE - DISTRIBUTION EXPECTED FROM FIG. 3 6 a t 8 -138_J <x: Be+ d > Y-RADIATION hv 0 = 2 . 9 MEV COMPTONS FROM 59 MG/CM 2 Be a::: w tz + ELECTRONS X POSITRONS (ARBITRARY ZERO) ELECTRONS FROM 0 CARBON- FREE TARGET- ++ a::: w a.. E 0 FIG . 37 0' (/) 0 1- (0 rt) 0 > z ... ::> 0 W Tux :;; 0 (0 .a.E . 0 0) r<) (!) ! rt) II .s::. I LL (/) <x: w _J en <x: "'- x_ 0 1" \ 0 ---- ~ ! (/) u.J ~ -X- <x: l~+-1. (/) tT~, ---------- X o I l 0 ~__/ -X---X---x- --- 0 0 u.J 0 0 u.J (/) (/) <tW~ w a::: a.. -'-"---" WWW <]<] 25 26 27 a:: N ~ > )(. ! 3 Cl.. ::> (/) _..__ 28 _____________ -t 29 30 POTENTIOMETER READING (MV) 31 r-- r0 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - . 0 LL ++ (J) <{ w _J <{ 0 (J) FIG. 38 + +++ ++t + t 1;/+ Be+ d y- RADIATION hv0 = 3.4, 3.6 MEV w ~ SECONDARY ELECTRONS FROM <{ (J) - .59 MG/CM _J 2 Be <{ > a::: + ELECTRONS + w ..... z x POSITRONS I t-' \.,.) '-0 ~ ++ :::J ..... z w ~ • -+ 0 ~ ..... ----------------- ~ \\ . 1\f++ ~ --- -- - - - - - - - - - - - - - - - - - - ---~--j--+-i-ELECTRONS FROM ~ CARBON-FREE TARGET z ~ 0 Q X X 29 30 X 31 X 32 33 34 35 POTENT_IOMETER READING (MV) X 36 37 -,----------------------------------------------------------------------------------------!'rt) + t (!) LL \ ,.,_-+---+-,, • t t- ±t..J)';"t.\ (/) <t + w _j <t +-, 1:..--7 SECONDARY ELECTRONS FROM \ ~ 59 MG/CM ~ t <t - (/) 2 Be + ELECTRONS w ~ Y-RADIATION hv0 = 3.4, 3.6 MEV 1 1 - - - - - - -- :,-_-,;/ (.) (/) Be+ d FIG . 39 ~ X POSITRONS \ ?x _j <t > a:: \1~ w 1- z . E (,) I I-' d, ~ 'r 0 f,+. ~ :::, 1- z w ~ 0 ~ <.O - - a) ,. C\I '=r-+,t ,.,......_.....,. - - - - - - - - - - -- ---:;...---~°°: IIX +'t\ ..c.E t "' . C '.f- :f- • x::E 1- z ::::) ' (/) 1- z::::) --- "t ++ .1 - - l#,. . - - - ~ -..---r- !~ 1.&JWW -- ---- -- - ----{tr- - -I ----ELECTRONS F R O ~ CARBON-FREE TARGET 0 (.) ol 28 ¥ 29 ~ 30 , 31 I>:< , I ).( , >f 32 33 34 35 POTENTIOMETER READING ( MV 36 , 37 I -141- san1011-o woJJ- - lfJ.Jaua uoJJ:JaJa JO JJW.17 ► + + I IC) -+ IC) 0 0 - Q ,q: ~ 0 ~ )..._ C) -t: ::, (.) "'E "'E "' Lu (.) -J ~ CJ\ )... II -+- Lu'tJ <l> Ct) CJ\ E E lC) f'.... ~ CJ\ +- +- -= ,q: (0 lC) a ... / l\at,,.J gt,·t, Cl) I I I II ---.. ~ i- ~ + ~ '- - ~ Q ,q: + I + (.) Lu + I E ~ E u - a: ' ' Lu . I I + 0 IC) +/ (.) a:I lC) l'C') + ► ) l\aN ,.~ ._ <l> Cl) ._a:: Lu + I lL.. ~ + + ~ ,q: + Cl) LL ._- + a:: (!) ~ + I I I I I I • ¢ 0 I + + IC) 'lit I ._lJ..J + + J Lu + ~ I ~+ ._0 + IC) )( ,:; / /+ \... 0 I +/ I + I i /+ + I I + ►/ ► +:...------ llat,,.J 8f'f +-~ ltt/1.~3.1.NI wn.1N3WOW .1/Nn ~3d 5.1Nnoo I •' ~ /T +~+- ' 0 OQ.. I l\at,v 09'f .. ._ + + + ~ Lu + /+. lJ..J a:: a:: IC) N) +-+"+ ..J ~ \ \f ~ Be 9 + D Secondary electrons from 25mg/cm 2 Th +250mg/cm 2 Be Lu ~ \ I- lu ~ \ co I'() 1 ~ - 1- \\ ::::, ~ Q ~ FIG. 41 0) l't) r,+"+- tI ' "'-. + ~ " t :::::,. Lu ~ ~ a , ::::, ~ ++-r + :::::,. ~ • :::::,. Lu \ ~ I\) I t +. Lu ~ +\+ :::::,. l.u ~ "~ \\ j +\ t a C..) I I-' Y O R D. x/0 +\ I ~ 300 Kev Be Targe~ £ 0 = 1.5 M_ev, :::::,. :I 7- RADIATION +. C) C\J io + "-+-----+-- + -+--_+....____+ 0 30 35 40 POTENTIOMETER -- 45 READING (MV) i ----+-' 50 + + _+ 55 +---;, -143- C 2.52 2.058 Be9 +p 5.94 8 Be +d 4.08 CIO 3.6 3.06 2.85 --L - lI -- 2.14 1.42 (1.02) 0.713 r-rrn-t-t---+-+-1--+-_j_...,LJJ., (0.411) 0.55 10 Be 1=3 L ,7 L1 +a-n FIG. 42 -144NEUTRON INTENSITIES I EVANS WHITEHEAD a ET AL MANDEVILLE 3. 584 ~..,.__...,._ _ _ _ _ _ _l;..;;.3- - 1 2.856 - - 18 8 16 18 ? ~4 39 46 - - - - -,- - - - - - - 17 2.14 l{) lO I I f'- I I 3 1.432 I.{) I'- rt) 10 1.022 0 32 .7166 ~135 FIG. 43 -145- -j f--t .6 Kev -..J ~ Be 7 (K) Li 7 * Lil(pp') Lil* Q: Lu I- - <': l: ::::, \Xx I- '\,~ <': Lu l: C) 9 Be (d,a)Li 1 1 7* ::,. <I., ~ \x \ t: I - I- ~ I \ X/ \ -..J X Rt' <': ::::, Q: '\\ \ ~ Lu l 0 1 Xi •X X a.. ,\ , I (/) \~X I- \ <': ::::, ) / / \ \ 340 360 350 ELECTRON FIG . 44 \. 370 ENERGY x'-x- \ - - - - - - - - --------- 330 \ X /X ~/ C) u \ X (x'x 380 IN KEV 390 400 Be 60 + D Y-RADIATION SECONDARIES + '.'02 VACUUM + 7.0 mg/cm 2 Th 50 ++'I T\ t FROM 0 . 14 mg/cm 2 Be }\ f,/T 1: > w :::.::: 40 l'- 2. 39 % ...,..,/I -lw ~ : _v( 30~ /i 1 :,,:: I'- ,. \-- :~ \t ~ I. 6 2 % - - / :.:: § -L__------+A -J\\ 1'+-++ 20~ I I-' ~ + I II t +"t 10 + QL__ ___j__ _ _ _ _ _-:1::-------:1-:-----;;-;;~:------;}-.;;---~--,~ 41 42 43 44 POTENTIOMETER 45 166 READING (MV} 67 68 FIG. 45 69 -147- ...J ~ ct liJ I- ~ 330 340 350 ELECTRON 360 370 ENERGY IN 2 2 8.9 mg/cm Be+ 7.0 mg/cm Th 380 {I-/2/0 Kev JI- 510 Kev 0 .14 mg/cm Be+ vacuum+ 7.0 mg/cm Th FIG . 46 400 KEV z 2 390 tlII- 1180 Kev Ifl- 1485 Kev I / -148- Be9 (d,oc) Li7* COMBINED EFFECT OF DOPPLER BROADENING AND ANGULAR DISTRIBUTION ...J <{ > er: w I- z COS E= .548 Fold+ background >- (!) Fold + background er: w z w > w :::-:: r<) I- ~ z ::, er: w Cl. Cf) I- z + 0::> + 0 Background (ofter Be°'(K)Li7*) K Photo-peak from Be7 (K) Li 7*folded in . "--""----N{y)oc (I-cos oc) . N( r) oc ( I -0.8 cos ex,) N( Li7*) oc: (I-cos 8)~-i - - C O S € =.548 ..-.--cos€= .796 I ~ Doppler _ _--.i~ broadening • t trt• b u t ions • f or ~ D 1s l>p =0 , energy loss in converter= 0. 330 340 350 360 370 380 E L ECTRON ENERGY IN KEV 390 FIG . 47 400 4 1a) • 1 3 71~' MAXIMUM EXCURSION FROM AXIS 2~~· (FROM PREVIOUS EXPERIMENTS) I I-' -I=-" '-0 I r C\J z (t: ~ 8 <: '120 COUNTER OPENING FIG. 48 RAY TRACING TO LOCATE RING FOCUS (+, X - EXPERIMENTAL POINTS}