UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Electronic phenomena in liquid argon and liquid helium Williams, Robert Leroy 1955

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata


831-UBC_1956_A1 W4 E5.pdf [ 7.02MB ]
JSON: 831-1.0085422.json
JSON-LD: 831-1.0085422-ld.json
RDF/XML (Pretty): 831-1.0085422-rdf.xml
RDF/JSON: 831-1.0085422-rdf.json
Turtle: 831-1.0085422-turtle.txt
N-Triples: 831-1.0085422-rdf-ntriples.txt
Original Record: 831-1.0085422-source.json
Full Text

Full Text

A N D L I Q U I D mum by Robert Leroy Williams A THESIS SDBI'an-jLD IN PARTIAL FULFILMENT OF THE SEQUIREKfiHTS FOR THE DB<3tBE (F DOCTOR OS* PHILOSOPHY la the Department of PHXSICS W© accept this thesis as conforming to the standard required from candidates for the degree of DOCTOR OF PHILOSOPHY. IJembeafe of the Department of Physics SHE UNIVERSITY OF BRITISH COLOMBIA October, 1 9 5 5 %\xt Jlttitueraitg al f b i t b l j Gkilmnlua Jrlimtl (BKBI ^ xmximtiaxx lax tlje pnn^e ROBERT LEROY WILLIAMS B.Sc. (Western Ontario) 1951 M . A . (British Columbia) 1952 F R I D A Y , O C T O B E R 21st, 1955, at 3:00 p.m. I N R O O M 303, PHYSICS B U I L D I N G C O M M I T T . E E I N C H A R G E Faculty of Graduate Studies P R O G R A M M E O F T H E H . F. ANGUS, Chairman R. E . BURGESS A . M . CROOKER E . V . B O H N F. M . C. GOODSPEED B . A . DUNELL G . O. B . DAVIES C. A . BARNES G. M . SHRUM External Examiner—D. K . C. MACDONALD National Research Council of Canada E L E C T R O N I C P H E N O M E N A I N L I Q U I D A R G O N A N D L I Q U I D H E L I U M A B S T R A C T The development of low noise electronic equipment has facilitated the observation of ionic conduction pulses in l iqu id helium I and II, and a substantial extension of previous observations in l iqu id argon. Electron mobility in argon has been measured in fields between 2 k V / c m . and 200 k V / c m . , the high field values agreeing with the order of mag-nitude previously reported. The scattering cross section for electrons is found to be of the order one hundreth that observed in gaseous argon. The low mobility of positive ions in l iqu id argon, observed for the first time, also shows that the l iqu id does not behave as a dense gas. Mobilities of both positive and negative ions in l iquid helium I and II have been measured also for the first time. The positive ions have low mobilities of the order of the positive ion mobility in argon, but the anomolously low mobility of the negative ions has not been explained. Ionic recombination, investigated in these liquids through direct current and pulse amplitude methods, is not described by the existing theory. Considerations are given which invalidate the model on which the theory is based, and an alternative model is suggested. GRADUATE STUDIES Field of Study: Physics Properties of Matter A . J . Dekker Electromagnetic Theory W . Opechowski Theory of Measurements A . M . Crooker Electronics F. K . Bowers Nuclear Physics K . C. Mann Quantum Mechanics G . M . Volkoft Spectroscopy O. Theimer Theory of Magnetism W . Opechowski Electron Optics U . F. Gianola Solid State Physics A . J . Dekker Oceanography G. L . Pickard Other Studies: Differential Equations T . E . H u l l Chemical Physics K . Reid Integral Equations T . E . H u l l Theory of the Chemical Bond K . Re id th& doTelopa»nt of low mice electronic e q u i ^ n t hatf ftttttttsfeea the obttepvttiou cf aaal© eoitfutftien puistws under elpha bafiibai^toeiit i u liquid helium I end H, antf a eulietaaUel oxtonaloa of previous oboorvaUoas i i i liquid arg*n. Slootron nsobility i n ergon had bsott caesumi In botyoen 2 Mt/m* sad 3fJ0 kV/ca^ the b£#i field vjatios agrcalog *&th the a*a«r roagnitttri© prcrviausly reported. scattering arose section for electrons ie faunS to to of the order one hundredth that obeerved i s gaseous ergon, Ifca low nobility of poeitiva ions licpitl argon, observed for th© f i r s t U©©* also ohova th&t the litjuid does not behave ae 6 dense JfobiliUoe far tooth positive una negative ions i n liquid balim I Bad II hsva been eoaevred, ai09 for tha tine* H» poaitive ions haw lot* twbilitioB of the ordor of the positive ion mobility i n argon, but the anorak oiuOy low ©ability Of the ragatlw ions has not been osplainoa.' Xoa&o rocoobinetion, Invcstiseted i n theco liquids Uurou^i direct current find pulao e?aplltude cathodfl, i a not described by tbo existing theotfy* Considerctiona a#© givan which invalided the codel on ufcich this thsswy i e based3 and on alternative* sagel ie ftflgptftta*' I uleh to oxpraofl agr dnearo gratitude tso Professor B*l* Surged for hio euggaetiane asd dlccu&uiono cotKwartdng the a-^riiaentnl roaulte, and for bis bclpftd cocEonta relating to tbd preparation of the th«eifl, I am also grateful to BJ?» P »JJ, Stac^r for tho tiea ha dovofcod to nany <Iiseu3sio»e of tba exparimntal technique and results «fe£<& enabled th© significance* of tfea data to ba interpreted, fend for 24s holp i n prepfiTftUon of th© canuscript, I m iadcbtod to the Defence Beaearch Boavd «ho oupportcd the reootroh, to tbo JfeUonel Research Council for a otudentehip 1951-52, to ths British Columbia Tolephono Coaapway for a scholarship 1952-53, and to tiie Rosoarek Council of Ontario for a fellowship 1954-55, S IBPQ&BOT® M I' H M « • H t « M M M » I si mmm -$mmmm& Mm • * • » » « » « * « » * # i ft« Icjateatios Proooeffl , « « , * . . * , . 4 3, I^obility Keaatarwaosrts . * . . * 6 3 0 Puieo **s&itKdi Distrifcution » • • « * • * V 4» Bireot Curreat mmmsmm • * • • • » • • 8 £Ct SaSQRSTICAL BAQiCGKOOra) , , • « » * , , , « 9 2« Kinetic ?h«*y - Geaaral CSoacopta 9 • , • « 16 $# Sloofepoa £5o&lity • « • # * » » » « * • • • 80 4« CSstribiitlon of electron Energies » . # , « S# Jlsuwssaw Bffotffc * • * * * • ? • * * « « • * 24 6. fhao*^  of DAmelon i n Liquids » , • • • , 25 !• S&a Elsotrode 3yet©a * t • * # * # * # * • 30 2* High Volteg© Supply • • » * « * * « • * • » |2 3, Signal • « • » • « » * « • « * * • • # • • 3& 4« Slee^wslo Soi@o • « • * • » • * • « # • • 33 It Amplifier Itandultftb fot nobility rtoaeurooonta 35 6» Eendwidtii for Anplitade Disfepibutiooa 35 t«. Boise I M M B I 36 S. ©arreat JJeaswaiamts • • • • • « « « 33 0* ^Molding . a . . . . . . . . . . . . . . . 33 V A r a n s a s OP i m jmuiTAL J?AS:A . . . . . . . . . . . 40 1. Rise S im » • • * • • • • « « • * « + • • 40 d« Puis* Aoplitud* Distribution . . . . . . . & 3* GeoDotrical Effect of Alpha Ferticle Rang* 42 4« me Effect of tfei** on Pulse Biefcributtons 44 5. Further ttaie© Goacidoration* . . . . . . . 47 6. Holco Correctiono Used , . . . . , . « . . 50 7. Itoooafciration aa a Itetioh of Angle of Sedation • » « • * • • • • • • • • • • • SO BxraRZH^ SAi. assies - mmmm $2 1. Bioatom Ziobilitty In Argda . . . . . . . . . 52 2. fobOity of ftwitive lona In Argon . . . . . 53 3. Obaanration of lonio liabilities in l«liu© » $6 4* Values of the lonlo HobUitioo la Helium . . 58 5. Temperature facts in aalira 60 1, Infliteaco of the Geometrical Effect in Argon . . . . . . . . . . . . . . . . . . 63 2* Raoacblnetion m Argon Detiaated froo Pulaa AEgalitude MeaeurecantB » • • • • • • » 65 3. Direct Cumat liKHRsraasftta * Argon . . . . 67 f 4. Mm £fei#»fc Distribution * Hellra 3. PUJLBO Height Metributioa * Holitsa 6, Dlroot Current ll|Ma*tfmrt* - fioliws » . • * 72 X* Mobilities i i i A^goa « « • • » • * • * * * • 74 2« itobilitl©a in 8&litK& 76 3« R©coc3biaatio3a * » » » « * * « * 9 « a « * * 79 BIBUC I EXectrodee * * to follow 30 2 Block Diegra it of ^>aratue « « # , • to follow J2 $ (hJWf#&t^ 0il#ij sgd Bursts • to follow 33 4 Circuit for J 57 5 l&ooretlcaCL 1 Pt&fe DiatritMtlona <G) * # • 49 <b> * « « * » * » * 47 I Argon Puiaee * . . • # * . * .* . . • » to follow 23 Helium PulfleO * « * » * * * « « » * * t o fallow gables 1 ..IUXIII • B i » • • * » * * • *, • • • • S4 2 yu<^  ^8 $ * * * * * * # * * *• •# * * #• * » # * * * 54 | EstinateB of JH * fteVBTOed Field 63 4 Eatiimt^a of Jt ? Single Metribctions . 4 , • , • • 64 0 Beliwn Pulso Heij&t JSeaeureaosita f * 1 .705 • • . • 72 AnpXitudo ?§ Per<antago of ft&ges for ftot#» . . . # • 4 * * * * e • • « f * « « » • * •• W In Gaseous H * »ft ' * va S i n aolii« at f * fetptt * « » Bavema* Field Dietrlbutlone i n Argon (o) Q vo at, Retribution of tula* Sielgfrt i n Argon (b) Q w % CiatrlbuUon of Aside Seigii In Argon nj vt S i n Ax@on • * • • « • « » • • * n vs 1^90 E i n Avgion • 4 « « (t) Q 1» * i n flaUm at T » 4*22% 4 *» •!$ l ^ j ^ i i v * f&aJUl '# • » • • • » • » # • (b) 9 II $ i n Holiya et T » 4*22°K, 6" ** «l$ QaS*^  Begstlvo $&$3MI • « • • « • * • * * « Q v# * i n Relim «6 ff * i»Z&% £ « .33 (a) $ V8 x In m$m fci f •* 4*32?$* 10 53 65 65 6$ 67 16 (fe) $ «* * .Ift IteOitaa at f * 4.22% & *» «3@ « M 3 * # Pasitavo Field IS 1 , 9 HoltMKork Phases i n £$$ffi * , » # * « * * * * *. « 72 i w , mmm^Mj^m»,mm m , m m mm After the discovery of nuclear particleo, tha Gaiger-KuUa? tuba t*»a devalop&d to study their properties i n mm detail* Ute §&e©s need i n CMS* tuhett acted aa ionieablo .stadia* using the energy of ttuclocr particles to aaparata electrical chargea. Amplification of this primary ionisation, which wao proportional to tha energy af tho particles, V B O obtained by collision of electrons with atoms near the positive electrodes, ftibee -usad for this purpose contained g&sm vdth low energy per ion pair — tho average energy aspaadod i n ionising a einglo ato&« She properties of tha gosee could bo otudied mm effectively by othor ©eans, and too tubee war© need for investigation of tho proportion of nuele&r pertideOc Particle rangeo In vericrtiB gescs war© Eoaeured. at different pressures, ©3tabliohiag tho constancy of range t$m& density i n each gaa* Owing to the electron avel&nchea vhich developed i n tho tubes, they had long daad tisaa or recovery ti&ea« In tho aaareh for counters with short recovery Ussee, liquid argon was used as a detecting saadira by Hutchinson (1943)« Following thio, attention vao turnod from tho feasibility of using ergon aa a counter, to the nae of alpha particles to etedy electrical proportiea of tho liquid. Information «hleh can he gained from a detailed atudy of ionic collection i n liquids i e throe-fold. a relating to ionization. reeecMnation, and ionic nobility i n the m&Ltm Alpha partielee, entering e gaseous or liquid sedinm, lose energy by ionia&tion of the sodium* |he electrone produced i n thie prooooo have energy ic^artod to them i n exeeoo of that nec&eeery for ionization, and vasdor i n tho iB0fiiu% being rapidly reduced to thsrcal energy by repeated collision tdth otos&s* In the absence of m eleetrle field* they enoowitsr their parent or other positive loss* end disappear by recombination. An olaetric field existing i n the rsediun et the ties of icnisatioa, tends to separate the electrons end positive ions* vbi<sh dr i f t to the elects-odea between vision the f i e l d i e applied* from © etudy of the current puleee produced In this nanner. and the neanuresaent of tho average direct current produced by charges freed at an ionising event* &om information nan be obtained about the recoBfain&tion prooeoe* In previous direct current investigations of recombination, the field range never exceeded 1000*1. In such canes, nouever. the variation of the dlract current eeceurcd seldom exceeded 3«X«, 8&nee those jaeasureEents were confined to the region of oaturetlng ioniaation current* they provided no adequate test of recombination theories* end larger ourrost variations usually suggested digagrement t&th theory, fulee ea$litude seaaureffiente have been of l i t t l e value as the signal variations are even orcaller* I^provexaente of sigaal to holee ratios i n the nmsuromnte described i n this thesis have refuted i n the observation of laueb wider ranges of currant. 3 She titt&lAtar of th© Ions (their ds-Ift velocity par unit floltl) hc3 baen eoMa&tod by csaouring too tins taken for collection of tho ions at the electrode*. I t beet been related to the cross Gectian for collision of ions with atone and the overage energy of the loos* IVevious iscoevriffiisnts ouggoett that KiaaUc Shoos? ie appUceble to electrons i n liquid ©rgo% tut eloctronic noise raatrictsd tbeea laeaswreEHJtite end prevented the observation of pooltiv© ions* Iaprovarcents ea&odled i n the epporates ^ ooribod i n Chapter IV nave m a d e possible e m a r e oahauotlvo study of both the positive end negative ©arriers i n liquid organ at f « 90°S end these imsuren&nts have boon extended to liquid holiun I ea& 11 over the t e E E ^ r a t u r e range i,4°X to 4.22*5. 4 ^ She loaiatntian Pgaeesa Serly work on alpha particles, using gad tubes* attempted to establish relationships between the energies of particles and the lengths of their ionization tracks. Aa aoon ao tho proportional counter had boon perfected, a great deal of work was devoted to detersina the effect of pressure end energy on particle ranged (iivingeton and Bethe, 1937)* It haa boon v e i l ectabliehed that for any substance, tha range of an alpha particle l a inversely proportional to the density. Aoienson (1955) 5 using a scintillation technique, haa obtxwn that particle ranges i n verioue liquida can he predicted from tha naesgefi i n the gaseous statea of the asm mteriale within one percent, the error of his apparatus* the accuracy of these roeulta Justifies the use of tho values of alpha perticlo raagoo i n liquid argon and liquid heliue, calculated from m&mmmti^s on tho gasea* Haebarli, Hubcr and Baldinger (1953) perforaed detailed eaporlmonto to ©assure the energy per ion pair expended by alpha parti oleo i n ionising gaseous ergon and helium for which they found the values 26*25 ev. and 29*6 ov., respectively* Freeaures froa one to five atoeaphsree shoved that density did not appreciably affect tbeoe values* Earlier, lees extensive work by Sharp© (1932), Valentine and Currnn (1932) and Jease and Sadauakl (1932) a l l produced valuea i n 5 agrooEent w i th those* Eovsver. an i n d i c a t i o n o f how l i t t l e th© $mmm i o understood was provided by Bortnor and Kursfc (1954)j uhe* i n esporifflonte u l t h h igh ly p u r i f i e d h e l i u % obtained an energy par i o n p a i r o f 4&»3 ev . Ca lcu la t ions raado by EreMne (1994) g ive egreessent wi th t h i e value* and he a t t r i b u t e s the love r values reported by ethers to email aKsounts o f impur i t ies i n the h e l i u a . I t i e necessary to know whether any o f tho alpha p a r t i e l e energy i s expended i n tho source i t s e l f * %dey (194$)* us ing a oses spectpogrepha has aeaeured very accurate ly the s t ragg l ing ®? energies of alpha par t ic le© from sourees deposited on n i c k e l * sine* s i l v e r end cadedum* B i s r e s u l t s shoved that f o r s i l v e r only .3$ o f the p a r t i alee had energy losses greater than 1/3$* OedB&um based sources had a wider spread than the others* but i t wee s t i l l very smll, Haeberl i* Kubor and Baldingsr (1953) a l so showed the s t ragg l ing i n t & o i r sources t o be neg l ig ib le* In experiments described i n t h i e thesis* euoh s t rang l ing e f f e c t s ere much essaller than the inaocuracios o f jaaacmreiBent* Ones the ranges end energies o f p a r t i o l o s had been establ ished* i n t e r e s t was aroused i n the i o n i e a t i o n process* Cloud caesaber ^hotogrnphd of a lpha p a r t i c l e treeke shoved a m l l l a t e r a l spurs* the energies o f these 9 I r a y a 9 vera e s t i m t o d from t h e i r t rack lengths , uhleh ind icated that they vera h i$a energy e lect rons ubose nmabere could be estimated f o r any i o n i s i n g event. AUQOV (1926) and Chedwick and SEBleue (1926) considered t h i s problem and achieved soiae egraecsant between calculated and measured energies* According t o t h e i r 6 calculations the energy electrons should ha*#- had'-a large* forwnrd component* cat evident frsu the traeh •photegra&hi* iMeh'appeared to justify the .earlier aas«es$titta that tha electrons a l l ejected • n^rpaBaistilfira^ to .the track* !Jo xaathod hes hson devised for determining the distribution of ©ioctror, ejection velocities. Hutchinson (19-43), i n a search for a faet nuclear counter, attested to seaaure the electron sobiUty Is liquid argon* Technics! Imitations restricted bis conclusion to the atateneat that the motility io greater than 4@ cat^/volt-eooona at fields greater than 13 Wf/m» BevMeoa and Sarah (1943) carried out exporimoats an conduction puiaea i n liquid argon i n an a t t e s t to iBeasure both electronic stability anil the effects of impurities on recombination* ©ley experienced tho mm d i f f i c u l t A S Butchinaon i n oeaauring nobility* fho firot j^eareiaenta of saebllity were obtained by t'alidn end Schulta (1951), •whose values appeared to vary as E* 2/ 2 over the range 12 kV/ca. to 83 kV/cn. Shey obaerved a cofallity af 20 cG2/wlt-aacond at a field of 2$ kV/csm., within an estimated %3$ error. Aaaucing Kinetic theory relationahipo to hold, this yields an electron collision cross section of approsicntely one hundredth of that observed i n gRseoue argon* 7 Walidn end Schults reported having found conduction pulses i s liquid helium* but gave no information eeneernins their ohareoterietics* JSareholl (1953) developed a lipoid ©rgen counter to cseeuro the beta spectrum of I t 4 0 but hie apparatus use unsuitable for fundamental asasttresente on the argon. A second series of esperioents was reported by Davidson end Igrsh (1950)* «ho attested to study recombination i n argon from an analysis of the distribution of pulse sides. Iheir distributions w e roughly accounted for by the effect of alpha particle range on tho frcotion of electrode spacing traversed by liberated electrons. Their distributions uere codified by the dependence of rocorsblnatlon upon tho angio of en&aaioa, but they did not eso&ain the apparent disappearance of this dependence at lev fields. I t i s shown later i n the thesis that this difficulty arose from an incorrect interpre-tation of the effect of a j ^ l i f i e r noise on tho distributions,, Shis noise l i d t e d their ro&eur&sente to a field range of 7 i l . 8 AH oaparlcEnt&i work on racosbin&tlon In ionization colusns forced by alpha partioloa has-' boon rolatod to tho theory developed by JeTfo (1913) • Jaffa was able to f i t to his theory the results of his own ezperiisenta with gasao-ue carbon dioxide, air and hydrogen* and tilth liquid stathano and hexane. Oerritsen (194S) perfonaed eiiallar o^erimente with liquid ergon* h e l i u % nitrogen and hydrogen* She Held dependence of the currents i n hydrogen and nitrogen agreed vdth tho Jaffa theory, but agreement was poor with argon and holiue, i n uhieh there was ten Urns aa nach variation i n current. Baeberli* Huber and Baldinger (1953) performed direct current and pulee e&plitude ©eaaurofflenta with gaaeoue argon* helium* nitrogen* osygen and carbon dioxide to censure the energy par ion pair. Hbey eoaparod the field dependence of the direct current aeaeuroEents with the Jaffa theory and found that i f the current variation was hot large that reasonable agrsesseot was obtained. Bear saturation the pulse aag&itude diatrlbutionf aloo agreed with the Jaffo theory. 9 Wtmn any Esediua ie ionised* coae of the positive end negative ions reesE&dBs* unless a very high field ie present. Ihe behaviour of the ions during roeo&bin&tion i s classified according to tho Eothod of Ionization. (Loobs 1939a). Alpha particles produce ions i n small* dense columns along their trades* and tho reeosMnation process i s known as columnar recombination. She Boat extensive verls on columnar recombination has been carried out by Jeff© (1913). His analysis applied to recombination i n substances i n which the electrons icaediately forn heavy negative ions. This analysis i s sicplor than that of electron»lon recombination as i t allows the use o f one mobility*yt/ f and one diffusion coefficient, B * for both charge carriers. /Q. though argon and helium atoms do not form negative ions* and require a modification of tho Jeffs' theory* discussion of the theory illustrates the problems Involved. Xn Jaffa's theory i t i s assumed that before any soaker separation of charge from the track of an alpha particle can occur* the electrons a l l bsee&e attached to neutrel atoms, and that the positive end negative ions centred on the alpha particle track* have a Gaussian spatial distribution vith the same standard deviation* b « Ilia density of the 20 ions io sodlfied by diffusion* transport of the charge duo to en applied field, s , and the removal of ions by recosMnatlon. She eosbined offeete of these prooaesos can be repreaented by an equation i n rectangular coordinatees* ^ 2l \ ^ r (1) the Held io parallel to tha y aada i n the as • y plana. -Tl =L represents the density of positive and negative carriers. o( i a the recorablaatiao coefficient* and <fi tho angle between tho applied field direction and the particle track, toe charge densities have cylindrical eyeasetry* so that only the dri f t component perpendicular to the track has to ba considered. She track ends are apodal cases* dealt with ceparately. Jaffe aolvea the diffUEion-oobility part of the equation* neglecting recombination, and then eppliee a correction to include Ions drifting laterally out of the column cannot r e c l i n e once they are dear of tho cloud of lone of the oppoaite oign* and although their density jaay change* their sassbere do not. She masher escaping laterally i s tho solution of equation <1) for t » oo m the caution obtained by Jaffa for <p = 90° laa* \ oo _ t L _oo being the nusfcer finally escaping, % tha nunter i n i t i a l l y bV 1 2- 0 end %jhare i® the Hanleal function of the firet kind of order aero, Bur the condition I , &,e« large flelda, this baa tha A/ , Ho which can ba teated oacily. Ions drifting along the coition, <P a 0, only eacepa recorMnation by reaching ita end* 3b determine the anchor, B ^  , escaping, the velocity io multiplied by tho linear density, I I (t) the s o l u t i o n to ( 1 ) , and the product integrated ovor the t i ra j i n t e r v a l reqti ired f a r e s i o n t o t r a v e l the whalLe length d o f the column, sL 0 where /* • * Z'1 •>» assuoing 4. » • Subst i tu t ing f o r K ' ( t ) g i ven , vber© and t mini 1 in * 2 / x . B Aa tho length of tho colunn i e such greater than i t a breadth, the nusfcer eecaping a column t o which the f i e l d i a p a r a l l e l i o l e s s than tha tniEber escaping i n a perpendicular f i e l d * J a f f a concluded that tha r a t i o of the nuzsbere escaping i a the two instances i e roughly proport ional to the r a t i o o f the eclissn disansiona which ha eat ioataa t o be about l i lCQO. 13 In eoi^dering the direct' current observed vdth e source -'' enduing alpha fartielee i n a l l directions randoMy. one can neglect tho eoBspono&t of ionic escape longitndiie^lly along the tracks* provided that the fie l d i s not largo enough to produce an ionization current approaching saturation. Under these conditions, the solution of equation (1) for tho average nuefoer. S <*> . of lone per alpha particle escaping recoahioatlon 1st-U A/a Strb 5 where and <Pn i e the angio of es&seion at whioh the taaaber of ions escaping recesMnatien i s the sa$e as the average number for oniosion et a l l angles. I f ? > ? / t this equation can ho simplified to, M0 . . u Jaffe applied bid theory to the special cases of ah alpha source; -collicated parallel end perpendicular to the field* Applied to GO^ * air* % at atmospheric pressure* the theory agraod reasonably vith o^sri&aatfi*' Ihe field variation Da the cOTorlnsentD wm of the order 50tl hut the measured currents only varied by a factor of -fm or three* indicating that they vers mar saturation* Ho further test of the theory was provided until Gerritsen (1943) performed e^erissentn vith an alpha source emitting partialoe randonAy i n a l l directions. U^uid nitrogen* nydrogen* argon and hellutu mm used* and the ionization currents measured over a wide range of applied electric field* Gerritsen una dissatisfied uith the agreement of his data with the Jaffa theory* and Kramers (published by Qexriteen, 1992) produced a solution of tho transport equation i n an attempt to obtain a better f i t . Xre&srs neglected ionic diffusion which he assumed to be Very smell i n liquids et low temperatures* solution WB s&sdlar to Gaffe's theory at high fields* but the discrepancy with Gerritsen's data vhich appeared «hen a wide range of field van considered, necessitated the inclusion of a diffusion tors* Hydrogen and nitrogen appeared to obey Jeff0'a theory* but argon and heliUD did not* Ihia i s not surprising* ainoo the theory developed by Jaffa' applied only to ions* allowing the siaplifications ^  + » - and 8* # B„ * *&en one of tho elementary eharge carriers i s an electron thia sdk^tificstion cannot apply and the equations beestse even ssore difficult to solve. In spite of this* Gerritsen and Erasers attested 15 to apply tho theory to conduction i s liquid argon ana helium In which the electrons regain free* Haehtfl&f Buber and Baldiager (1953)? using a pnlae teehaiqns to &&t®ms&m the energy per ion pair with poloniun alpha particles i n various gaees, eonaidered raeoEhinatlon for rendoa esaiaaion and the field dependence of the ma&tam charge collected per ionieing event* Seing Jaffa*a theory of 1913* tha equation for the nunbar of ions escaping can ba written eat-N - , !_ No I +• " For a fijjod field* the distribution of pulse he&ghtd las« i&ere k and k* are constants* obtained reasonable agreement % 1 with thia equation and linearity of va* - | r - for the largest puleee* except a i high presaurea. So explanation wae given for the lack of l i n e a r i s e& tha higher preaoureo* 16 Kalkin end SchuLta (1951) uaod foraolao from tha Kinetic theory of gaeas to calculate the scattering cress section, Q * of the ataae of liquid ergon for electrons of csastired eobility . kinetic theory alee used to deterMaa the average eaergy* £ , of the eleotroae under the conditions of the ei^ericant* 2neee relationships and the concepts on ubich they ero baaed are very holp^ul i n tinderatanding the proble% and especially i n interpreting the results obtained with liquid helium and the positive lens In argon* In the discussion to follow, and i n the remainder of the thesis* the following notations will be needs* <o aean free path of ions k m 3ean free path of electrons «» olectrie fi e l d © <m electronic charge m *» laaaa of electron «• A t&ss of positive ion a» naae of negative ion I a average velocity $ <• r 0ci,e 4 velocity k «» Boltsssan'o canatant * absolute temperature £ - energy of particle M • mea of atom 6 dielectric constant 17 ^ «> density r d» radius of atom r • radius of ion Q • arose section ( O E I 2 ) Subscripts affixed to the shove symbols mUl have the following meanings* i - ion, positive or negative 0 • eleotron * * positive ion - - negative ion She units are c.g.s.. e.e.u., except where otherwise stated. the taodei considered i s a gaseous oedima of 3 perfectly elastic spherical ooleculoa per e.o. having a cross section Q § between tMeh ions of tho earae size are moving. She average distance travelled by an ion between collisions i s L « n . ^ , A , . . , , She \ffi 4 a % factor 4 arises frse» the asfiue^tion that the ion has the sane cross section as a neutral atom «hieh allow the centres of the two particles to approach within a distance 2 the factor fz arises from n consideration of the relative velocities of the colliding particles. I f tho motion of electrons i s considered, the factor fz i s cMtted as the electrons usove so such faster than tho ntoas, and the factor 4 i s osdtted because the electrons are regarded to have negligible cross sections. f&esieatary Kinatlc Theory ohowe teat i f tho onorgy of ions i n en electric field ie essentially therssl* their mobility i e , end that. In the 8&Epl© analysis, two effects have been neglected uhieh oust be incorporated into tho above forssalae* 3&a f i r s t of these relates to tha laaeees and velocity distribution of the ions* langevin (1905) shoved that i f the velocity distribution io Kaxvellien, then the stability l a given by«-7 nc<- V r<\ U ) Una second emission of the siople theory van the Increase i n ionic energy due to the presence of an electric field* Cotton (1923) gave an analysis of this effect, assuesiag a l l the ions to have equal energies, and Cravath (1930) extended tho theory to include a velocity distribution* Gravath found that the average fraction of the energy lost by an ion of energy* £ , on collision i s . For high fields, 1» «hloh £ }7 teT, and % < < H, this fraction 2bis fornula la normally applicable to electrons* fhs introduction of tho factor f to the theory, allows an ion to retain ease of the energy i t gains froa the electric field, so tfa&t i t continues to aocntMate energy until the fraction, f , of i t s total energy lost per collision i s equal to the average field energy gained i n one mm free path* This aacursulatlon of energy results i n a root taean square velocity of the ions vhioh i s greater than the theraal velocity and i s given by, becomes t- EL $-3 n JL Shis changes the mobility foraal© to 'fhe assuoption that tho ions and maiecules eon be treated as oiastlo spheres appears justifiable i f tho ionic ensrgy l a 8»eh grootar than lcT„ Since the field energy of an electron ie given by £ m .Jfe** , end **X» * even In hydrogen, l a opproxirflatoly * f t (2 for eleotrona i n a l l useful fields* Electrons have relatively very s&ell areas stations so that when they collide with atoms* they approach within J~£p • Ifcue x ° - i f -Tho above inforssatio% coupled with tit© fact that the M of an electro© i s very attgh leas than that of any atom with which i t tssy collide,, allows tha mobility equation to be reduced tat* the cross section. Q * i s of aero interest than A » which i s saade th© subject of the above equation and used to calculate Q 8* Q -_ Q-3 She average energy of such a system of electrons i s * £ » 1/3 where 6 3 .922 6* ax j^eleculcs of a gas i n equilibrium at temporeture 1 hev© a Maxi&lllan distribution of speeds, u , given by, A M J « = (jft.^ -^(r r # ) " J t t vhep© «. it) the speed considered, H( u.) d tho nua&or of iffi&LecUlea with speed i n the range u. to irr^eetiv© of direction i n space* Khen an electric field l a applied, the charged particles of tho systea dri f t i n tho direction of the field, gaining energy each taaan free path, end losing a fraction, f , ef i t at each collision with a molecule i n the aediuta. After cany collisions, the charged particles have a steady state energy distribution. Bte f i r s t successful a t t e s t to find this distribution use that Of fteuyvestsyn (1930) Uio assutacd the absence of reco^dnaUon, Ionization and excitation* the ions travelled distances isuch greater than t , end the nolecules «ero elastic spheres with cross sections independent of £ • the fractional loss of energy per collision van f «* 2.66 fhe distribution obtained me siiniler to a Haxwalllasi* K i t h average and r*ie*a» values not very different from those of the sere field Kaawellian distribution* 22 Ss&t (1937) attempted to salvo tho oore gotterel problaa uhich included imlestie collisions and Ionizations,, In opocdUil eases tho solutions ©greed well with previous work, hut unfortunately tho general torn of the energy distribution was not staple and involved tedious calculations. Horse, Allie end Laser (1935) considered the energy distribution vith a Variable cross section. Xhey vers able to show that the velocity distribution use no longer of the tiexvolllcn fora, but shifted to higher or lower energies i f A ua® respectively a decreasing or increasing function ef energy. 2he values of the seen energy did not differ strongly from that predicted by the Siople theory unless the X - £ dependence use strong. the nein consequences of e l l the theories are the following, the ions, because of their large Eiasees, do not acquire enough energy to deviate seriously from the Maxuellien distribution. If the electron density i s 10 9/c.c or greater* the electron interactions produce ths EaxuelUen form (loeb. 1939b). Even for electrons tdth fei$i average energies, l&portont deviations only occur for the tails of the distributions, not C end 0 « On this basis, the general aquation (a ) for the root Keen square velocity i s applicable to electrons i n practically a l l cases. She error involved depends on the deviation from the Masyelllon f o r % and i s greatest uhen A i s energy dependent. 2$ #or liquid ergon at 90% the aseun^tion i s E&fie that the electrons are liberated i n tho ionization pyoceeo, and do not form ions* so t h a t ^ e i e given by (aquation 5)i-Me. * 2*11 a I© 6 M • ^  . 7 c volt-sec. She oorraspomlins Bean fife© path io X » 1,88 s l O ^ / e E etaS*, (6) yielding a cross section of Q « 2«?3 38 10"*° CBS2 , and a staaa energy <f i s £ » 2*14 a 10"**Ae B 2 electron volts* For liquid heliua at the boiling paint, the corresponding equations for electron cotion ares* volt-ooc. A * 5*96 a 1 0 - ^ A £ (7) and £ n 2.18 x H T ^ ^ B 2 electron volts* 24 Leonard (1903) found that tha probability of collision o f electrons with atosia i n organ exhibited a itetttaiuirt vith respect to aloctrio field, bat decreaaed ooaotonically vith an inoreaae of electron energy l a He," H 2 j, C 0 2 and air, Ba^&aner (1921} repeated the exporicssnts i n argon and extended them to low energies, at which he observed both a itaadwaga and a mining. Bolt-oark (1929) derived . a Quantum ffechantenl Gaplanation of this effect. In the Quantum S&cbaniosl approach to the collision process, the incident particle ia considered aa a group of partial waves, each with a given quantised angular mcentum about tha center of scattering* The total collision cross section i s than tho sum of the partial Scattering cross sections, calculated for each partial wave, i*e», tOier* % i s the total orosa section for elastic scattering, and q ^ tha cross section of the partial uave of angular oon»ntum^C • the term v\jt represents the phase shift experienced by this partial wave as i t passes through the potential of the scattering center, and is l a the wave vector of the partial wave* HoitE-erk found that e aodifieation of tho Hartree field, produced by a Ssall snount ef polsriaation, gave phases end a resultant total cross aoctioa exhibiting the choracterieUee of the Raossuer effect. She phases are reproduced* along with calculated and observed Croee sections for collisions i n ifessey and Borhop (1932* a»b)» Only the partial u&ve* wltfc X C O , has a large value of ^  » at snail energies^ end i t s phase ^ 9 passes through a multiple of vr * giving a sinisaas cross section* &% a higher energy the staa of the partial cross sections exhibits a madmm* In liquid argon* the prositdty of neighbouring atone effects tee polarisation codifying this picture* Calculation of cross sections fron aohiiity Koeauroaants described i n this diesis desaonstrate this effect* She behaviour of electrons i n liquids can be inferred from the application of Kinetic llheory* developed i n Section 7* to cobility sti&suronsnts* this i s based on the assus$>tlon that liquids can be treated as very dense gases* but* since liquids have properties distinct from gases* a consideration of theories nor© specifically developed for liquids i s relevant* Shoorlos of diffusion i n liquids have been developed* end aa nobilities can be calculated from diffusion coefficients through the Einstein relationship, those can he used to interpret mobility EeeowoiBBats. The cost successful theory of diffusion In liquids i s that developed by Eyring (1936). She diffusing parti olae spend East of their tisa i n potential wells of average depth, U , vibrating with a freniaanoy ^ • *&>en trapped* a particle, being i n thermal equilibrium teith tha sodium, has a probability of escape of "ft ~ jjper oscillation* Slse iaeaa t l m spent i n a potential veil i s & * She diffusion coefficient ie proportional to the average velocity of tho particle, v , ticoe the average distance, d , i t travels fro© one well to the nest** D » const* d«v This i s rewlttens-P o d 2 s « s i s the rata at which particles leave tha potential wells, and specifies the laoat probable direction of Eotion. It i s caressed as whore 0 i s constant related to the progress i n tho direction of diffusion* Using the concept of free VOIUSBS, Byring (1936) calculated a value of c \) , deriving the following equations* % io the heat of vapo*u»is&tioa par atoa, & the atoMe ©asa, 8 the gee ©oast&nt, and % . the free volume. , > For ^natosaie liquids* l a the vapour pressure at twapature T « Daing tha Mnsteia rolatdoashlpp the squatioa for E&billtar 6ale**latioas b&aad oo the above equation produce* valuea of E 0 which are on the average 2.45 tlajas too assail. (Jest, 1953). She equation i a used i n Chapter VI to estimate tho valuea of % for ergon and heliUB liquids. Bolog known valuea of the constants, the equation can be reduced tos-Lk = .i*r W- ~J_-£ffiL for liquid halloo, (0) / L f}SrV-sec. at T = 4.22°K. beesHs©®, 23 for liquid argon. et f » 90°2* B 0 being i a csl./gcaton. It ma% too noted that In tho ease of liquid fce>liu% no eonsMmtion has teen given to possible effects resulting from the aero point energy. I t Is comparable to the thermal energy at 4.2°K, and suet inflnenea the behaviour of the electrons and atoms* She stability can also be predicted through the use of Stokes* Imt rMch relates viscosity* ^ * sahiiity* t( » and the radius of diffusing particles* •* this formula only applies to particles, e.g. ions which are not small by comparison vith the ato@0 of the liquids. audenfeo and Jchubniteow (1934) Jaaasured the viscosity of liquid argon* obtaining a Value of 2. $2 x 1Q~3 poise at G7.5°K. Masasy and Barhop (1932b), give for the electron collision cross section of an argon ©.tea at therssal energies a vales very nearly 4 Bohr orbits* uhence a « 1.0S s KT® cs. {Substituting these values i n Stokes1 fonmla gives an ionic a b i l i t y of 3.2 as W$ e^/voitosegsnd* Tho viscosity of bulk helinst ct the boiling point* given by Banot and Sadtl. (1994)* i a 3*05 s IO" 5 poise. She gaseous cross m section of heliaa atosas at tbercal energies l a apprajsiiaatoljr 6 . 4 Eohr ophite (Kassey and Burhop, 1952c)» vhenca a » 1.34 x 10*8 ess. Shea© yield for tha : ionic oobllity. ^  ** 3U4&; a IO"1: a^/volVsscond, Tfauc there are two cheeks on tha nature of argon and beliua liquids, aassaly that af Stohes* law ant the diffusion equation &t % r i a g . Sine© the viscoelV of 11<$&S 'nelina has a strong toi^ratiir® deues&&he& below - 2,19°K , the ssobility in espeated to have a a i d l a r ts&fserature dependence. 30 Tho essential features of the electrode system and associated leads are Illustrated in Figure 1* In an attest to achieve parallelism of tha electrodes, the ©nail electrode discs, epproadiaately 6 a.a. in dirasetor and 2 o.su thick, vera oachined after counting on hakeHto. Sheir parallelism could he ascertained from travelling telescope ceasureaeats of their separation and van constant within 1056 of the smallest separation used, 6 % 10*3 cos, the polonium alpha particle source, deposited on one of the electrodes, vas restricted to a contra! spot one to two E * E W in diameter, cinitaising the effect of any entiparallelism. As other instm&ntsl errors ware asora important than non-uniforidty in field, no further iaproveaant vas felt to be necessary* She alpha source was deposited on the electrode from a 3/10 hydrochloric acid solution of polonium* Rutherford, Chadwick and SUis (1939) reeasBsended deposition on silver, and i t vas found that teeeuuroEisnte at tha highest fields could only be ©ade vith polished silver electrodes as the surfaces of other materials vara pitted during deposition of the source* a very fine polish did not Eatorially increase tho breakdown field* She ffipsifflum field for which t^asures^nts vera cade vas 2G0 idlovolts per est* 16 irv . tungsten wi re ^. tungsten-glass seol ^ _ -to ga ss supply ___.--.py rex tubing x^no- 30 Cu-wire .pyrex support bak elite — s i l v e r e lectrode opening for o b s e r v a t i o n polonium source j C u - lead If- I in—)l Figure 1, Electrodes 31 fhs bakelite aeseiably me used only at low t©s$>®ratares end provided adequate insulation at 4100 volts. 3b prevent stray currents through the batellto during direct current measuressents, a grounded ring separated the upper and lower parts of the outer supporting bakolite. Bio high Voltage tungsten seal utve surrounded on the outeide of the glass system by a grounded ring of silver -paint* Inside the -systessi, glass tubing surrounded tho leads to a l i c i t balov tbat of the liquid* preventins breeisdown or conduction in the gas. for each adjustment of the electrodes* cutting era! resesliag the glass ma zaore satisfactory than the use of a ground glass joint* Gocmrcial argon vas liquefied and tsaiuteinad in tho sealed tube by iflaaereion in liquid osygen* Bubbling of the liquid osgrgen Induced Slav voltage fluctuations on the leads and necessitated silver painting and grounding the outer tuba for direct current CbservntionS* For experiments in liquid heliu% the bottom half of the outer glass tube una reooved and tho electrode system suspended in a bath of liquid helium* by an '0* ring seal at the head of tho dsusr system* the electrodes «ero reaoved from the system for adjustment* She use of liquid nitrogen elislnated the difficulty of bubbling in oxygen, but en an extra precaution the outside of the helium dower vae silver painted and grounded daring the direot current esperic&nts. With the eyatea described above, tho total capacity of tho electrodes, signal leads and amplifier input was from 15 to 20 micro* ralerofereds for argon experiments, end 20 to 25 for holius* Figure 2 i» a block diegran of the Gicctrodee and the exraageaent of the electronic apparatus* & mximm voltage of 4100 volts was ohtsinsd flrora a 2000 volt Cintol power supply* and a 2100 volt better/ box* It was found necessary to add smoothing outside the Glutei supply. She reaistoi? of-one df two B»0 fi l t e r s was used as a part of a voltage attenuate**'' which provided voltages down to 0.05 volts* She Seconi eaoothlng unit was placed at the head of the electrode cyetua. i i t h these smoothing units, tMch contained 0*1 r&erofarad condensers and 10 5 ohm resistors, ripple was reduced to lass than 10 microvolta i n 4100 volts* So devise the best electronic appafsatus for observation of a signal, i t s characteristics oust be known* £h alpha particle i s considered to produce a rectangular current pulse of solitude* 1 , lasting for a tiiae, T » Figure $ (a). For such a signal tha largest voltage which can be produced i n a system of total capacity, C , i s i T/c , This voltage Is realised by waiting tha incut resistor* R , a l p h a source ele c t rodes 4 1 0 0 volts to 0 0 5 votts R -o o s c i l l o s c ope o— d i s - rafe-criminator mete r Brown recorder Figure 2 , Apparatus ( a ) of on esgUlfior largg OQ tiiet ? ?• jla l i ^ r t s»oolstGnce of ' lfi$ ohssi «®s required to Mnindfrs noise end this vaiua satisfied tho above rociaiifcaont. As tho- signal i s lasreraaly proportioael to the oapaoity* C , G tept to e M n £ m i n tho oxootrtwlvi oyotsm end a*aplifi«r inpnt» Hth a. large input tee constant tho voltage acrooc the. . capacity increases linsarly vith current* i » (Figure 3 (©))• this , voltage decays to l/« of i t s value i n tha tie® fig (not shown in the difisrec). I^ssaga of such a signal through an a ^ U f i o r of bandwidth, fg modifies the signal to tha fens of figure 3 (c). las carreat duration i s taken to bo th® ttaft feund by ostrcpalatins tha fastest rising pftrtioa of the signal to sere and to i t s issj&aiSBt ais$&itssde« <4m M<i<$X.x&8J&\M fho wan square nalso voltage* V , referred to tha input for an amplifier of ©#siv®lent noise resistance, % * having fracpaacy limits % p 7 a 8*^ our^ont* Ig , asd an input ttoa constant mm that JtafgBR ' i e greater than unity* i s given hyi* ^2 n 4 & ? f ^ • where U i f ifeltsaftttn«a constant* f io the absolute teffiparature nf the input* and n the oiootronle charge. In n&nloising the f i r s t ter%' the value of % wan reduced to 508 ehns by the nan of o cascode and selection of the iajrat tubeQo IVo ft-C coupled or^jUfiore vera need* one of vbicfa led an «pper cut-off frequency of 13 aogncycles* and therefore lou gain per stage* so that cftseodes i*>re used i n the f i r s t tvo stages* She second %m a ..lever frequency wsp&U&t. with only one caocode. the second tera* arising from tho fftld current of the f i r s t .stage of an certifier, vao ointalsed by edjtistaont of the grid bias applied. 4 bias of approxiirately & volts produced tho best signal to noise ratio. t A sisp&e oaans of reducing the third tern was to use a large value of a * ttbich also produced the largest signal on the input. A resistance of vP Gloss reduced tho third torn to a negligible quantity for o i l values of fx . For observations of pulse rise tines the «lde band amplifier u&s used vith f ^  up to IS ^ c» anl as a result the f i r s t term of (11) predominated. In datordning pulse amplitude distribution©, the etedsm bandtddth «Stich could convey the pulses i n a fona taii table for the dio<3ricirAtor m* used, f r l a l yielded opttnuo conditions with f l c 20 Kc and f j| » 250 Kc. Ao a large input Una constant van used* l i t t l e loss Of signal resulted fron the lev values Of f ^ and f 3 » the decay of the amplifier s t i l l being short by coE^arieon with that of the 2Ui8eo on tho lapft* Onder theso conditionti a signal of 1$ micro-volts produced by 1500 ajtaFfcaoas collected In a total stray capacity Of 16 tdero-J2icrof€urade could be observed. •fas taabUitiae of the charge carriers cro determined free; tho ticae taken to travel the distance between the electrodes* and are calculated fron the rise tiise of the voltage pulncs on the Jtig&ttfojp input. To measure the faatasst rise tinea the f u l l bmsdvidth of the 18 Mc aaiJlifier van used* but for olover pulses* fg Has adjusted by the use of i& and $ Me filter©. The frequoncy f^ van fixed a t approxinstely 100 So* Very slow pulses vera isensured vith an amplifier vith f 2 variable from 50 Kc to 1.5 l-io i n sis steps, and % fiscedi at 0 Sc. Vi«mal observations v&ro ssade with a Tektronix Synchroscope ^517 vhoso trace wae photographed for accurate cDfeeuroneots. fanrMtitft for, .yelf^ teUt^e. ^Bk^itniUanfl For pulse etjplituda Koasnranente the glove? aa^OAfior with fg = 250 Kc vae uesd. Zto riea tico was iongor by a factor of 10 than tho slowest pulses i n argon* tout the aaplifier suspended fully to tho amplitudes of tho pulses as their decay tisss at .the input van 36 of tha order IO*'2 sofxmls, tHa&m theae conditions the riso Uaes of . tho puleaa &t 'the injait did nat effeit .their ispUthde at tho output so thai : $x aca % were solcwsted .solely to give opticus signal %& noise mftte* Ska observation of poises i i i liquid- hatine?*, each slower than those observed i n argon* vas reatrictcd by olectrouio iitsitotlone, and a tcodiflad intgrpratation of omplitude Beastireraonts Is discussed i n Chapter VII, Section 4. She frequoncy f 2 contralled l a the ar^pltffgy end tha input of the discriminator, vbtcn una part of en Atooie Instrucwnt Colony Unear i ^ l i f i e r nodal 204-C, tha dieoriciinator vas followed by 4 ecale-of-64 to reduce tha eount rato im a Trccorlab ProdKion Rate-Meter, l a the ooiwideraUon of poise affipXtttato neaeuremats, a Gaussian dittfibutio*. df noiee pulso» i s assused. arsi i t io nocoetiery to obtain 4 valtta for their standard deviation, & distribution obtained from a large washer of equal pulses, vhosa sines modified by Gauosi&n noieu, appears a* a straight Una when plotted on a r i t t o t i c probability paper. Such plots vara obtained to find the standard deviation of the noise* A voltage pulse generator vas eousactod to the Input of tho w^plifier sysgem via a large resiataaej, so that i t aotad ac a eurrost gensrates? $m&Mm tk* «»flBWti»ii-f!fti*# being IfivsatlgatenV l a aft , to jpe^laa® idanfcicfci soan t^4a&% thrpu&#* generator^ *£4«b bod «n output xtt&flftettOQ of anproxiEdtoay 200 ^ consented botweoa the grid bias supply to the e.ffljiUfisr i£$ut end. eround. lbs grid reoistox «ao thus ussd as part of tha currant gomrator, ana no certification of tha input circuit vas roquirod (Figaro 4). this van dona with argon or helium liquid i n tho «y*fett». Sha puis® aiae distribution at tha output gave tha standard dsviaUon of tha distribution of hoiss pul^»$ha#tar ?* Section 6), bat te ry pulse generator | t v v W amplifier 8 discriminator Figure 4, C i r c u i t f o r Noise Measurement She generate? pulse tha high roaistanc*, R , vera fi^atiaa* T p # of the «uWat electrons, -n£ * flowing into the pulse una given hys-• V p , and duration -7" p , and so that the- ac^Utisde, i » and vara calculated,• She mrcibor of capftcity of the input during each 71 * 98 % T t3E but oorraotion as ntedai for 4tttgp3&«g between the ,pt&se generator cad the iojTUt.. Tho oorrcoUoR vas avoided by redudng S . awing . calibration and adding an cdditionel fssovn oupaoity to tho stray eapaoity of the input, . fhe produce (3C) vaa kept constant during <3iaKgee in & and C , to rsprwJuoe the form of the conauctlaa pulses* fbe direst curront observations vere mde vitb an Applied Physica vibrating reed electro^tor driving a Brovn recorder* Ihres ranges of sensitivity recording one volt to one millivolt f u l l scale vera used, vith input resistances frota 10 9 to lO 3^ obrjj. $0 derive any advantage, from the yotegtfaft of intorpally - . generated noise i t vas necessary to. »«roon the apparatus, from exberfiai sources of noise pick-up* this vas achieved by enclosing the electrode system coraplotoly i n woU-groundad electrical shioMing* A battery f ilessnt supply also enclosed i n the ohiolding to prevent pi ck-up froa the filaoants to the grids of tho f i r s t stages of the amplifiers* the er^lifiors and the head of the vibrating reed oloctrocetor vere olso enclose i n the seraftttiag, t&th these- f^ge^tieoft* Q%ten£& |iic&*«® vas ,is$|3, hgr om^aplsoa vith the naiae of the ss$CUfior« ' m m She f i r s t as^easaaht of the rise ttea of any set of pulsoo was m&9 visually* using tha flttftNtsa frequency ranga af tha sf#rcp?iato se^lif&efS* A f i l t e r vas thou selectee* to reduce noise vitbout introducing tec great a eorractton for tha rise of tha MpllflatY Photographs-, taken af tha oscilloaeop© trace©, vara projected on to n screen end enlarged spprxatla&teiy three t&aes* Iho rise Mtass vers seticetod by extrapolating the sharpest rising portion ©f the traces to tero and the wwlww solitudes* lasastafeQants being facilitated by the oscilloscope screen, also reproduced on the photographs as fg dstan&nsd the rise tins ©f tha amplifier* f f t » corrections vara necessary for status of tha observations* If tho observed rise ttas vas J e * tho rise tiao, 5^  , of the pulse at tho input i s given by (HsBsta and' Sands* 194.9} % van ssaaeured by observing very fast pulses from a aoadeniaf eannscted through a laercury switch. Ionic Eobility, /A * vas calculated froa tho d r i f t v&looity, 41 V # detsiuinea from the corrected rise tins ef tho pulses* vharo E i s the applied field* Average energise* mm free paths* end ocatterina cross sections we& deduced from laoolllty m&mtmm%e on both electrons and ions to esacdno the possibility of oj^laining their behaviour "|ygas-type ainatlc Iheory or by theories of liquids. An enantin&tlon of the process of reeo&bln&tloa of electrons and ions i s cado by considering tho distribution of pulse amplitudes* TnlG necessitates correction for three other factors uhich influence the distribution. Strangling of alpha particle energies* the geoffietricsl effect of a range caEparahlo with electrode spacing, and the m31fication of the distribution by electronic noiee have been Investigated* Tblo aHovtf the separation of the affect of tho different degrees of roconbiimtioA occurring for alpha particles cMtted at Various anglos to the applied field direction* 42 tfadey (1954) has s&owa that alpha pavtiela# es&ttad froa a source deposited on silver suffer very l i t t l e lose of energy due to the prosonee of hseMfcg aatarial* 'la the present vatk i t ' haa been aseunsod that the alpha particles 'all had' Identical energies*. the nonber ef particles eaittod per aoeond i n directions staking angle* of 9 or less with the electrode surface i s H • % sin 9 , vhere % ie the total ttunher of pulses observed per second* In view of the experiments of Anianaon (1955) i t i s reasonable to assume that ton Bragg lav established for alpha particles i n gaaeo i s explicable to liquids SO that the center of gravity of the ionised particles ie at approximately $/$ the length of the alpha track* (Wilkinson* 1950). She average distance travailed by olootruno rslecaod by an alpha particle van therefore a function of i t s onslo of eaisaion. In argon* tho positivo ions vers so slow that their effect una not observed vith the aaplifior owrcally used* no that tho effective numbor of charges ooliootod, , ie the product nf the tmsm of electrons roloeeod and the fraction of the SfioaraUon of the electrodes which they traverse* For alpha particles of range, K « » producing n eloctrons between electrodes of separation* d • the proportion of of the pulses of acpUtuile equal to or greater than pulses due to the collection of charge* n ^ f •* 1st* 43 02) Ihte distribution correeponde to e rectangular probability dlGtributiorsp vhlch i s shown later to be raadily corrected for tha added effect of noise pulses* Revaraal of the field causes the electrons to travel a saalldr fraction of d f giving a diotributions-$as ratio bf the nasdrnm pulse sites for the two f i e l d directions i e i -^henoe E<* could be dotoralnod, i n tho absence of other effects oil the aiotributiotts. Ileoerubinatian alec isedifias tha distribution by i t s dependence on the angle of emission. Sines i t i s to be cxpooted that tha rocosblns* tdon far alpha tracks at a particular angle i s the ens® for both f i e l d diroctiona, i t iaust have tho ease offset on ( « ^ f f da on ( n ^ ^ ) ^ » tJhenoe toe equation!* J l (13) ©an be used to find & «: independently of tho r^oonbinetlon effect* tho noise voltage «f any electronic systeci haa been snovn to have » Gaussian fluctuation *gr Rice (1944). ?fce probability of the noise voltage being between x and (x • gx) l e t -29* 2 P(S) dX « . ; : ; n r # n i : © djt vbera G~ i s the standard deviation of tho noise* tha euparpooitlon of noise <m a aerie* of poises of the sans amplitude £3 prodtioeo a distribution vitas a curailaUve probability of x or 2 W * ~ fir J e Hotted against J t on assalativo probability paper Q(x) appears as * straight line* 3he gradient of the line i s detorc&aod by (T , and vas used to calibrate the noise of tha amplifiers* She experimental ftrrongenaat ism to generate this distribution i s described i n IVfl Section ?. CoabiBfitioh of noifto vith * 5 C»)# »0 ii j p M dietributioo, D Fight* $ (o) **(*) * 0 Lelds tho distribution:-ic ^ % < * < % 4 6 >t(x) dX a 4 which Integrates to the euaaOsttv© diatrlbnUoni-- 2 2. (15) I f a - X3 « & » then <•(•<$)• Q(+ £ ) « 1, shewing the Con^&soantsJy flyiasjtry about s * *| » Q ** lA. 3nr convenience ve vrlte» then ?(*j) * erf <r * and Qfeg) » For cueh a distribution the slope of tha caasalatlve. probability curve at Q •» 1/2 ie and io that value of % at vhlch Q © 1/2, I f the standard deviation (T i d kmvn, P can be determined, and hence % and % • the test for titfft distribution 16 syntaetry about 4? She influence of Gaussian noise on tod pulse ainplitud© distribution indicated i n Sigur* $ (b) cannot be s£ s&asOy analyzed, not belhg ejTOSfitrioal, For nost of tho exparlBants porforcsd, the cussOativ© distribution bad a a$# degree of sycaaatry. which would b© expected i f too gooaetrleal effect occurred utta no recoBblration, In a l l cases noise eorreotians war© Bads by aasuaifig a "rectangular0 jBrobBbility diatribution* 5* n l^J^^ f^^  9f^ a<rtlgaa ft*o further effects of noiae wost bo coaaidored before tha distribution of pulses without noiae can be obt&indd, mm the noise 0 pahs ai«a enmll by ccn^jerisoa iith the eipi&% tha a&Sy con-aetdoa to bo tsade i s that given is the previous eoetdon. When tha oignals are of cospcrcbla aggAitude vith tha soiae fwtiMk*. atJ^itionel effects are encountered? ens I D the addition, of noiee poaka to the pulse distribution, and the eooond is the ttaeftiy tic* of tha discriminator 0 Rica (1944* 2qvistiona %b * 11 ead 3,3 * 12) eetobliohed that the uttttfea? of 3»iae tasaiffift j ^ r decoraS, sfcseeediag ejs^litudo? TT , stuch greater than <T * is** vhere (T in tha steward Oeiriation of the noieo, ena f ^ f 2 **• the frsajueaey l i a a t i * vhleh for cast of tho varfc on pulse distributions vara % x c/ssc. iftd 2 x IO 3 c/sec., rospoctively. Jhe fTequaney af alpha partlole induced pulses vas about ^K>/seo. the above c a t i o n shows that rtolm neahs af a value % » 3,64 <r or greater occur vita this frequency* so that guises Bust be of tho order three tiraea tha standard deviation of the noieo to be detected* M the noiso peaks ens coEpletoly independent of any signal* tfceir micbere, as datet^nad i n a ezpartte es^ertesnt* tea. be eubtracted from an observed Oiat^ibution to give tho truo puloe distribution* ® Another EKdlficsatlon of the pule* distribution Id caused by the response of a diacrteinatnr to pulse* of different decay tliaesa A dl8oi?is4natar» ones triggered by a pulse* bos a cortala Mood tisos* during which i t eanmt be reset* When this tins hm elapsed* the discris&nator w i l l be roectivetod i f the value #f the signal on i t s input i s s t i l l above the discrjrdnation level* so that i f the decay tins of the ac?jlifior i s longor than tho dead Um of the disoristotcr* a pulse my be counted tvo or nere tim&t depending on i t s length* Altbou^i a pulse nay have fallen below the* dioericdnatlon level during the dead Um$ a QESU electronic noise peak superlffipesed on the t a i l of the pulse nay raise the amplitude above this level* Aa the oKplitxaJoe of tha noise peaks have a Qauaaian dlistributionfl the occurrence of a noise peak of sufficient s&gi&tude to raise the t e l l of a pulse to the discrimination lev^l i s such acre probable than the occurrence of a noise peak of tiiocritdjietiofl level i n tho absence nf the puloa, this effect i e therefore snore important than that of the noise peaks above* and has been found to predcdLnato for pulses ss&Hor then 6 <T . Ih© aEplltude distributions of pulses larger than this ware negligibly affocted. A simple correction for t e l l noise has been found only for the unimportant case of pulses of equal sisee* but the stains dependence of the effect en the sine of the puisee e^Qjrdns the incorrect interpre-tation ef tho results of Davidaon and Lareb (1950). As a result of the reduction of naiso level achieved i n the present e^orlcente, analycie ef distribution for pulses sacHsr than 4 C" was not etteapted* 0 I f the pulse diotributloa i s oyajaotriaal, then tha ©f foots of salsa scales and pulse ta&l noise arc sot prseoflt, and tho analysis described i n Section 4 i s eppUcRblo. She oorrectioas aro nainly very oinpl*. Qreph 1 i s a plot of il/B) erf 9 vs. B, whore 9 » »/ /8 < T « a graph of /3 (T ^{a^) va* B « If (T id known, and H*$) i e determined from the slope of the Q distribution, than B can be read iiacGdiately from the graph* and bancs P detJuced. I t stay be noted that for S w l . f * (1/S) arf 8 differs Irani 1/B by only 2,32, oo that for D > 4.2 vory U t t U correction i s nooesosry* fhia vas the case for oast of tho results, so that % and stg ware read directly froa the graph by extending the s l o p of Q et x 3 to Q « 0 and q ° l , Caro had to be taken not to apply this aatfaod at , tho lower H a l t of observations, Graph 2 i s tha cusulativa probability dietribution resulting from the suporposltlon of solas on a series af pulses of equal amplitude, plotted on an arithmatic probability scale, linearity of tho graph indicatea that the solas i s Gsuceian, the standard deviation bdng detersdned txm i t s slope, Saving corrected a staple distribution for tha effect of noise* i t i s necessary to re-aiaBdna i t for information concerning to* 1-254-Graph 1 Graph 2 recombiimUon of alootvono end ions. In Chapter IV. Section $$ tho _ oeatarption vaa tsede that the amber of electrons eseapiag en alpha ... partid© track van indspendent of l t d angle of ©Kisaion. That tide .-. ie sot too case wae seen from the distributions from which the angular < dependence of r e ^ $ ^ ^ She expression for the effe&ive aiaber of alectrons reaching the collecting oXactrcde itf modified tot* ' % ® * * ft* f f S t t o t ) . * « » where % i s the aos&er of oloetrona escaping receaibinatdon for an alpha particle perpendicular to the fioid end f (8) i s the fraction of this ausibar escaping reoccibiaaUon at angle * , The oxpraflBion i n brackets i s due to the geometrical effect of alpha particle range* As f (9} i s not a function of electrode apecdng 4 * tho geoiaotriail effect van estteted f i r s t by varying d * end thence f (9) doterestced. Uta stability of electrons l a liquid argon* at a t«j$Hsratura af 90°K, deduced from rise tiK» observations nado vita photogrepbs similar to those i n Hats I, a - d, had bean plotted i o Graph 3. At a fixed electrode spaaing tha oaqperintintel points follow a lav. the difference between the lines being due to a ivstesaatie error vhich la dependant «u spacing. 3he terns e^ end Og are constants and appreciable possible errors occur i n aost of the factors used to 7% 7S 556 Observation of Rise l i r a fatal probabls errors i n /J %$% Total probable error i n applied field 0* U&a gives an effeetiv© possible error of 11$ for/* * She dotted Una i n Graph i gives the average values of observed usability for vhich the probable error i s batter than (a) E = 100 kV/cm, (d) E = 3 kV/cnu d = .20 m.m. 1 div. = .02 sec. PLATE I I3r ° 5 8 •I2r ' 1 1 2 * 21 8 08+ 06+ 04+ 02+ d-100 cm-o 2 0 A R G O N aver age I f J_ V - s e c /J cmz x> Ot , 1 1 v 0 2 0 4 0 6 0 80 100 120 140 160 F (KV/CM) Graph 3 m Tho results indicate that Eobility i s nearly Inversely proportional to applied fi e l d . Ihie follova from the fact that electrons i n ergon are observed to aeve with nearly identical d r i f t v.lodty of 10* Shi. »*at c n t ^ i c W tb» «rf EUJsin «aA Sohulta (1951) **» founO, Xt Is believed that the reduction i n electronic noise 4M estensioa of meacurocante to a much wider range of field Bake the results ef the present research mere reliable* At high fields tho values of aobility agree roughly with those of Halkin and Schults. jgxoerii&anttii values of yu are given i n fable 1* with the values of scan free path* A » aoattering oross section, Q * end electron energy, £ * osleuOatea froa using Kinatic theory equations <?)# Chapter 111* Graph 4 i t a n M of Q TO. JT which i s cospared with the curve for geeenus argon* plotted on * different scale. erese section for eleotron collision i n the liquid ie sanallor by a factor of the order 100, but the curve shows that an energy dependence eimllar to the Wiffima& effect i n ;gases; occurs. tk ..IHtttttr, M • fo&tm J i m M M m Positive ioiai were not detected i n tho work on electron debility or puloo amplitude distributions, fhis was due to their 54 RESULTS GAicnuii-i) mm umiun mmmmm ' 2 1.5 * 10* 1*40 0*36 4.S I.© *10* 10.0 8.0 a i o ^ 0*25 4*3 $.0 * 10* 20.0 3*a x i s r 6 0.13 4.6 2.5 *19* 37* 6*3 at 16P6 0*073 4*1 1.4 a 10* 1*0 x W% 0.049 4*0 7.0 IE 10* 105* 1*5 * 1ST* 0,033 4*0 38 10* 141* 1*5 * 10*5 0*057 2.6 & 0 x 10* 200* 1*5* io w* 0.032 1.9 <» tt$3m of SooJ? o*fei* * *$89 x 10"8 en. Seal* 2 m m n w p o m m ions a * 1*07 *ie" 3 «*». EkV/cm.' IU7« ••140. 94* 47* 24* 13. 5.7 /V 3 8^- ..•:*** 2*8 3*a 2*e 6*1 u.a V-sec. Graph 4-55 c a r ^ s i n g l y lew jMfeilltp,. An os^ricjant was ^sjfcfpttB^ *| an ©!®©tr$ds aep&r&fcioa af•. «Ul s 10* 2 «KS, toiou the GB^Hfior, wfeoeo lay frequency lia&t af • 4tfai&te*A t&» &tcsy titae af tha syet^a, Mtb a field applied an that tha . I f f * travorcecl asst of the elojtsode eeparatioa, pleas vith vary slov rise tinea vstfe observed, Xha vsOuas of oobility union vara attalae* ere given In Sahio 2. At fields less than about J© &v/«su they are tinr^iiebla, feeing ostiaatsd fiwa rAoo tlaos cicdiey to tte decay tim of tho e ^ l i f i c r . If'these Valines' ors igoored, va ' aay <w»cluds that tha s o U l i t ^ of the positive ions i s ' ac 10"^ <ssrV volt-^^etrnd, constant vithin the Ussifes a# the e^aKteht* > ^ i o ^ o i i ^ e i*th * M u ^ frun this a ^ U t y i a I a 10 - 1^ ess., vhich i s m .short «# to b» ppaain$Uss i n tores Of ordinary Kicotic ffe©o?y. the isjfeUity predicted ^ Stotos5 fomsla, (iQ), Chapter HI* ie 3»a7 • ca^/v3lt-3«caM, i n eseallt>nt £@&@E#gt the observed wig** the theory devoloperi by Eyric^ (1936) iMicat*s & aenstant nobilitj.r, In * & s 4 M « 8 & vith- the obasa?^ rssul&u 0eiag ^Mma (9) and the date, given isi Cbaptoy III, $Mt'fN4£ttty-4$ 2*3 gt 26*3 socond yields a value of 3?0 cal/aole for % , tfel& io fsar titass as «&§&i m the M t of vuporiaiitioa, ead an atari®© potartUel v#H depth of S at 10*^ ©.v. vhich i s tvics tha. avefaga idrntio eaorgy at# a ttsnpaMrtttto of ^O^S. In obeerTAtlons of the rise t&oes of palms due to electwno in liouici argsn* a rovorcai of too H & M offoctsd o roiSuotion in puloa eic©„ $sen tho f i o M wa» rovaysyd in ffieo-tita© ospcris»nte vith liquid ho!lu% i t had l i t t l e sffoot* indieat&ng thot tho mobilities of tho poEitdvo and »epi&*e carriers ware approxlffiotoly t^unl* With a low fraquaaqy Unit of 3Kc, and i n eleotrode spacing of 0,50 E M S . * pulseu of tho- typo shorn in ftUfer$*# (a)* were ofcsorvod. (5ho fangs of a Polonium alpha particle in liquid hollum id 0.23 B . Q . ) 3Eb© tvo distinct sections in the rice of tho puleoo ere attributed to tw noteUiUoa, jMfe&tt. slightly different oollaating W K O O for the positive ana nGgntivo carrlere. It was obijervad that in ease inetenoae (Plate II, <b)) with a negative f i e M (defined ae that cautsiiig negative earrlero to '&m awey froni the source* oleotrodo) . slowly rising puleas could be observed with one rate of rise* These were due to alpha particles enttted very nearly parallel to the electrode surface, so that the pulses resulted froa the tranait of the negative oat*rior3 mm» aost of the electrode spacing. the alpha parUclas .emitted, nearly porpsoSioular to tho electrodes gave pulses to which both positive end negative carriers contributed. the lenses ©f these .pulses. indicSted the tig® at whioh the positive ions had been oore or lees oos^lotoly collected* tut the negative carriers were » U H contributing to the pulses. Ibis iisplied two distinct sabUlUes /4 + andyK ^  and tha long slow rise E = -30 kV/cm. (a) 1 div. = 10 sec. E = +45 kV/cm. (d) 1 div. = 2 sec. PLATS II ef the pulses with negative fields ©hows the*/'* ie greater than / / . • $p Increasing the ceparetien of the electr^dee the cffoct' df the range of the alpha partioloo was reduced* eo that tho pulses observed tdth the two field directions were due elraset entirely to tho collection of positive or negative ions alone* ^sse pulses, which vera used to measure fit + are shewn i n Plate 11* (c). In most oeelllogratas taken with negative field® there ere a ««ft>er of different pulses due to alpha pnrtieles ejected at different angle** fbB rise tims of the largest were recorded since these were due to electrons travelling across the entire fi e l d gap frost tracks parallel to the electrode surface, for D3&sur*c»nt of // & positive fields were used so that the negative carriert travelled only a short distance end did ant codify the observed rise tlEos (Plate 12* <4))e i e a result of rocoffibinatioa processes, canai<lorwl i n Chapter VII, the alpha particles emitted nearly parallel to the electrodes produced the largest pulses* so that by recording the rise t&s&g of the largest pulses with positive fields and the longest pulses with negative fioKs, the transit tines of the positive end negative ions were manured Separately* - The use of very large electrode spacings to separate completely the l^asareiacnts of ^  4 end/4 * wen net possible because the resulting very slew pulses would not be passed by the &$>li£icr. She lower l i c i t of observable pulse riea Use was set by tha low freguoney lic&t of 3Ko. i n the E a p l i f i s r . Thiu l i a i t wen loosed by noieo considerations as noisa povar i s proportional to i n this;' region. $he use of spa&ags greater than 1 c a * by reducing f^ bslow 3 Sc. would have resulted i n an Inoreao© i n noise off sotting tha gain i n clarity of the pulses and reducing tha useful range of nsseuroffioata. Host nssaawaaantG .vara soda vith epectngs of Q*$ or loas, at which the voltage supply produced tha cajteaa field* determined by breakdown i n the liquid. ' for nelium at i t s boiiift^ + and ^  * have been plotted i n Graph 5 as functions of fie l d for several electrode separations. /U . «*a fbund to be iiiSependsat of fi e l d , vhlle y 4 shows a tendency to a olnisasB at epproidmtely 30 kV/ca# I^acrapaacioe up to 50^ i n values of raotrllity obtained at different opadnga nave not been oxpleined. At each enacts^ the individual readings agreed well xdthln the octlreatod W$ mxtem possible error. In Spite of this non-reproduoibility, the gensral Character of the pulses at the boiling point i s veil oatabliehed. ^ ead y # are alaost independent of fiold* having a coaetaat ratio of A l l vithia Tas results oay be ssascariaaa by tha average valuess* H ELI UM" 2 f T = 4 - 2 2 ° K d C,I5mm- .o- /j + set P. p+ d = * 4 4 m m -d = - 2 8 m m-4 9 mm 8 0 E K V / c m -120 Graph 5 For on ioniaed atoa In 14qute twliura Stoko9» tap equation <io)f given * 19*0 is. 3J9*^  c)^/«nlt*&»^ which i a ssaro than tvioa toe average observed value ef ytf 4 * Sbie dieoropency can tie partielly accounted for by esnsidoriag the helittfi aero point energy. 0 I t lead* to a COXICUE value of 2.6 A for the radiue ef the helium atoaw London (1954) euggeatcd thet the vclue we less than 2.6 X end he chose 2.3 ! . If accepted, thie suggests e nobility of 942 ca2/volt-ecjcoa3, tfcieh differs from the ©apsriiKntal value by fl$* SUtting the oxparicantal value of JUL + into Eyring's theater (1936), equation (8), Chapter HI, one obtains Ik value ef 14. cal/taal© for % vhieh i e 3/5 ef the hast of vaporisation, end icplieo an average potential v e i l depth of 6 x K T A ev* or 1.7 tines the average thenwl energy at A.22°K. lack of raproauoibility i n the siability jssaeurenente led to the suggestion that in$uritio3 might he present. During one cjxporliMttt the heliuD dewar was opened to tho s i r until particleB of solid s i r could be seen suspended i n tho liquid, there wcJ no observed change i n the aobilitios, but this brief test use not conolunive, since even i f a i r had been the effective ix^urity, the IkjaM nay neve been .saturated with' i t already*. IKlttqttitl .ttriU* gfegn which -thugr IAHT* t i i a r ^ U ^ 4j*$fcs&*. dat«K4»». «fcsthar such t*a#p$£ olecti^oag S B » M ba Uaccdi^t^ly r e l i e d % . photon©, a 100 bulb vas placid Gpyt'^rAttiXj four laches te tha ©isetros&os so that tha Mght £Uuai.uatesi the liquid batman tboa* llo increase l a e oMiiV vas obsaw^i, $gt this |# ebons later to b© i^oaa^^lvs,. Shs deferens*- bstv»#a tha pasitlV« a i i ^ tiajgativ© mobUltics tsahos i t tailikely that m>0Mw Ivtm era Graph 6 $&&wyu + ftrfyu * a© fuf*cti#t8- of ta^ar&t*»^* tha roprKhiclbiXitir #1 paints i e not pcti* bat for any ona oapcitent at fdissd {spacing, 'eurv&a" can b$ *i*&us t f i i ^ s h tha ^ i ^ l & ^ f i t a l points* Sha tu© durv&e witia tha etsOlor fcaahey of pcinti ag*t»s with tha fern of tha tsam dataAXoti atsrvos, AS «Mia&tate& i n ^ actdena 6, $hs»ptsa? i l l , & afel&tiy teaaafBtare dtjps*Kten«te youl<3 bo e^ects^, tfef& i s JtateaA f$8a% ezr^visllf boiot? 2,19°1S» SBC value & JUL + tends to decrees allghtly with daapsaadrig toqgpe&t&M M M * $te A point-fafanflition, but ^  tt iacrososo vith G-3<^nalng tsgg^&tttir® mm tha fssfeira rafig^* At left? t^aratures tha taobiliUeQ te&sm f i a l d t2«pa»i©ut, ae i s indicated by t&o plot 34-V - s e c 2 + 0 H E L I U M d = 4 4 m m • Q < ; 0 - , . . „ — -c r ~ — " - o z r - -2 3 KV / c m . Q " — " x ~I2 K V / c m -2 3 K V / c m . '*" • • ~a ' l 2 K V / c m . - t — i -t-4 T ° K Graph 6 1?) of yU <p. 1; at 61 3*M nm ,%lf*% . t® ; rst te -but ^ eercceea t$ , 1.3 at . 1«4°K» 6 0 L 0 H E L I U M d a •44 mm-I • 4 5 ° K I 7 ° K 40 E (KV/c m) Graph 7 60 that tho geometrical effect produced nost of the spread of pulse sixes for snail spacings was shown by using a positive field* causing the electrons to travel the snail fraction of the electrode separation* As the ions voire too slow to effect tits enplifiere used i n pulse distribution iseajsuresanta* the recorded pulse sines passed by the es^Lifiere vers due to electrons only and vers ehovn i n Chapter V* Section 3* to have a distribution given byi* where Q i s written for * | j being the cusuletive prebebiiity of collecting n or core electrons per pulse, that thie i s not seriously nodified by recombination i s shown by Graph 8 which gives pulse site distributions with high positive and negative fields. 2hla epacing ie only slightly greater than the alpha particle range* en that the geonetrieel effect was largo* As required by the geenete&eel effect* the positive field curvee oxtrepoleto to earn amplitude &t Q - 1 . n m ^ | ^ . o * Q ) 'ihat the anguler dependence of rs cochins tion ie Qcell at high fields i e shown by the fact that at wide separations* the ratio A R G Q N . K V / c m A T T d - - 0 6 0 mm- ° - 8 4 I 6 0 2 0 4 0 6 0 Xamp' Graph 8 0 of KczlwJia to ninisgsa pulse sisoe approaches unity* At tho large value* of n « tho positive field earvea af Qraph $ ehov aaOl dips vhich cm ha explained i n ter»e of haevier reoocbiiifction i n tracks of alpha particles aaitted ^ rpeudlcular to tha electrons. She procedure described i n ouaptar V for detoralning tha value of ^ R cx frost reversed field &aaanras»nta vaa used to ces^iie tha data of Table 3. the friction A i s tha factor vhich must replace 3/5, asauHdng that tha dletributions are oiqjlicaola entirely by tha geoOTstrical effect vith R<* 1 3 0.51 sue* the average value of & lo 6*$3i vhich Is acceptably dose te the exacted valve of 0*6. fable 3 d x IO 2 « $ • # kv/ca, j | 0.60 84. .60 0*60 43. .39 0.60 '' at* ' «$9 ©•60 10, *$? 1*9 65* • .49 1.5 33. .A? 2.3 6£* .73 2*a 4& .13 2*2 23. .73 3.0 23. .78 Average £ » .6$ 64 $able 4 gives values of* % / % ebtsAned fit tho highest field for each electrode spacing, XJ/ZQ being the raUo of Elnicaiffi > to Basttaen pulse aiaes of a rectangular distribution* corrected for noiso ae described lh Chapter V, Section 6. d * Table 4 0.60 urn 2.62 99 2.18 4.4* 60 69 11.2 37 19.1 22 21.3 19 .$7 •47 .83 .73 .03 1.43 .90 •87 .98 The experimental values of *|/% were used vlthout correction for caeottbinattOB to dotoriBlno the effective values of & needed to explain the observed dietributiona by the georwtricsl effeot clone. Host ef the results suggest that reoabiration i s strongest in alpha particle tracks perpendicular to the electrodes. Corrsction of t&e values of fl l a table 4 fe* sueb recoBblnation causes furthsr reduction £& j*. * 'Sines 4.' i s alrscdy loss tban th© estimted value* 0*6, this mggmtv th&t the proceaeao of roeoEbination tro awe oaopiicat^l than has bean envisaged, $sa ©s^tsatoafcei value of $ has been taken as 0,5 i n correction* of -aalire distribuUons for the ^©ox^tj^Lcal &ffest* ' - • Graphs 9 (a) ftod (b) show experfjwntal points tafeen froa tho diacH^rainiitor end reto as&of* 3&e data of Graphs 10 ttai 11 for the eopretion 6 e> ,20 % % i n ergon uera calculate Iron those points* Correction hm bsan IME2© for the geoHotriosl effect i d the values of 03 plotted as Q function of field i n Graph 1% n| being $bei avorago Kuabar of alactrons oolleetad per jmleo, calculjstsd fron the pulse else at B/% * Q f 1/2. lbs ouHbsr fepfeeenti the cejdaaaa elootroa collection, for uhich there i s no coyrectioa fofr alpha- particle range* Its iiafclafity i n fans to s$ < i t eueh that the tve era aot considefed aeparRtci^, but their significsnoe fcseoraae apparent whan they are cotepara5 viith the direct current Eeasurooonto. ' She variation of *d>tb field' i» platted i n Grape 11* If the cntpsriniantal value of fi i s incorrect* the values ef a$ and X amp Graph 9 (b) Graph 10 Graph 11 66 atj/jsg are l a error by faotoro Indepenlant of floia. eo that Grepha 10 and U indie&to the true f i e l d depaadeooa. fields greater than 29 kV/cze., indi eating that the- angular dependence of recombination i s net a function of field, at high fielde* At lower fields i t appears that the field dependence of racofflMnation i s a function of electrode spacing* which i s not oaplicahle i n ieatm of errors i n A * RooambiBaUoa i n tho tr»cic of en alpha partiol© depends• upon the angle between the track and the direction of the applied field* By oliidnatlng or can*ecting for the gcotaBtrical effect the pulse sine distributions can be used to give this variation directly. Since pulse else in believed to decrease noaotonicelly with increase i n the angle* 9 * between the track end, the electrode* we obtein tho relation* Using .this temMt pulse dee hen been rsplottsd (Graph 12) a function of 9 for high f i o l d i and vide epncinge (1.12 swa. end 0.58 at which the esrreetiojRa for nolfte end the geonsotrieal effect were ecall. these curves chow a strong angular dependence* and i n particular that reees&lmtlon ie very strong i n tracks nearly parallel to the applied field* Bo satisfactory analytical esojTrseelon Graph 11 shows that XjAjj i f ai^roxinatsly constant for A R G O N m has bee* found for the angular dependence of the wttdwr of ©lootronc escaping roooGMnation. AH readings of direct current* i * have been converted to give the average nisabs** n c of electrons oolldotod per ioniiing event* using the aquation*-Graph 13 shove the conduction current $& Hcjold arson as a function af applied fie l d for a source giving about counts per seesna* The curve vas reproducible vlthla the isasdiaum randon error i n current readings being such of this being due to uncertainty i n calibration of the input roeletenoos to tho vibrating reed olectroaater 0 She graph shove that the current i s proportional to the applied field* B , bolov 100 V c m . > and to intermediate fields* She observed currents vere the sees vith both The value of i s alee plotted on the ee&s graph* Being the average masher of electrons escaping rneaoMnatlen per ioniaing event* estimated from pulse mmmmtm» i t ehoold correspond to the direct current. She agroonent In esagaitude i e vary oatiefactory 9 but dxlOO cm Graph 13 the field, dependences of the ts» show a significant disagreement, whieh 10 diSeusand In tho neat chapter. Tho ionic labil i t i e s i n helium wre found to be of tho Order ef ores hundredth of the elocrtronie «»billty i n liquid argon, $Me introduced serious difficultioo i n fletaralniag the pulse amplitude diotributloas i n heliunu . The lower out off froGjaeaey of the diecrirainator aaplifier was about 10 lcC« so that puleeo with collecting tines .longer then about 2Q iiAerct^conds were etteauiited proportionately T n tbjUl liadtcd tho use of tho diacricinator to a^erfeaents pestferaad et high fields* end with spacings amall enough to &ssp the collecting tJL«»a below 20 ^ see* As e laonsenuenee of the alow aobllities, only oj^eriaenta at tho snailest oeparations (0.15, 0.28 and 0*34. m.a., Oraphs U , 1$# and 16, respectively) yielded useful Information. The range of the alpha particles van calculated to b« .28 cm. so that for separation* less than this* tho distribution of pulse enplitudes use eo&pUeeted by the fact that QOBU alpha particles lost a fraction of their energy i n the opposite eleotrodo. the two oxporirants with epacingo greater than B oc eetabllahed that H i s not greater then 0*28 HM&*» and were used to investigate recombination off sets. X amp-Graph 14 ( a ) Graph -I4. (b) \ H E L I U M d « - 2 8 mm- T » 4 - 2 2 ° K 3 6 K V/c m 75+ •251 0 0 2 0 4 0 X o mp 6 0 80 Graph 15 H E LI U M T-4-22°K -KV/cm- ATT d = -33mm- ° '20 22 • 60 14 9 30 8 X* a m p • Graph 16 (a) Graph 16 (b) 69 An isspsrtent i ^ U e h e l effect, vMeh does not occur In argon* i e that both charge carriers contribute' to the pulsee. Tola i e an itdvantige since at high fields and email epaeings i t coapletoly elicdaatos tho gooaetrioal effect* Greph %% above that- vith a Ganaration af 0*28 is*©* there ie no evidence of a reduction i n pulse aspiitudes due to the alpha parti dee oapending energy i n the opposite olectrode. Graph© 14 (a)» M (b)» giving distributions at a separation of 0,19 &•&** shev die-continuities at Q » 0.5 . Shts relation, Q * ain S , gives the H a t i n g angle at vhich particles Juat reach the electrode, and whan used to calculate % * gives 'the value 0.51 a*a* » vhicu i s not . greatly diffetsht from the calculated value* Coupled vith Graph 15, this iadicetee that the. calculated velno, C.23 m^m , i e certsinly correct within the mm of the e£$erteat* The pulse ai*e distrleutione for a separatien of 0.15 K * B * sbev diooontimiitioB, as only the largest pulses vara due to alpha particle tracks vhich did hot- intersoct the opposite electrode* 1ft the seat fawourablo aspsriaants the signal to noise ratio vas large enough for the effect' of seise on the distributions to be neglected* so that a si&ple oatrapolation of the distributions Observed vith large pulses vas possible* Sale indicated the chap© vhich the distributions veuld have had i f sens of the alpha particle trac&s had net intersected the electrode and lead to the value 0*5 for the ratio :. 79 The results ©f observations at 0.33 *a*o* are given i n Graph© 16 (a), 16 (t») and Table 5. 3fee raaanm&nte vith positive fields yielded an a&aost conat&nt value of 0.33 £br %/a$ > vhleh la i n excellent agreement vith the rough value obtained from the Keaeureaente at 0.15 *M6* labia % mmm m mmmmm m d » 0.3$ n>**a* 123 .45 .75 12sd0* 13800* .97 0 ,93 ,01 3.3 7.4 M 6*9 30 .57 ,66 5.6 4*7 1.2 4*4 1$ o54 .49 3.7 2.4 1*5 3*2 7.S *53 .49 1.7 0*3 3.0 1*3 the * end - iuffices indicate the polarity of the source electrode end hence the sign of the carrier traversing the greater distance for the observation considered* t&th negative fields* the ratio decreased te 0.5 at lev fields free 3*3 at high fields* She effective offifcere of electrons * "a- * celleoted i n pulses vith both field directions are also given In Ueblo 5* to show the eonsietcnt difference betveen the apparent charge collection with tho two field dlroctlono, ©zat the difference i s not reel ie shewn by the fact that the direct current oet&ure&enta gave identical results with bath field directions* It i i explicable i n ter&e of .the different rofcUities of the two charge carriers* whioh resulted i n unequal effects oa the pulse ftt^lifier, and a teat was sade for thie by increasing the lower cut*off frequency frora 30 kC to 200 sct which attenuated the negative f i e l d signal by a factor of 5. fheee observations ere In oxcellont agreement taita the results of the previous chapter* in which i t was shown that the negative Ions had a lover isobility then the positive ions. A pulse whose rise time i s sis&lar to tho decay tise of the amplifier i s attenuated by en eoount dependent upon the ratios-decay Um With a high negative fie l d a. distribution of pulse wee observed* of which the largest had the devest risee* being due to negative Ions traversing aoat of tho cloctroda separation, i s the field van decreased e l l the pulses because clover* so that the largest enas* (x2) being eiouaet* were attenuated f i r s t * increasing the ratio *tAa • Further reduction i n field caused the puleee to vtoch tho positive ions contributed to baeoa» the largest end the pulse else distribution vac inverted* causing to denraejte to 0.5* the strong . attenuation of the pulses (observed with a negative fie l d of 125 caused by innreaeing tho lower eut*off frequency ef the amplifier supporte this arguisefit. 72 With an electrode spacing of 0.33 o.nu ot t *-JUWSr . puloo euiplitude jBeeeureiaentS were laede for fields of 6% 31 and 10 • . icV/oa, fh© diBtrlbuUono are plotted i n Graph 17* and the calculated values of ^/xg listed i n 3bblo 6. fraia tho tabl* i t ie apparent that the pulse* observed vith both positive end negative fielde vere nearly identical end that rooasMnaUon van similar to that obeerved at 4.22°£. At 1.7°£ the ffioMlitigo of both charge carriore are very nearly equal end larger than JU* at 4*Aft*s* Share i e therefore no nadifi cation of the distributions due to the collecting titesn of the ions* Table 6 62 • *66 «66 31 .62 .64 16 *59 .16 6* gjr,^, G u r r ^ ^sff^^ta,." - the assaults of the dirsct current tteasuroaants are plottccl on Oraph Id* It i s a plot of average ounbsr of electrons released H ELI UM d = -33mm- T=I-7°K 4 0 Xamp 6 0 Graph 17 10 Graph 18 per alpha particle e i e function of applied fie l d * R > at 4*23% ' < betas identical few both fie l d directions* M inso^ilicablc feature of tho curves is the change of slope at a field ef ebsut 1 kv/ctta. the currant i s lineal? vith fi e l d bolov this value and roughly proportional to $ ^ boWaon one and four Wf/m*. Gerritson'e (1948) data agree well vith the present results* but as bis gaai&re&enti extended only dovn to a field of about 5 kV/cau, ho did not observe tlaa region i n vhich the coraiuotion eurrent ahevo an enoEaloualy . strong field depeatlenoei* A fev values of a * taken at 1*6% and 1.4°K, aro also plotted* to shav that he sig&ifleant difference i s ebaerved* % U i t s the ionic mabilitiesi recombination shove no tc=?>cr&turo dependence* She values of inj calmtUted froa pulse ssg&ltude-G^asureisents at a spaelag of 0.33 a**,, are also plotted on Graph 18. Over the limited range of observations they agree reasonably vith tho direct current Beaouroiaenta. 1 Basalts of tho presant sxjierliaents suggest that liquid argon cannot ho considered ad & eoopreseed gas* hut that apodal theories relating epocdficelly to liquids era needed to describe i t . An &ttes$t to f i t the positive ion laobility to gae typo Kinetic Theory yielded a tseeoinglees value of mm free path, but Stakes* Law gives a value for the nobility af positive ions remarkably olese to the experimental value* Ins theory of Eyring (1936) appears to give a satisfactory physical picture of the ootion of positive ions* vhich are considered to be repeatedly trapped i n and theroally excited Htm potential veils* vhcee average depth, , deterained free the present experia»nte agrees reaeombly vith independent esttatee* an important agree^at vith Syrinx's theory i s provided by the observed constancy of stability* She application of Kinetic Xbeory to tha motion of electrons i n liquid argon i e acre successful, the reaaon for this appears to be the nature of the electron scattering process* i n vhieb electrons* experieneiag collisions* loss* on the average* only a small fraction f of their energy* In tho applied field they therefore aecwsulete kinetic energy greatly i n exeesa of the th&rael energy* isaJsiag tho probability of being trapped by potential veils very esall* %& scattering cress seetien of argon atone for deotrons, calculated from electron BObllity i n the liquid i s smaller then i n the gseeeus state by *a factor of to* order 103, fha values cannot be considered absolutely correct since tho nee ef Kinstic Theory fersnlne developed originally for gneres «$ift@$ a conatect oesa free path* '. vbich i s not observed* Hovevw both the absolute veins of the croee seetion and i t s dependence on electron energy ere cansitfarotl to be sppro3d«at«ly correct (Chapter Ug Section 6), I t does not appear eetinfactory to explain the aasll eroso .eeetion by aodifyiag the value of ' f used for the geeeoue etate* Since i t occura en , i t would bs> necessary to deerseea - f by a factor 104 and, hence to suppose that the effective naso of tho electron ie deereased by the easae faetor. As Ghovn i n Graph 4# liquid argon exhibits a Modified tteosauer effect. It i s pos»iblo to oxploln the behaviour" of electron© i n liquid ergon by considering the theory of the tasaner effect, discussed i n Cnepter 111* Section 7. Graph 19 shove the phases of the partial vaves ublch contribute partial drone sections for tho scattering of electrons by gaseous argon atoms. She contribution* of plumes v i t h ^ ~? 0 ere very eroll et lev energies, se that the tainLmtn of the Reosauer effect i s due to the ear© of sin y\0 * A change of form i n ^ 0 causing the sdnijuuia i n ein \ 0 to baoo^ very broad ia therefora needed to enplein the total cross section ehovn i n Graph 4. ttdn' A RGON Graph 19 Holtzmark Phases i n Argon change could result from the proximity of neighbouring steiss or possibly the high value of applied fie l d used i n the liquid* Jfee ionic a b i l i t y i s liquid heliust i e chcraoterietic of a liquid, and tho suggested explanation of the totality of positive • Ions i n argon applied couaUy to positive ions i n heUun above the A point* the behaviour of the negative ions i s * hovever* nng^pleined. Stokes* gives a value for the ©ability of positive lone vhich i s i n satisfactory ograejoent vith the obnervod values* particularly vheu the atomic cross section suggested by London (1954,) i s used* (Chapter 71, Section 4). She potential v e i l depth racniired by the application of Eyring's theory (1936) to the ionic mobility i e i n satisfactory ftgreousnt vith other dotercimtione 0 Ibat tho positive ion mobility decreases slightly vith taE^eraturo dovn to' the A paint i t 2*19°X, i s i n egrsojaent vith Eyrlag'e thaory, but dees net asrea vith Stokae' Lew, sines visooeity decreases vith decreasing tsanperature, Although Mgh©r§ the ionic mobilities i n liquid helium at 1*4°K are s t i l l such too lev to be explained by Kinetic Theory. Since they are apprexlgfttely given hyt* oC 6 77 they are not e^olieable i n terns of Eyyi3ag*o theory* either.. Analysis o f a»rey measurements by GoMetoin and Reekie (1955) shove that tho change et tho X point i n the potential experienced by atone of liquid helinm ie snail* en that an ©Kplenation of tiw ionlo nobility bolov the /\ point ennnot be aado ixm n elopl© oodlfieation of the gyring isodetl. Jjendon (194^) suggested that oriontatlon i n EOiBsntua space could produce the peculiarities In physical properties eueh cs. viscosity i n helium II* # ionic nobility decreases with increasing field* i t uould be nscoeonry to assuoe tbat en applied oloctric f i e l d destroys this orientation* iaplying that the viscosity of halite* J | l a reduced by en applied, field* It nay be significant that both the positive and negative ions are ferciions, {saving i n a mtilm $f helium atoiao vhich ere bosons, described by different statistics* She negative charge carriers i n helium are mm difficult to understand* Sheir behaviour does not appear to bo chcractaristic of free electrons and three possible e^&an&t&eus of their lev mobility {^f J ere eohaideredi* (i) the formation of negative aeliiaa ions* ( i i ) wgetivo ic^Mrity ions (of radii satisfying • Stokes* lev)*. ( i i i ) the electrons ere repeatedly trapped i n potential veils* resulting i n e behaviour 78 dcdlfir to that of the pemtive ions. the f i r c t possibility i e not fsvourod IKICCUSO at &,22°Z # i s a quarter of 4 , vhereii i f Ho*° vera fovastl, there i s as reason for believing that tho oobilities would he different* Stokao» Law reqiiirao that for ©abilities i n the ratio li4» the lonlo nlae^tem oust he i n the ratio and the sxistenee of a large cluster appears-very unlikely. Hass spectrograph ceesuraiaantc by tluga (1936) reveal the existence i n helium gas of Ss£ as vei l as He4 .bat no uvicenc© of any negative ion* If ispufity atoms were pres«mt i n the liquid helium used far sobility laeasaremontc, i t i s passible that their asiafeers need only have been ana i n 10$ m 106 to have had en important effect* To have an effect upon the observed mobility i&jrurity atoni at this dilution vould need to have a high probability of capturing m electron i n travelling a dietanoa of 10*3 a^j, %% i s v e i l fcnovn •teat io^urlties of this concentration can c^pletaly alter the properties of a. aaGi-conductor* St 1$ hot Known hov easily i3puriti*& dissolve i n llcjold holiucw 3he attaint to observe a change i n isobility by increaeing the iegjurity content vae inconclxieive, since the solution isay veU have been entorated (Orftedy. tfe» third possibility io that elections i n liquid h a l t e do hot fern negative Ions, but ere trapped by the potential veils* Since the depth of the potential walls ie not necessarily the sasa as those for positive ions* a different' a b i l i t y and different taroereture dependence vou34 m% be unseated* - • -A conolderatioji of the a t t e s t to oxsndae thie third possibility by illnffilnstiag tho liquid ehova that the Uluolnatlon nas toe faable, by * large factor, to have bad any affect. & 100 ^ t t bulb operating at ZiWG v&th 100$ efficiency gives a flux of about 10*9 pbotons/see./oa2 'it 4 MM** If. Heitier ' s value (1954) for •,. the' cross sssWLcn of n free electron for Interaction «ttfc rjaJlatlon, 6.6 110-25 ca 3 t i s e^swd| ; i t indicate* that on .the average* an electron i n this light intanaity vould be excited onco every 10 5 seconds* She probability of optically exciting an electron frets a potential v e i l i n l&fuid n&Hus ie very anea too eaall to have effected the mobility. ' She negative effect of light on the osporiceat iodicstas that variatoon i n intensity of tarn illumination could not cause the variation obtained i n reeulte of ©ability. lbs present aeasuresente indicate that i n liquid the ranges of alpha partidas end the ion densities i n their tracks correspond exactly to the gaseous state* Sfeie vae the hmis of corrections to 'the pulse si$e distjdbuUone which vera used i n oatlrating the off acts of r^rtr?,;,?^r*\i*tion. 30 Wte asplitudo dJottdbrtS-cms ft*** ©tow* that tha depaodenee af rQcoEMnnUoa u^on tha QOglo between tha portiel® Jaffa theorj' (Chapter VII* Section a), (tha diraet aKrroat Jaffa theory. Ctorrlts^o cosxtactien currants i n )* l a hoth «*f . as # Uaear i n tha light of tha -iHpftiiaitalft*. date. We any of tha J&££Q azmm& (Chants I I I , Soction 1)?-2 * > * i - ^ [ a lover H M t en tha v a l « 9 of b (tha $tsJ»ii»d tha track) by putting at vhich field tho o^arizfiaofta and using tha Eiast y k T tha value b • 1.1 x $ «S 1 * Ufting E » 1 VVi.AU/ ahov that tho ourrent ia ISftegt vith i n relationship* indicating that «fiS« this i s unacooptably large* * error in the Jcffo theory vhai values Hr helium give b = 9 a IO" 9 «M$& mm &®m$k Imgy* tern- the vaiaa of .,. «aa M- m0gtg$«& by Mt* &»£ $er*&tseh* fo* % < ( 1 Jeffe" findes- • 7 1 " "i v Since thie i s far frost linear* l i i s equally unacceptable. . mm*& <19S2) theary S&vo (far the conduction currant) at law f isMa, & vfcleb i s t d a M r linear o w a liMtsd ratsg©. Howvsr i t gives a -value for b of i s 10"^ CEB* , vbi<?h i a just as unacceptable as that af Jaffa* oo that vo are led to coaoltede that their method of approach i s not applicable to liquids, /n elteraativo approach i s suggested by eeai&dering the fields vhich art gonoratsd whan tve exactly Puperlinpoeed oolutsns of opposite charge d r i f t apart laterally i n the satmsr envisaged by Jaf f a end Krwera, Sines i n liquid argon absnt Ion pairs pe? alpha particle escape rec&ablaaiion l a a HoM of 10^  volts/eei»« the Jaffe^Kraasre s&del rsquiros the field to pttil apart two cylinders of charge vith linear density 2 * IO 7 icma/cR. Ths applioa field • can only eoopota favourably vith the e&tuelly attractive force between tvo Guch colmana vfeen thay are already asperated by at least 2*9 * 20*$ <sae. 4d thio diatancs i * appreciably greater than the diameter union the eolucns ere eoneidered to have, thie taeehanifisi l a inadequate to esglala tho collection of charges of tho observed mgsdtude* lift tsodel here proposed nakes use ef calculations by srsi&ne (1954) *&&eh shev that electrons elected from atotas near to the track of en alpha particle ere given higher kinetic energies than electrons frora etesas on the perineter of the of i n i t i a l ionization* Being attracted towards the alpha particle, they continue through the centre of the track ani cut the other side* Sino© the e&jaa precede occurs for snny electrons oicaltejwmely, an expending cylinder of negative charge i s formed vith the outerccsi electrons iaoving fastest* The posiUve ions neve oaro elovly and are considered to fern a line of charge along the track, understand the escape ftedhfetf&m we mat consider the fields experienced by the elootrona. The f i e l d nt a radius r i e m « * » 8 u tte mmmmm<*t***w-Urnmw» length inside the radius t § the field ie thus given by the attractive force of positiva charge et the centre of the track corresponding to the nus&er of electrons, jl , «ith larger encrgieo than electrone at the radius considered. 33 She radius et vhich the eppllod fi e l d le equal to that of the central fi e l d of the charge diitributteit. « ^ t e r M ^ # w - -of electrons ei&g&hg In rospdnso to the applied f i e l d . I t i s net necessary for the dectrona to be on ona aido of the eolusn to oacapa einea they lose l i t t l e energy by eppsarins en the wrong side of the distribution *b& Gh&oting through i t again. She-' feinoUo energy i&ieh they flr e t acquire detendnos vhethar they ultimately escape, Sloctron onersy i s mt greatly reduced by eolliaione during this precede oinoo the Sean freo path to about 1 0 - 6 date** vhich ie gesparnble with the radius of the eolwn* and tfeoy %xm only o assail fraction of thai*' ansrgy at each Q&llsloh* &i#etreni vhi& do net ao^aire enough i n i t i a l JdUtotic energy to escape hare no mam of leaning the cr i t i c a l radius, and hence they uitlioately reee&iblne vith positive ions* f t i s icportanfc to note that i n this codcl* ionic nobility, diffusion and the r^ao^lnation coefficient do net have any influence i n recorabimticm for fltelde psrpondioulex to tha ionization oolusais. With fields parallel to the alpha partislo tra<&3» the electrons return to the positive ion colurona and eventually lose their onergy, poselbly after several oooillations throu$* tho oolusaiG* Longitudinal escape f*m the coluians io probably ade^Uateiy deocribed by the Jaffa theory* This code! i e based on the aeeu^pUoa that* after ionis*ition* electrons are projected parponoicularly to the alpha particlo tracks, that this cast be the case for the cssjority of ^lQctrons can be seen by ooneiderlcg the conBarVfition of energy and Eomntua during the process of aooisfctlon of * elude <&m 1% v#m not t» -WW&A i* #• • the few electrons vhlfih ere feet ©it&iga to give oseoDdery tracks of lojilBoUon, hot thane & reyo ere* i l l feet* obaorved to be very nearly perpendicular to alpha particle tracks i n cloud chaabsr photographs. ' Stm justificetion for this picture can be draw* from the e$pSriiB&Kts» Bar alpha particle tmetss at any angles vith the fie l d * there ere tve s»thede of oecape — lateral Qseepe detensineci by the i n i t i a l kit^US energy ef the Gleetroni3, and longitudinal escape, which io such less effective* letdd to the obeervod very strong dependence of recombination en the angles of treej® JMfttfflr parallel to the f i e l d , ' (Chapter VII, Gcetion a). Since the mober of elphe particlee for' uhlcb loagitudinel escape i e Important i s assail* the nesJftspad conduction enrrent indicates the field dependence of escape for fialde pcrp©ndicKler to the coluon. Xt i s Significant that the angular deparrience blooms a constant at high fields, i n contradiction to the Jaffa theory, by vhich the' angular dopaalonea ohcuM tend to vanish. Aa even core -convincing' juctification of the Basel here preeGntyd erisos fron the.' results vith heliutu i n vbieh the conduction current i s almost • independent ef tcjpsjNftwt* and the poles dietributionu appear identical at 4,22»S end 1*7%. although the BobUities era very toapareture dependent, CorreDponding changes raaat also odour i n the diffiioion cocfficicate so that by the ^affe theory rsco^natAon vould be a strong function of t&^er&ture* 85 Toe dicagroecont (Grapa 3$) between the dtr«i=t3y oba<?rvttd direct current ctsl that c a l c u l s ^ f m i pulse aeamiro35onte v l t h srgc3B appears to bo oisalficp^t, and i c coasiBi^nt vith tho depesrietic© of pulse sl«e on olsctrodo spacing with constant fields (Graph 10)* Both are esplleable i o teres of trapping of elaotrona by icEJurity atoaa. I f as electron ie trapped by aa iqpurity atom i t forsa a alow negative ion vhich cannot contapibuts further to tha pules, but i s hot withdrawn froo tha direct currant, Toc»?orary trapping ouffieietit to delay an elaotroa by two ederosaooado i e sufficient* at fields ebcm SO W/m*t a^reBaont betvosn tha pulse eiaos at different epaelhp Indicates that ouoh trapping io improbable* but at lov fields i t i s sufficient to reduce the current as calculated from pulse sroeure&ents by a factor as Inrgo as two. $t$ variation of pules also vith spaaing say be attributed to the greater probability of trapping at vide epaoiiass. this Sfi&ee i t uoll&cly that the effect i e duo to etractural traps fuadssranial to the liquid elnco theso wouli be cuffidonUy nuisertwa to safes tha trapping CM^leta at a l l opacinga, the negligible effect af ss&li ^unhtitto of c a m i n ixfipuritios addt^ to liquid argon by Bfivideon and lareh (1943) W be attribute to tho fact that e l l their imsuraisante fieu^e abova '£$ &V/fi% Anlenson* 0. (1955) ®m* S§* 300* Auger, f. (1926) Jour, Be* Paya., 2, 69. Bortner* f * B » and Burst* $.d* (1954) Rev** 22* Chedulek* J« and Etaeleus, (1926) M l . Mag,* i , 1. Cocpton* K**% (1923) Flare* Ber.* j f r $3$* 432. Cr&vath, A.M. (1930) Hjye. Rev.* j&» 243* Pennt* J*G* and &&tn* a.S* (1954) Mad* fhya.# 172. Davidson* ». and lareh* A*'S* (1946) Phys. 2ev., 233* Davidson, 8* and larah, A.S* (1950) Ihya* 2Z» 706* Bruyvosteyn* J3.J* (1930) Physica, 1& 69. Blocre, w.C. and Bands* & (1949) j§jaatrnn|#a. HcCrav-iiill Book Cos^any* Ins.* Toronto* P. 139, aq* 19. Erefcine* G*A. (1954) Proa, Hoy* &*e** London \ k ;» 224* %*ing* 0* (1936) «T* Chss* fhya., i , 233* Qsrritson* A»B* (1943) Sfeyeioe* &* 331. Goldstein, t* and Beeki** J* (1955) ffeys. 2ev** ^ * 357. naoberll, W „ Huhar, P. and Soldinger, (1953) Helvotica fnysiea Acta, 14$« Beitler, V, (1954) .^ i..^ tm Pf Bftd>ftVffif $sdM at the Clarendon frees, p* 53* HoltBmark, J . (1929) Salt, f* Phys., £5* 437* Hutchinson* G.U. (1943) Uature* 162. 610. Jaffa* G. (1913) Anaelen Der ffryslk* £2, 303* Jesse* H.P* end %dsnfik&* J. (19$2) l%ii« Msg** 4$* 964* Jest* W* (1932) ^ f ^ ^ ^ ^ r ^ g t , , Acadetaifi w Kramer** H*A* (1952) ffeyeiee, 665. langevin, P. ( 1 9 0 $ ) Ann* Oheffi. Riye., j$* 2A5. Leonard* P. (1903) Aha. d* Pnynlls, ig, HA* Uvingeton, aasS Bethe* H.S, (1937) RoV. lied* Phy».» £* 24& $ m 1 flbhe* p* 86* ^ ^^^ Loob, L . (1939b) ^jqte^Ttffirawafl „*«? ^ i ^ i ^ ^8fteeaa,in fin^f?» London, P. (1946) Report of m IntermUoma Conference on gaftdfaea^ • : Freneie I*td»* £ficaden« London, F* (1954) John f&ley end Sone, p. 31* Kalkin, H.8* ead Sobults, H+L. (1931) Pfaye. Bev** 1051. Karshftll, Jf8» (1953) Hays* &e*»* 905* Maessy, B*S*tf* and Eurhop, £*B*0. (1952a) ^ t e g l g . f l ^ ^ ^ i f f l ^ i ^ i f W ^ * oainrd mvm&t? treaty p* 1 1 5 * F^coy, S*a.W* and BOffbOp* 3,a.3, (1953b) Flfttofflfi ftni Ifflrtfi? Xrtwt ^isnomQnfl. Oxford M v e t i l t y Frees* p* 126* S&ese?* H » B , M C and Burhop, 1*8*§» (1952o) Sftg ^ r A f l AKd fal&fl tofiS S&m&m, « J H J * I «ni*$r*itr $*ede* p* 10* 4S&V torce, ?«M** Allie* V*P.* end M S.S0 (1935). Phys. lev** 4§* 412* Rojaasuer, C, (1921) Ann, d 0 Jbyslii, j ^ , 513. Mce* S,oe (1944) Bell* % * t * feeb* J»* 232* Rudanlio, H*S* and ScbubalJmw* X*W. (1934) Wff* Z* Sonnet* ^  470. Rutherford, B., Chariwlck* J. sal S l l l c , G.E. (1930) lledfotldnq fro^ ^ ^ ^ y g . ^ k ^ M ; . easkridge snlvemty ^eis# tendon* Sharps, (1913) free* Fhyeft £oc. A, , $59* #*$* (1937) l^eles* J * §&* • 'iuxea, 0. (1936) 2eit. f, Phye., ££2> 463. 


Citation Scheme:


Citations by CSL (citeproc-js)

Usage Statistics



Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            async >
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:


Related Items