UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The annihilation of positrons in helium Lee, Gregory Frank 1969

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

Item Metadata

Download

Media
831-UBC_1969_A6_7 L44.pdf [ 3.31MB ]
Metadata
JSON: 831-1.0103738.json
JSON-LD: 831-1.0103738-ld.json
RDF/XML (Pretty): 831-1.0103738-rdf.xml
RDF/JSON: 831-1.0103738-rdf.json
Turtle: 831-1.0103738-turtle.txt
N-Triples: 831-1.0103738-rdf-ntriples.txt
Original Record: 831-1.0103738-source.json
Full Text
831-1.0103738-fulltext.txt
Citation
831-1.0103738.ris

Full Text

TEE MNIHILATION OF POSITRONS IN HELIUMbyGRE)ORY FRANK LEEB.Sc., University of British Columbia, 1966A THESIS SUBMITT) IN PARTIAL FUT2ILMENT OFTHE REQUIREMENTS FOR THE DREE OPMASTER OF SCIENCEin the Depar±mentofPHYSICSWe accept this thesis as conforming to therequired standardTIlE UNIVERSITY OF BRITISH COLUMBIAMarch, 1969In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the r e q u i r e m e n t s f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h C olumbia, I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and Study. I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g of t h i s t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department or by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . Department The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada ABSTRACT Lifet ime techniques have been used to investigate the annih i la t ion of positrons i n helium as a function of e l e c t r i c f i e l d and density . Positronium formation has also been examined as a function of e l e c t r i c f i e l d . Results obtained for zero e l e c t r i c f i e l d y ie lded a l inear dependence of the d i r e c t annih i la t ion rate on density of (0.7214 - .0082)D x 10 6 sec 1 amagat 1 , with no evidence of non- l inear i ty . This corresponds to a Z of 3.628 - .041. Assuming the free ortho-positronium annih i la t ion rate of 7.2 x 10 6 sec" 1 a value of (0.0991 - .0067) x 10 6 sec amagat was obtained for the ortho-positronium quenching rate . A dependence of the d i r e c t annih i la t ion rate on applied e l e c t r i c f i e l d was observed and compared with several current theories describing the positron-helium i n t e r a c t i o n . The predict ions of the theory of Drachman (1968) are shown to be i n closest agreement. Measurement of the amount of positronium formed as a function of e l e c t r i c f i e l d disagrees with previous resul ts and based on the present work a value for the momentum-transfer cross-sect ion of positrons i n 2 helium at 17.7 ev i s found to be at least .13 5 77"a . i i i TABLE OF CONTENTS page ABSTRACT... ... i i LIST OF TSBLES. . . v LIST OF EKURES . . . . v i ACTvNOWI^ EDCS-IENTS • • v i i CHAPTER GS3 POSITRON-ATOM INTERACTIONS. . 1 l'.l?. Introduction 1 1.2' Positrons i n Noble Gases . . 2 1.3 V e l o c i t y Dependence of Positron-Atom Interactions. . . . 5 1.3.1 Scattering Cross-section 1.3.1.1 Theoretical 1.3.1.2 Experimental 1.3.2 Direct Annihilation Rate 1.3.2.1 Theoretical 1.3.2.2 Experimental 1.3.3 Positronium Formation 1.3.3.1 Effect of Impurities 1.4' J u s t i f i c a t i o n of Lifetime Measurements i n Helium . . . . 12 CHAPTER TS© EXPERIMENTAL PROCEDURE 16 2.1. Basic Techniques . . . . . . . . . . . 16 2.1.1 Lifetime Measurements 2.1.2 Valley-to-Peak Measurements 2.2: Chamber and Positron Source 17 2.3.; Gas Handling . 19 2.3.1 Method of F i l l i n g 2.3.2 Estimation of Gas Purity 2.3.2.1 Impurities due to Outgassing 2.3.3 Titanium P u r i f i e r 2.4: E l e c t r o n i c s . . 21 2.4.1 L i n e a r i t y 2.4.2 Resolution Checks During the Experiment 2.5 Data Analysis 27 i v page CHAPTER TIMES PRESENTATION OF RESULTS 28 J . I Scope of Results 28 3-2 A c c e p t a b i l i t y of Results 28 3.2.1 Maximum Like l ihood F i t 3.2.2 E lec tron ic S t a b i l i t y 3.2.3 Gas P u r i t y 3.2.3.1 I n i t i a l Indications 3.2.3.2 F i n a l Acceptabi l i ty 3.3 Experimental Results 31 3.3.1 Li fet ime Measurements 3.3.2 Val ley-to-Peak Ratios 3.3.2.1 I n i t i a l Results 3.3.2.2 F i n a l Results 3.4 T h e o r e t i c a l Results . 42 3.4.1 D i f fus ion Analysis 3.5 Discuss ion of Results . 43 3.5.1 A n n i h i l a t i o n Rates 3.5.1.1 Comparison to Other Workers 3.5.1.2 Comparison to Theory 3.5.2 Val ley-to-Peak Ratios 3.6' D i scuss ion of E r r o r . . 47 3.6.1 E l ec tron ic I n s t a b i l i t i e s 3.6.2 Timesorter L i n e a r i t y 3.6.3 Applied E l e c t r i c F i e l d 3.6.4 Gas Density 3.6.5 E/D 3.6.6 Gas Composition 3.7 Recommendations for Future York. . . . . . . . . . . . . 50 CHAPTER; FOUR CONCLUSIONS 52 BIBLIOGRAPHY. . . . . . . . . . 54 APPENDIX A EFFECT OF IMPURITIES ON POSITRONIUM FORMATION. . '. . 5& APPENDIX B CALCULATION OF INITIAL GAS PURITY 60 V LIST OF TABLES page Table I Published %e£f f ° r Thermalized Positrons i n Helium 11 Table II Positronium Formation Thresholds of Common Gases 14 Table III Direct Annih i la t ion Rates at Zero F i e l d 32 Table TV Direct Annih i la t ion Rates as a Function of E l e c t r i c 33 F i e l d Table V Ortho-positronium Annih i la t ion Rates 34 Table VI . Val ley-to-Peak Ratios 41 vi LIST OP FIGURES Figure I Typical Time Spectrum page 6 Figure 2 Theoretical Z „„ and Momentum-Transfer Cross-Sections err 8 Figure 3 Typical Energy Spectrum 13 Figure 4 High Pressure Chamber 18 Figure 5 High Temperature P u r i f i e r 22 Figure 6 Block Diagram of Electronics 24 Figure 7 Integral Linearity of Timesorter 25 Figure 8 D i f f e r e n t i a l Linearity of Timesorter 26 Figure 9 Zero F i e l d Direct Annihilation Rates 35 Figure 10 E l e c t r i c F i e l d Dependence of Direct Annihilation Rate 36 Figure 11 Ortho-positronium Annihilation Rates 37 Figure 12 I n i t i a l Valley-to-Peak Ratios 39 Figure 13 F;inal Valley-to-Peak Ratios 40 Figure 14 Theoretical E l e c t r i c F i e l d Dependence of Direct Annihilation Rate 44 Figure 1? Theoretical Positron Energy Distribution Using Results of" Drachman 46 ACKNOWLEDGMENT I wish i o express my sincere thanks to D r . G. Jones for h is great help during the course of t h i s research. The value o f the many lengthy discussions we shared cannot, be overestimated. My most sincere appreciation i s extended to Dr . P .H.R. Orth for the long hours he spent, inaugurating me to the nuances of experimental physics , and for. h i s fr iendship over the many months of th i s projec t . In addi t ion , I wish to thank my wife for her forbearance and encouragement. Thanks are also due to my parents who were also a source of encouragement over the past years . F i n a l l y , a id i n the form of a National Research Council of Canada Bursary i s grate fu l ly acknowledged. I CHAPTER ONE POSITRON-ATOM INKSRACTIONS 1.1 Introduction The study of* the behavior of positrons i n gases i s of considerable interest because of the contrasts and comparisons that can be made v i t h the resul ts of e lectron sca t ter ing . The-processes'that contribute to the low-energy e las t i c scatter ing of electrons or positrons from a complex atom or molecule are (for the-most commonly used theoret ica l approximations) i . the average in terac t ion with the undisturbed atom or s ta t i c f i e l d (M.S.P.) i i . e lectron exchange (for electron) or v i r t u a l positronium formation (for positron) i i i . e l e c t r i c po lar i za t ion of the atom by the Incoming p a r t i c l e . For the electron the s ta t i c and the po lar iza t ion f i e l d s are both a t t rac t ive , whereas for the posi tron only the po lar iza t ion f i e l d i s a t t rac t ive .^ Hence the two f i e l d s tend to cancel . Comparison of the predict ions of ex is t ing models of atomic c o l l i s i o n s with experimental resul ts obtained from the behavior of positrons i n gases should allow the assumptions underlying the models to be checked. Unfortunately there i s no d i rec t method of determining the e las t i c scattering cross-sect ions because of the very poorly defined energy of avai lable pos i trons . The most commonly used experimental method involves 2—8 the measurement of the annih i la t ion rate of positrons i n gases. By means of a d i f fus ion analys i s , which computes the ve loc i ty d i s t r i b u t i o n 2 of the positrons, the annihilation rate can be calculated. This method requires the use of theoretical values of the scattering, annihilation 2 and positronium formation cross-sections. A much more stringent check of theory can be obtained i f the average energy of the positron is raised 2 3 8 by application of an electric f i e l d ' ' or by increasing the temperature 9 of the host gas. The technique used, assumes the positron velocity distribution has attained equilibrium. The. average velocity i s calculated from the velocity distribution which is found for a given temperature and electric f i e l d by the diffusion analysis techniques. The comparison between experiment and theory is most often expressed as a value for Z ' . Z .„ is; the effective number of electrons per atom eii e i i (in terms of the Dirac cross-section) for the annihilation process and is dependent on the positron energy and temperature. Experimentally this value is directly related, under ideal gas conditions, to ^ /D where is the annihilation rate and D the gas. density. Theoretically, 2" is. calculable from a knowledge of the wavefunction of the positron-atom system. 1.2 Positrons in Noble Gases Only a brief description of the fate of positrons in a noble gas; w i l l be given here since i t is well described elsewhere.2»10>Hjl2 22 Positrons emitted from a Na, source have a continuous kinetic energy 13 distribution up to 542 Kev with a peak at about 170 Kev. In a noble gas. these positrons are slowed rapidly by inelastic collisions. In helium the time for a positron to slow to 10 Kev is approximately 52 nsec—atm.1^ The time involved for most of the remaining energy to be 3 l o s t by i n e l a s t i c c o l l i s i o n s i s uncertain but a ca lcu lat ion done for 2 -10 argon has indicated an upper l i m i t of 5 x 10 seconds and th i s should also be an upper l i m i t for helium since the las t ine la s t i c l eve l i s more energetic than the corresponding l eve l i n argon (19.9 ev compared to 11.6 ev) . The time taken for positrons to slow to a few e lectron-v o l t s i s therefore approximately 3 nsec for helium at 20 atmospheres. 11 14 15 Furthermore very few positrons annihi late i n t h i s t ime. ' ' Once t h e i r energy i s below the las t ine la s t i c l eve l of the host gas positrons can only be slowed by e las t i c c o l l i s i o n s with the host gas;. During t h i s slowing down period the positrons can annihi late by one of three main processes. F i r s t , many of the positrons annihi late with atomic electrons during c o l l i s i o n with the atoms. These are the d irec t annihi lat ions and they predominate at these energies. This rate , of course, depends on the gas dens i ty . Secondly, a large number of positrons annihi late through positronium formation. Positronium^ the bound state of an electron and posi tron has two spin states:, J = 0 and J = I . Positronium can only be formed i f there i s s u f f i c i e n t k i n e t i c energy ava i l ab l e . The positron must be above a c e r t a i n energy, F j ^ r * i n order to form positronium. This threshold energy r E t h r , i s given by E , , = E . - 6.8 ev t h r ion where E j . o n is; the i o n i z a t i o n energy of the host gas and 6.8 ev i s the binding energy of positronium. In helium =17 .7 ev. It has been shown that positronium formation occurs within a few nanoseconds. 1^ The a n n i h i l a t i o n of p a r a - p o s i t r o n i u i n „ the s inglet state J = 0, 4 occurs via the emission of two photons and has a mean lifetime of 1.25 x 10 ^ seconds in its ground state.^ Ortho-positronium, the triplet state with J = 1, annihilates through three photons in its -7 17 ground state and has a calculated lifetime of 1.4 x 10 seconds. The positronium lifetime may be "quenched" by the collision of the positronium with a gas atom, during which.time another channel for, two photon annihilation exists, which can compete with the normal annihilation process. In the noble gases; up to pressures of about 50 atmospheres the quenching rate is not sufficient to shorten the lifetime of ortho-positronium significantly. For helium the measured quenching rate is 4* 6 1 1 18 (.086 - .008) x 10 sec am . This; reduces the ortho-positronium -7 lifetime to 0.88 x 10 sec for helium at 50 amagats. The effect of such a quenching rate on para-positronium is negligible because of its short lifetime. A third channel by which positrons could annihilate is by formation of a molecular complex with the atom. This possibility has been discussed 4 19 with respect to argon both experimentally and theoretically. These results disagree and the situation is not clear. For helium, no such results or calculations are available. A variational calculation which + 20 predicted the- stability of the He-e system has been questioned on the basis of energy considerations."'' Theoretical estimates of scattering 21 lengths of positrons in helium also indicate that no complex is formed. The results presented in this thesis are based upon the assumption that decay from He-e+ complexes, if such exist, is negligible compared, to the direct annihilation process. Besides those positrons annihilating in the gas there are a number 5 which annihilate in the chamber walls, source and source holder. These occur in the first 10 ^  sec.1^ The source and chamber used are designed to minimize this effect.1^ A typical time spectrum (Figure l) illustrates the behavior of positrons in gases. The prompt peak, occurring at zero time, (the method of defining zero time is described in Section 2.4) is due to th& wall, source and para-positronium annihilations. The width of the prompt peak is about 7 nsec, a value within the resolution time of the apparatus. As earlier stated para-positronium is formed in the first few nanoseconds and decays; in 10 ^ sec. Hence this annihilation radiation is recorded in the prompt peak. The next feature, the shoulder, occurs if the direct annihilation rate is velocity dependent. It has been well documented in all noble 2 3 6 gases; except helium ' ' and is attributed to direct annihilations of free positrons as they slow by elastic collisions from energies near that of positronium formation to thermal energy. After the shoulder is the exponential component representing the direct annihilation of free positrons at thermal equilibrium. This is a constant rate for a given energy distribution, with or without velocity dependence in the annihilation rate. The last segment of the spectrum is the long—lived component caused by the decay of ortho-positronium. The observed lifetime is that character-izing the slightly quenched three-photon emission previously mentioned. 103 Velocity Dependence- of Positron-Atom Interactions 1.3.1 Scattering Cross-section \ I XT? a O 0 7 CO o LL. O O . Prompt Shoulder Peak Direct Lifetime RUN 53 3 6 . 3 2 RMRQRTS Q V/CM RMRGRT 1 . 6 0 9 NSEC/CHRNNEL 4-'JHA a II II II Orthopositronium Lifetime Random Background 70.0 110.0 150.0 190.0 230.0 CHANNEL NUMBER 270.0 310.0 350,0 Figure 1 . Typical Time' Spectrum 7 1.3.1.1 Theoret ica l The t h e o r e t i c a l approach to positron-atom interactions i n the noble gases, except hel ium, i s based on semi-empirical po lar i za t ion terms. and.Hartree approximations: to the s ta t ic f i e l d . The exact solutions to the wave equation describing the interact ion i n untenable without such approximations. In the case of helium, however, the task i s not as formidable. Calculat ions using various approximated wavefunctions 22-25 for the positron—helium system have been performed. The r e s u l t s o f such ca lcu lat ions , i n par t i cu lar the v e l o c i t y dependence of the scatter ing cross-sect ion i s summarized i n Figure 2. It can be seen that a l l models representing the positron-helium atom in terac t ion have a v e l o c i t y dependence, the magnitude of which depends upon the p o l a r i z a t i o n used. 1.3.1.2 1 Experimental Experimentally v e l o c i t y dependence of the scattering cross-sect ion cannot be unfolded d i r e c t l y without the a v a i l a b i l i t y of mono-energetic pos i tron sources. The present methods of analysis calculate the effect* of an e l e c t r i c f i e l d on the v e l o c i t y d i s t r i b u t i o n (using the scattering cross-sect ions) and hence calculate a new d irec t l i f e t i m e . Such a method can only say whether a p a r t i c u l a r model i s i n error . It cannot predict what the cross - sec t ion should be for a given v e l o c i t y . Recently, by combining e l e c t r i c - f i e l d and temperature, dependences of the d i r e c t ann ih i la t ion r a t e , a value for the scattering cross-sect ion i n argon o 8 at 25 C has been, a t ta ined . Zeff 7 6 5 Zeff for Positron Annihilation in Helium 0 -1 .2 .3 .k .5 .6 .7 .8 .9 1.0 K F i g u r e 2 from " P o s i t r o n s and P o s i t r o n i u m i n Gases'* P.A. F r a s e r Advances i n Atomic and . M o l e c u l a r P h y s i c s , V o l . 4 Academic P r e s s , New Yo r k (1968). T h e o r e t i c a l Z (a) K r a i d y ( 1 9 6 7 ) (b) Massey et• a l . , (1966) (e) Drachman, (1966b) (d) K r a i d y and F r a s e r , (1967a) (e) K r a i d y and F r a s e r , (1967b) (1967b i n c l u d e s Temkin-Lamkin p o l a r i z a t i o n ) ( f ) Drachman, (1968) T h e o r e t i c a l Momentum T r a n s f e r C r o s s - S e c t i o n s (a) Massey et a l . , (1966) (b) Drachman, (1966a) (c) K r a i d y and F r a s e r , (1967a) (d) K r a i d y and F r a s e r , (1967b) 9 1.3.2 D i r e c t Annih i la t ion Rate 1.3.2.1 Theoret ica l The t h e o r e t i c a l s i tuat ion i s , again, best summarized by Figure 2; (where the d i r e c t ann ih i la t ion rate 7\ i s given b y = x D x 2.01 x 10^ sec The magnitude of the ve loc i ty dependence i s dependent upon, the degree of p o l a r i z a t i o n . Notice that i n a l l cases the annih i la t ion rate i s l e s s for higher v e l o c i t i e s . 1.3.2.2 Experimental There, are three experimental indicat ions of a ve loc i ty dependence in. the d i r e c t a n n i h i l a t i o n r a t e . These are 1. the shoulder i n the time spectrum i i . the e l e c t r i c f i e l d dependence of the. d i rec t l i fe t ime i i i . the temperature dependence of the d irect l i f e t i m e . The shoulder i n the time spectrum has previously been seen conclusively 3 4 5 8 3 in. a l l noble gases except poss ibly helium. ' * ' Falk and Jones d id 26 not, observe.a shoulder i n helium. Later experiments indicated the presence o f a shoulder but these resul ts were not conclusive. The second i n d i c a t i o n , a reduction i n the d irect annih i la t ion rate 2 3 upon a p p l i c a t i o n of an e l e c t r i c f i e l d , has been seen c l ear ly i n argon. ' The; a p p l i c a t i o n of the e l e c t r i c f i e l d also reduced the width of the shoulder u n t i l i t disappeared. Since the e l e c t r i c f i e l d has the effect of increas ing the equi l ibrium v e l o c i t y of the positrons th i s l a t t er effect indicates tlae v a l i d i t y of the assumption of the shoulder as a slowing down part o f the spectrum. For helium, no apparent effect of an e l e c t r i c f i e l d on the d i r e c t l i f e t ime has been o b s e r v e d . ^ 10 The t h i r d ind icat ion of v e l o c i t y dependence of the d irec t annih i la t ion rate i s a temperature dependence. Recent -work has observed such a dependence 9 i n argon. As expected the annih i la t ion rate decreases as the temperature increases since the average v e l o c i t y of the pos i tron , as determined by the host gas, increases. No effect of temperature on the shoulder width was found. This was interpreted as ind icat ing the annihi lat ions i n the shoulder occur with positron velocit ies- wel l above thermal v e l o c i t y . For helium no ind icat ion of a temperature effect has been reported although measurements have been made over a wide range of temperature (Table I ) . There i s , therefore, no experimental evidence avai lable at present ind ica t ing a s ign i f i cant v e l o c i t y dependence of the d irec t annih i la t ion rate of positrons i n helium. 1.3.3 Positronium Formation The formation of positronium i n a gas i s ve loc i ty dependent since the formation requires that a minimum energy i s reached. For helium = 17.7 ev. At thermal energies the v e l o c i t y d i s t r i b u t i o n i s such that very few positrons a t ta in suf f i c i ent energy to form positronium, and hence the contribut ion to decay through th i s channel i s very small . As an e l e c t r i c f i e l d i s applied however the v e l o c i t y d i s t r i b u t i o n i n the -gas; i s shi f ted upwards u n t i l a s ign i f i cant number can form positronium. 2 When t h i s happens the d i rec t ann ih i la t ion rate appears to increase. Therefore as the e l e c t r i c f i e l d is: appl ied, there i s a decrease i n the d i r e c t ann ih i la t ion rate followed by an increase when positronium formation becomes s i g n i f i c a n t . 11 Table I Published Z . for Thermalized Positrons i n Helium ef J eff References Conditions 3.2 Daniel and Stump (1959) Gas, 7°K to Room Temp. 3.25 + 0.22 Duff and Heymann (1962) Gas, Room Temp. 3.92 + 0.04 F a l k et a l . (1965) Gas, Room Temp. 2.45 Osmon (1965a) Gas, Room Temp. 3.43 + 0.19 R o e l l i g and K e l l y (1965) Gas, 4 . 2 ° K 3.80 + 0.04 Fa lk and Jones (1966) Gas, Room Temp. 3.96 + 0.04 R o e l l i g and K e l l y (1967b) Gas, 77°K 3.92 + 0.32 Paul and Graham (1957) L i q u i d , 4 . 2 ° K 3.12 + 0.34 Wackerle and Stump (1957) L i q u i d , 4 . 2 ° K 3.67 + 0.12 L i u and Roberts (1963a) L i q u i d , 1 .5 °K to 4.2'°K from "Positrons and Positronium i n Gases" P.A. Fraser Advances i n Atomic and Molecular Physics, V o l . 4 Academic Press , New York (1968). 12 A method of determining the amount of positronium decay r e l a t i v e to the free posi tron decays ,is the measurement of the r e l a t i v e number o f three photon events to two photon events. This i s the val ley-to-peak 2 r a t i o (Figure 3) and should increase as positronium production increases. 1.3.3.1 Effect o f Impurities Positronium formation, as indicated, occurs when the energy of the positrons become high enough to reach the E ^ ^ of the gas. For the case of helium th i s energy i s quite high but for many gases which may be present as impuri t ies t h i s threshold energy i s comparatively low (Table I I ) . This means that , even i f the amount of impurity i s very low so that the l i fe t imes are not appreciably affected, the pos i tron makes many c o l l i s i o n s before annih i la t ing and' the probab i l i ty of h i t t i n g an impurity and formirig positronium i s high (Appendix A ) . Impurities i n the gas can therefore effect the val ley-to-peak rat ios s i g n i f i c a n t l y . 1.4 J u s t i f i c a t i o n of Lifetime' Measurements i n Helium The importance of any experimental resu l t is; i n the check i t provides on theory. In th i s respect the l i f e t ime measurements of positrons i n the noble gases, p a r t i c u l a r l y argon, have indicated the need to modify ex is t ing theory.^ There i s at present a lack of adequate experimental data avai lable to check the v a l i d i t y of the theore t i ca l models used to describe the positron-helium i n t e r a c t i o n . In p a r t i c u l a r e l e c t r i c f i e l d resu l t s are required. Th i s thes i s describes an experiment which provides the experimental data required . The effect of an applied e l e c t r i c f i e l d on the d irec t • E / D - 10,72 v o l t s / c m - a m . ' 10 A • • •. • • • • « * • • • P E A K ( 0 . 5 1 J ' ) • < • • o »—» c i • • • • • • • V ' \ • • * • • *•. . . . . • 0X \ V A L L E Y : • *• * • COUNTS * * . • *. COUNTS • t » 128VCOMPTON * • • • • « 0 ^ — — — G a t e d to reduce kicksorter deadtime 0 100 200 300 • / . o o C H A N N E L N U M B E R Figure 3 Typica l Energy Spectrum 14 Table II Positronium Formation Thresholds of Common Gas Gas E i o n < e v ) E t h r ( e v > He 24o46 17.7 Ar 15.68 8.9 Kr 13.93 7.13 N2 15.51 8.71 °2 12.5 5.7 c o 2 14.4 7.6 12.56 5.76 H2 15.6 8.9 °2 H2 11.6 4.8 W 8.5 1.7 from Handbook of Chemistry and Physics, 43rd edition Chemical Rubber Publishing Company. 15 lifetimes and on positronium formation is reported and a comparison made with theory. 16 CHAPTER TWO EXPERIMENTAL PROCEDURE •2.1 Basic Techniques 2.1.1 Lifetime Measurements The method of posi tron l i fet ime:determination used i s the same 2-10 as that described by previous workers. Measurement of the posi tron 22 l i f e t ime r e l i e s on the fact that emission of a positron from Na is: —12 c lose ly followed (10 sec) by a 1.28 Mev gamma m y . This, gamma i s used to s ignal the "birth" of a positron and the "death" i s indicated by the ann ih i la t ion r a d i a t i o n . These gamma rays are detected by Nal'(Tl) s c i n t i l l a t i o n counters. The time in terva l between the 1.28 Mev pulse and the .51 Mev pulse i s converted to a voltage pulse by a time-to-pulse height converter. These voltage pulses are then analysed and recorded i n a multichannel analyser. The time spectrum so obtained i s then f i t t e d by maximum-likelihood techniques to the form where N, = number of counts at time t . . t = in tens i ty of d irec t component at t = 0 I ^ '= in tens i ty of ortho-positronium component at t X"j- = d irec t l i f e t ime "C, = ortho-positronium l i f e t ime B = random background 2.1.2 Val ley-to-Peak Measurements The val ley-to-peak rat ios (Section 1.3.3) as a function of e l e c t r i c 17 f i e l d were taken from energy spectra of the 0.51 Mev "slow" channel (Section 2 .4) . It i s necessary to record the whole energy spectrum up to 1.28 Mev because the 1.28 peak compton background contributes substant ia l ly to the va l l ey region of the 0.51 Mev gamma r a d i a t i o n . 2.2 Chamber and Positron Source The chamber (Figure 4) used for th i s experiment was the same as; 10 2 that used by Falk _ and Orth with two modifications, both designed to reduce the extent of impurity contamination. i . The neoprene 0-rings were replaced by Vi ton 0-r ings . Vi ton has a lower vapor pressure than neoprene. i i . The active material i n the gas p u r i f i e r was changed. The calcium-magnesium eutectic was replaced with a t i tanium metal getter which was considered more e f f i c i en t (Section 2 .3 .3) . The e l e c t r i c f i e l d inside the chamber could be varied from 0 volts /cm to 1440 vo l t s /cm. At the helium densit ies used (approximately 40 amagats) t h i s corresponds to a range of E/D up to 35 volts/cm amagat. The potent ia l difference applied to the chamber was determined by measuring the current through a 500 megohm {ifo) r e s i s tor to ground. The temperature of the gas was measured using a mercury thermometer i n contact with the chamber w a l l . It was not expected that the gas 2 temperature would be above the wall temperature. The gas pressure was measured using a high pressure gauge of estimated 2fa accuracy^ and the conversion from pressure to density was made assuming the perfect gas law. HIGH V O L T A G E C O N N E C T O R ' C O P P E R R I N G S o o o o o o o o o o o o o o o o o o o o o o o E L E C T R I C < " F I E L D ^ / A L U M I N U M P R E S S U R E C H A M B E R 0 * " Na' 22 POSITRON S O U R C E L o o o o o o o o o o o 6 o o o o o o o o o o o « > ^ G R O U N D E D A L U M I N U M P L A T E F L A N G E ^ T O G A S PURIF IER Figure 4 • High Pressure Chamber 19 The Na source used was the same as that used by Orth. It consisted 22 10 22 of a Na s a l t (NaCl) deposited on 30,/<inch aluminum f o i l . Since Ma has a h a l f - l i f e of 2.6 years the strength of the source was estimated to be approximately . 5 / O C i . As a resu l t longer counting times were 2 required than those described by Orth. The weaker source d i d , however, have the fol lowing benef i t . Chance of p i l e u p . i n the e lectronics was reduced and a reduction i n random background was obtained. 2.3': Gas Handling 2.3.1 Method: of F i l l i n g The emphasis on cleanliness and gas pur i ty was especia l ly stringent with respect to purnp o i l and other hydrocarbons because of the large annih i la t ion and scattering cross-sections of polyatomic molecules. The chamber was cleaned with T . C E . and baked at atmospheric pressure at 180°C before being assembled. A minimum of grease was iised on the 0-r ings and where used only a s i l i c o n based grease was allowed. In order to prevent pump o i l from backstreaming into the chamber a new method of f i l l i n g was followed. The chamber, with one atmosphere of a i r i n i t , was pressurized' with commercially avai lable 99.995/6 pure helium to 27 atmospheres'. This gas. was, af ter a few hours, allowed to escape u n t i l a pressure of 2.7 atmospheres was reached. A s imi lar process was repeated three more times u n t i l the estimated res idual a i r impurity l e v e l was of the order of a few p.p.m. The pressure f lushing was then undertaken to 40 atmospheres; with u l t r a high pur i ty helium (99.999/S) purchased from Matheson of Canada L t d . F i n a l l y the chamber was. f i l l e d to a pressure of 750 p . s . i . with the u l t r a high pur i ty helium. 20 2.3.2 Estimation of Gas Pur i ty The i n i t i a l pur i ty was estimated as less than 10 p .p .m. (Appendix B) but there was another source of gas impurity that evolved with time. This i s outgassing from the chamber wal ls , p a r t i c u l a r l y outgassing caused by sparking of the e l e c t r i c f i e l d . 2.3.2.1 Impurities due to Outgassing The chamber was not heated under vacuum because of the desire not to introduce pump o i l . I t was f e l t that the impurity l eve l introduced by pumping would be higher than that introduced from the chamber wa l l s . Some outgassing was, however, expected since the chamber had not been evacuated. A more important outgassing problem i s introduced i f there are l o c a l i z e d hot spots and evolution of complex molecules due to breakdown of insulators , both caused by the e l e c t r i c f i e l d sparking. Because of the high f i e l d s being used and the presence of ion iz ing radia t ion t h i s can be a major source of impurity. It was expected that these impurit ies would be read i ly absorbed by the t itanium getter . The effect of t i tanium getting is. described i n Section 3.2.3.2. 2.3.3 Titanium P u r i f i e r Titanium i s an effect ive getter for oxygen, nitrogen, carbon dioxide, 27 water vapor, hydrogen and methane. Of these only hydrogen can be 28 released by heating after absorption. Hence for work involving the noble gases i t i s idea l as a p u r i f i e r since they are not affected. This has the disadvantage that i t i s not possible to "get" noble gas impur i t i e s , 21 p a r t i c u l a r l y argon. This becomes important i n the case of helium since argon has, a known v e l o c i t y dependent annih i la t ion rate and i s therefore an undesirable impurity. Titanium metal requires a high temperature,, i n excess of 650 C for e f f i c i en t gett ing, compared with 400°C for the Ca-Mg eutect ic . As the p u r i f i e r used for the Ca-Mg was: not designed for such a high temperature, a s ta inless s tee l p u r i f i e r capable of withstanding the needed temperatures was designed and assembled by D . B . M i l l e r (Figure 5). A test was conducted i n order to f ind the correct heater current for ef fect ive performance. Th i s consisted, of pumping out a test chamber from an atmosphere of a i r using only the t itanium getter . The f i n a l pressure attained was that of the noble gas constituent of a i r . The heater current at which the t itanium began to pump was i n i t i a l l y used during the experiment. V/hen the gas showed signs of impurity (Section 3 .2 .3 .1 ) , the heater current was increased. It was f e l t that the cooling effect of high density helium could lower the temperature of the t itanium s u f f i c i e n t l y to be ineffectual with the i n i t i a l heater current . Unfortun-ate ly no provis ion was made to monitor the temperature of the t itanium during the experiment. '. 2'.4 E l e c t r o n i c s The e lectronic system i n t h i s experiment was essent ia l ly that of 10 2 2 9 F a l k , Orth and M i l l e r . Following M i l l e r both the slow coincidence (energy discrimination) pulse and the fast t iming pulse were taken from the- anode of the photomult ipl ier . In addit ion'the pulse height analyser used was a Victoreen PIP 400 with a teletype readout. A ® ^ ^ ALUMINUM CHAMBER SS EUTECTIC [ rV=Ch •Socket Wetd Connector 1" NPT Stainless Steel Plug •Cooling Coils •Water Jacket •S.S. Mesh -Titanium Chips -3/4" O.D., .065 wall SS. Tubing Mica Sheet .035" Nichrome Wire •Asbestos Designed by DB. Miller Figure 5 High Temperature Purifier 23 Unlike previous workers * * the pile-up rejector was; not used since with the weaker source (Section 2.2') the chances of pile-up were reduced to a negligible l e v e l . A block diagram of the electronics used i s shown i n Figure 6. The system i s b a s i c a l l y that of a standard " f a s t -slow" coincidence system 1 1*"^ where the " f a s t " channels are the 1.28 and 0.51 trigger c i r c u i t s into the time-sorter (time-to-pulse height converter) which gives a pulse proportional to the time between events and the "slow" channels, are used for energy discrimination to ensure that the time measured i s between the correct gamma rays. Negative time events were eliminated by gating the slow coincidence pulse by requiring that the 1.28 trigger pulse arrives before the 0.51 trigger pulse. The 1.28 trigger pulse defines true zero time which i s indicated by the prompt peak. '2.4.1 Linearity The integral l i n e a r i t y of the timesorter and pulse-height analyser 31 was mea.sured using a variable delay l i n e and a pulser. The delay required to s p l i t each succeeding tenth and eleventh channels; was measured and the resulting points were f i t t e d to a straight l i n e . The resulting integral l i n e a r i t y , used i n the analysis of results, was 1.609 - .007 nsec/channel (Figure 7). The d i f f e r e n t i a l l i n e a r i t y of the kicksorter was; checked using, the 32 29 random time generator developed by Falk et a l . Unlike M i l l e r , who observed a d e f i n i t e non-linearity these measurements indicated good l i n e a r i t y over the whole range of the pulse-height analyser (Figure 8). The data obtained from the d i f f e r e n t i a l l i n e a r i t y measurement, containing C H A N N E L KlCKSORTER I fGate Pulse N eg. Time Eliminator I Gate pulse _ . Slow S^C* • -> 5.C.A. — > Coinc. Figure 6 Block Diagram of E lec tronics 7 0 0 • • / -6 0 0 • • • • * 5 0 0 -* • • • • UOO -• • * ( nsec) 300 • • * • • >-< Best f i t to slope . _J UJ 200 = -1.609 ± .007 n s e c / c h a n n e l ' . Q • • 100 0 ( • i • i • • • D 100 200 300 C H A N N E L NUMBER ^ Figure 7 Integral Linearity of Time-sorter I .0 50.0 100.0 150.0 200.0 250.0 300.0 350.0 CHflNNEL NUMBER F i g u r e 8 D i f f e r e n t i a l L i n e a r i t y o f T i m e s o r t e r < . 27 about 6000 counts/channel, was used d i r e c t l y i n the maximum l ike l ihood analys is of a spectrum (Section 2.5). 2.4.2 Resolution Checks During the Experiment With the system described, the f u l l width at half-maximum of the prompt peak was 4.5 channels (7.25 nsec) . This value' was most eas i ly 22 obtained, for the purposes of e lectronic checks, using a Na source i n aluminum since the positrons annihi late In the metal g iv ing only a "prompt" peak. This value was monitored p e r i o d i c a l l y during the experiment, and the system readjusted i f broadening was observed. In addit ion to these regular checks the e lectronics was checked and r e -adjusted i f the prompt peak of any time spectrum showed signs of broadening. Occasionally t h i s would happen due to d r i f t i n the photo-m u l t i p l i e r ' s high voltage suppl ies . 2.5 Data, Analysis^ The analysis of each time spectrum was carr ied out b2/ f i t t i n g the 33 counts/channel using the maximum l ike l ihood technique of Orth. A l l f ive parameters (Section 2.1.1) were varied and the f i t was obtained over 220 to 240 channels, depending upon the shoulder width. As mentioned (Section 2.4.1) the d i f f e r e n t i a l l i n e a r i t y of the kicksorter 33 was incorporated into the f i t t i n g procedure. Details: of the f i t t i n g 2 33 program are given by Orth. * 28 aiAPT.GR THREE PRESTATION OP RESULTS 3.1 Scope of Results The d i rec t posi tron l i f e t ime and the ortho-positronium l i fe t ime i n helium gas were measured over a density range of 32 to 45 amagats. The d irec t l i f e t ime as a function of e l e c t r i c f i e l d was measured over the range 0 volts/cm arnagat to 35 volts/cm amagat. The upper l i m i t here vas the maximum f i e l d before sparking i n the chamber. The gas density for these e l e c t r i c f i e l d measurements was i n the range described. The val ley-to-peak r a t i o was measured over the range 0 volts /cm amagat to 38 volts/cm amagat. 3.2 Acceptabi l i ty of Results 3.2.1 Maximum Likel ihood P i t There were two c r i t e r i a demanded of a f i t before the resul t was accepted. i . The f i t converged for a l l f ive parameters, i i . The confidence l eve l for the chi-squared measure of goodness of f i t was greater than .1 . The value of chi-squared vas, calculated by summing over enough channels to get the number of counts i n the realm of Gaussian s t a t i s t i c s . ^ ' ^ Only two inns out of twenty-seven were rejected on these c r i t e r i a . Both of these runs could have- had s ign i f i cant impurit ies present (Section 3 .2 .2 ) . 29 3.2.2 E l e c t r o n i c S t a b i l i t y Before a r e s u l t was accepted i t was required that there had been no change i n the e lectronics during the run . In par t i cu lar the following two conditions were required. i . The pos i t ion of the prompt peak remained constant, i i . The e l e c t r i c f i e l d inside the chamber remained constant, i n p a r t i c u l a r i t d id not spark enough to turn i t s e l f o f f . Minor sparking, involving l i t t l e current drawn, would not be detected. This c r i t e r i a i s important with regard to outgassing (Sect ion.2 .3 .2 .1) . There were f i v e out of twenty-seven runs discarded because of these condit ions . Of these, four were due to the sparking of the e l e c t r i c f i e l d . In addi t ion i t i s possible that some of the high f i e l d runs became contaminated with impurit ies (Section 3 .2 .1) . 3.2.3 Gas-Puri ty 3 .2 .3 .1 I n i t i a l Indications Although the helium was expected to have a low impurity l eve l (Section 2.3.2) the i n i t i a l runs (number three to twenty) indicated that t h i s was not the case. These indicat ions were as follows;. i . The Z „„ obtained were of the order of 4.5 to 5.5. This ei i-i s far larger than the re su l t s of other workers (Table I) and higher than the re su l t s la ter obtained. General ly, the lower the g^t "the purer the gas i s . i i . There was no consistency i n the results, obtained. Reproductabi l i ty between runs was much poorer than 30 s t a t i s t i c a l e r r o r . This inconsistency vas most pronounced f o r zero f i e l d r e s u l t s . i i i . The shoulder obtained vas narrower than the shoulder obtained i n l a ter r e s u l t s . That i s , the shoulder, occuring as the positrons s lov from the positronium formation threshold to thermal energies, i s a measure of the time taken to reach thermal energy. Previous 2 experience with argon has indicated that the broader the shoulder, the more pure the gas i s . This re su l t s since the slowing down time depends on the scatter ing cross -sect ion and energy loss per c o l l i s i o n . Impurities with large scatter ing cross-sections, and low ly ing i n e l a s t i c levels would narrow the shoulder width by increas ing the number of c o l l i s i o n s and the average energy loss per c o l l i s i o n . Hence the ind ica t ion was that the i n i t i a l gas pur i ty was less than that f i n a l l y a t ta ined . 3 .2 .3 .2 P ina l Acceptab i l i ty The above indications, were that the gas had s igni f icant impuri t ies . As explained i n Sect ion 2.3 on the basis of these indicat ions , the temperature of the t i tanium getter was ra i s ed . The effect of t h i s was to lower the observed value of Z to a value comparable with those eff.. obtained by other workers, and to increase the shoulder width. The shoulder was not as well defined, but t h i s indicated a weaker v e l o c i t y dependence which i s , i n fac t , more reasonable on the. basis of exist ing 31 theoretical models of the annihilation process (Section 3.4). The results obtained vere also consistent within statistics from run to run. 3.3 Experimental Results 3.3.1 . Lifetime Measurements The: results of runs 38 to 64, obtained after the increase in the titanium getter, are shown in Tables III, IV and V and in Figures 9, 10 and II.' Where applicable curves have been fitted to the data. The least squares f i t t i n g of a curve of the form.?V = a^ D to the zero field direct annihilation rate results (Table III) yielded A X = (.7214 ± .0082)D ^ s e c " 1 with a chi-squared confidence level of 0.19. This; density dependence in the direct annihilation rate corresponds to Z .„ = 3.628 - .041. eti The direct annihilation rates at zero field v/ere also fitted v/ith a polynomial of the form = a^ D + BI^L? but no improvement v/as obtained in the chi-squared. confidence level. The statistics on the ortho-positronium results; were poor (Table V) and a least squares f i t of the form = a + a,D did not determine 2 o 1 the parameters; to an accuracy better than - 50fo. It v/as decided that 17 since the free ortho—positronium decay rate is well known the ortho-positronium quenching rate should be the only variable. Consequently the data was fitted to the form 7\ 2 = 7.2 + a][D (/'sec-1) 32 Table I I I D i r e c t A n n i h i l a t i o n Rates at Zero F i e l d Run No. 38 39 41 43 48 50 53 57 Density (amagats) 44.37 43.99 42.99 42.3 38.5 37.46 36.32 34.92 ^ ( A s e c " 1 ) 33.32 I 1.16 31.18 i .87 C^sec * am .7509 - .0260 .7087 - .0198 30.05 - .94 .7103 - .0220 ef f 3.745 - .130 3.535 - .099 33.28 - 1.45 .7742 - .0340 3.865 - .170 3.545 - .110 29.41 i 1.23 .7639 - .0319 3.802 - .159 27.94 i 1.03 .7459 - .0275 3.713 ± .140 26.31 i .99 .7244 ± .0280 3.606 ± .137 24.25 - .54 .6946 - .0155 3.437 - .077 confidence l e v e l .3 .77 .4 .6 .87 .71 .60 .38 33 Table IV Direct Annihilation Rates as a Function of Electric Field Run E/D No. (v/cm-am) 1 1 eff confidence level 40 3.77 29.17 + 1.09 .6699 + .0250 3.347 + .125 .53 42 7.56 25.44 + .95 .5996 + .0200 2.995 + .101 .28 44 5.15 27.19 + 1.24 .6571 + .0300 3.280 + .150 .65 46 10.72 25.61 1.24 .6343 + .0310 3.167 + .155 .27 49 9.58 25.22: + .98 .6622 + .0257 3.296 + .128 .59 51 2.22 25.57 + .73 .6909 + .0198 3.439 + .099 .27 52 14.52 24.78 1.42 .6750 + .0388 3.360 + .193 .58 54 17.86 23.68 + .70 .6572 + .0193 3.271 .096 .77 55 9.10 22.67 + .86 .6239 + .0242 3.106 + .120 .19 56 20.84 22.64 + .90 .6422 + .0254 3.196 + .127 .83 58 16.68 21.36 + .70 .6208 + .0203 3.090 + .101 .99 64 34.46 20.71 + 1.13 .6399 + .0350 3.185 + .174 .13 34 Table V Orthe—positronium Annih i la t ion Rates Run Dens i ty Ortho-quenching, "X confidence No. (amagats) ^ 2 ^ S e C ^ (/^sec"^ am L ) l eve l 38 44.37 12.67 + 1.01 .123 + .023 .3 39 43.99 10.12 + 1.01 .0639 + .02 .77 40 43.54 11.48 + 1.33 .098 + .031 •53 41 42.99 12.24 + .85 .117. + .020 •4 42 42.44 10.46 + 1.81 .0768 + .043 .28 43 42.3 11.31 + .54 .097 + .013 .6 44 41.39 11.27 + 1.38 .098 + .033 .65 46 40.38 10.16 + 1.82 .0733 + .045 .27 48 38.50 12.34 + 1.30 .134 + .034 .87 49 38.08 11.98 + 1.59 .126 + .042 .59 50 37.46 11.26 + 1.32 .108 + .035 o71 51 37.01 9.92 + 1.35 .0735 + .0363 .27 52 36.71 13.02 + 1.67 .158 + .045 .581 53 36.32 10.54 + 1.83 .0919 + .0503 .60 54 36.04 11.83 + 1.09 .129 + .030 .77 55 35.69 10.04 + 2.39 .0796 + .0672 .19 56 35.26 10.09 + 2.36 .0819 + .0669 .83 57 34.92 7.53 + 1.51 .0095 + .04 .38 58 34.41 8.75 + 1.65 .0452 + .048 .99 64 32.36 9.88 + 2.34 .083 + .073 .13 1.0? g>0.9 rcl e rd T S °.8i I a" ^ • 0 . 7 | 0.6 GL5' I 1 0 5 10 15 20 25 30 35 U0 E / D (volts/cm-amagat) Figure 10 E l e c t r i c F i e l d Dependence of Direct Annihilation Rate 15 10 in 0 3 2 Figure 21 o <> T 9 6 -1-/V=7.2 +.099D U'sec ) 3 5 U5 " DENSITY (amagatsJ O r t h o — p o s i t r o n l i m A n n i h i l a t i o n Kate as a F u n c t i o n o f Density. S t r a i g h t l i n e i s l e a s t square f i t v i t h 2\ = 7.2/^sec~ a t B = 0. 38 and the resu l t ing dependence was found to be \ 2 = 7.2 + (.0991 - .0067)D (/"sec" 1) with a c h i - s q u a r e £ confidence l eve l of .72. Since there was.-no theoret ica l j u s t i f i c a t i o n , a polynomial f i t of the e l e c t r i c f i e l d resul ts was not attempted. 3.3.2 Val ley- io-Peak Ratios 3.3.2.1 I n i t i a l Results The val ley-to-peak ra t io s measured during the f i r s t set of runs (Number 3 to 20) showed a marked increase at about 7 volts/cm-amagat (Figure 12). This was of interest s ince i t was i n good agreement with 34 previous resu l t s upon which the only experimental estimate of the momentum-transfer cross-sect ion of positrons i n helium has; been 35 based. These resul ts were obtained, however, with gas that was rejected as impure on the basis of l i f e t ime measurements (Section 3 .2 .3 .1) . 3.3.2.2 F i n a l Results The val ley-to-peak rat ios f i n a l l y obtained did not show any s ign i f i cant increase up to the maximum f i e l d appl ied , 38 vo l t s /cm-amagat (Figure 13). Although there i s an apparent increase at 21 volts/cm-amagat th i s i s probably at tr ibutable to impurit ies caused by the e l e c t r i c f i e l d sparking (Section 3 .2 .2) . The reasons f o r th i s assumption are i . The zero f i e l d valley-to-peak. ra t io immediately a f t er a high f i e l d run was also high (Table VT) 1.6 o 1.5 Q LU N j < cc o o < a LU ^ O-LU >-LU < > 1.3 1.2 1.1 1- A 0 9 OA I r A A A 0 10 A 30 15 20 25 E/D (volts/cm-amagat) Figure 12 Initial Talley-to-Ponk Ratios; Compared to Results of Harder et al. Marder et al. In i t ia l Results of Present Work • . i i i i 35 VALLEY TO PEAK RATIO o co o o o rT M o k CB E. KJ S» H> O .'w o o O p I—• <P • Q 21 m n 3 • 3 ft* o r—C—t I—0—1 I—0—I rv> co o co cn I—o—J o r-M. t o V i CD VALLEY TO PEAK NORMALIZED TO 1 AT E / D = 0 41 Following Run Number 38 39 40 41 42 44 46 48 49 50 51 52 53 .54 55 56 57 5S 64 after long time with no f i e l d after f i e l d on for long time immediately af ter above run Table VI '-to-Peak Ratios E/D (v/cm-am) Valley-to-Peak Ratio 0.0 .213 - .012 0.0 .212 - .012 3.77 .215 - .012 0.0 .212 - .012 7.56 .216 t .012 5.15 .214 i .011 10.72 .203 - .011 0.0 .214 i .012 9.58 .211 i . .011 0.0 .211 - .012 2.22 .217 - .013 14.52 .217 ± .012 0.0 .220 i .012 17.86 .219 - .012 . 9.10 .223 - .013 20.84 .246 - .013 0.0 .219 - .012 16.68 .216 i .012 34.46 .238 - .010 38,1 .229 - .009 38. .237 - .007 0.0 .229 - .009 42 and within s t a t i s t i c s of the high f i e l d po int , i i . A high f i e l d val ley-to-peak taken after two days without a f i e l d applied showed no s igni f icant increase (Point A i n Figure 13). It should be noted here that the other val ley-to-peak r a t i o s were taken at the ends of runs ;of two or tliree days durat ion. For those runs at higher e l e c t r i c f i e l d s , s ign i f i cant impurity levels from sparking may have accumulated In th i s time. It can be shown that the increase in positronium formation observed can be due to small amounts of impurities and that th i s amount of impurity would not affect the observed l i fet imes as the resul ts of Section 3.3.1 indicate (Appendix A ) . Hence a def in i te increase i n positronium formation is. not observed up to 38 volts/cm-amagat. 3.4 Theoret ical Results 3.4.1 Di f fus ion Analysis The theoret ica l re su l t s of Z and (5* (momentum-transfer cross-el 1 s section) given i n Figure 2 have been used to calculate the theoret ica l e l e c t r i c f i e l d dependence of the d irec t annih i la t ion ra te . This ca lcu lat ion 2 8 10 26 involves a d i f fus ion analysis of the kind developed by Fa lk and Orth. ' ' ' The so lut ion of th i s equation f o r the case of no i m p l i c i t time dependence 2 i s given elsewhere. The computor program used i n the present work i s e ssent ia l ly the same 2 as that described by Orth. One minor modification that was made was the replacement of the l i n e a r in terpo lat ion between points of the scattering 43 cross-section and Z ^ by S t i r l i n g s interpolation formula which f i t s a i quadratic through three points. This was introduced since i t was f e l t that substantial error could be introduced i n the v a l l e y region of the scattering cross-section where the cross-section changes d r a s t i c a l l y . The results' of the calculation are shown i n Figure 14. 3.5 Discussion of Results 3.5.1 Annihilation Rates 3.5.1.1 Comparison to Other Yorkers The zero f i e l d results obtained compare well with previous workers. The value of Z f f = 3.628 ± .041 is: i n good agreement (Table I ) . The zero field! results showed no evidence of a non-linear dependence on density as indicated by the least-squared f i t t i n g . No dependence.of the direct annihilation rate on e l e c t r i c f i e l d has previously been described. Falk obtained some evidence of an increase i n at 64.5 volts/cm - a f c i 1 ^ but saw no discernable difference at 13.7 v/cm-atm. As mentioned e a r l i e r (Section 1.3.2.2) these results were not conclusive. The- ortho-positronium quenching rate obtained compared favorably with previous; results. The previous value of (.0.086 - .008) x 10^ sec 1 am 1 i s within st a t i s t i c s , of the present value (0.0991 - .0067) T A 6 - 1 - 1 x 10 sec am . 3.5.1.2 Comparison to Theory . As can be seen from Figure 14 only one calculation, that of Drachman 22 i n 1968, i s close to the experimental results. The agreement between 0 2 * » 1 « < • <—* « — • — J — • — < — • — • — • — « — « — < — < — ' — > - — • — > — • — • — « — • — • — • — ' — 1 — 1 — ' — 1 — C — 1 — 1 — • — • — J — 0 5 10 15 20 25 30 35 hO E / D ( v o l t s / c m - a m a g a t ) Figure 14 Theoret ical E l e c t r i c F i e l d Dependence- of Direc t Annih i la t ion Rate. Experimental points are from present work. 4 5 this, theoretical result and experiment i s remarkably good. 3.5.2 Valley-to-Peak Ratios The experimental valley-to-peak ratios did not increase with electric f i e l d up to 38 volts/cm-amagat. This i s i n contrast to the results of 34 previous; workers which were, as mentioned In Section 3.3.2.1, consistent with the* i n i t i a l measurements obtained when the gas was considered contam-inated. As seen (Appendix A) a very slight amount of impurity can cause increased positronium formation. There i s also theoretical evidence that there should be no increase i n positronium formation at these electric f i e l d s . The calculation of the positron velocity distribution, using the scattering cross-section 22 of Drachman (whose theoretical results give closest agreement), gives a maximum positron velocity corresponding to 11.0 ev at 28 v/cm-amagat. The peak of this distribution i s at 3.9 ev. Hence there would be no positrons energetic enough to form positronium i n helium (Ey i r, = 17.7 ev). This is; consistent with the results of this experiment (Figure 15). I f we accept the value 38 v/cm-amagat as a lower l i m i t for the value at which increased positronium formation ensues, the previous estimate of the momentum-transfer cross-section (0") at 17.7 ev (it = 1.15) obtained s 35 by Teutsch and Hughes can be easily revised. Teutsch. and Hughes obtained a parameter £ e*. B PCT s where E = f i e l d i n volts/cm P = pressure i n atmospheres . 0~= scattering cross-section ENERGY (ev) Figure 15 Theoret ical Positron Energy D i s t r i b u t i o n Using Results of Drachman. Positronium formation threshold i s wel l above upper l i m i t of d i s t r i b u t i o n . 47 This parameter £ must remain the same for any experimental result in order to yield a given increase in positronium formation. V/hen analysed ' 34 with the results of Harder et al. which indicated a significant increase in positronium formation at approximately 7 volts/cm—atmosphere, this yielded a value C = .025TTa 2 •(- 25$) s o If we use the present lower limit for E/P and keep constant we get (T ^  (.025)TTa 2 ~ s o 7 or (T OS.135TTa 2 v s o as a lower limit for f^ T (at k = 1.15). This: is in much closer agreement • with present theory (Figure; 2). 3.6 Discussion of Error The errors quoted in the results have been statistical only. They do not include errors; due to electronic instability or inaccuracy or errors due to inaccuracies in the determination of the applied electric field and gas density. 3.6.1 Electronic Instabilities The error introduced by electronic instabilities has been estimated as having no observable effect as long as the measured lifetimes are 2 greater than the prompt time resolution. The acceptable, observed shift in the prompt peak was a maximum of one channel and the magnitude of 2 such a shift should have no effect. Whenever a larger shift was observed the operation of the instrumentation was corrected and the run discarded. The effect of a change in single channel analyser settings; has' been 2 examined and found to be negligible. The effect of other instabilities. 48 has been estimated as less than the accuracy to vhich the timesorter l i n e a r i t y has; been measured. 3.6.2 Timesorter L i n e a r i t y 2 The error i n the in tegra l l i n e a r i t y i s estimated at less than lfa, and the accuracy of the d i f f e r e n t i a l l i n e a r i t y i s l imited by the number of counts per channel. This i s an error of about 1.25$ since there are 6000 counts/channel. It must be remembered however that the d i f f e r -en t ia l l i n e a r i t y i s i t s e l f a f i r s t - o r d e r correct ion and hence the un-certa inty i n the r e l a t i v e channel widths must be considered a;s affect ing t h i s correct ion (when compared with the error i n the integra l l i n e a r i t y ) . It i s therefore reasonable to suppose that the t o t a l uncertainty i n the l i fet imes due to timesorter c a l i b r a t i o n i s of the order of 1$, t h i s being 2 the error due to the in tegra l l i n e a r i t y measurement-* 3.6.3- Applied E l e c t r i c F i e l d E r r o r s ascribed to the e l e c t r i c f i e l d are of two types;, i . error i n absolute magnitude i i . error i n spat ia l uniformity. 2 The error i n the absolute magnitude has been estimated at yfo. The present experiment uses only one minor modification to measure the e l e c t r i c f i e l d . A micro-ammeter (accuracy 1$) was used i n place of the Avoraeter (accuracy 1$). The- resultant accuracy was therefore the same, about 3$. The s p a t i a l uniformity of the e l e c t r i c f i e l d i n the chamber has 10 been investigated and found to be uniform except for a region immediately 49 surrounding the electric field rings, comprising about 8$ of the volume. A calculation based on the range of positrons in helium and the chamber dimensions; has indicated that about 2fo of the positrons annihilate in this region at 40 amagats. This; is; a small error when compared to the statistical accuracy of the results. 3.6.4 Gas. Density The density of the gas was determined from the pressure using the perfect gas law. The pressure was measured using a gauge of estimated 10 . 2$ accuracy. The absolute temperature was measured to within lfo (— 3°K) using a mercury thermometer in contact with the chamber walls. There was no indication that the temperature of the gas varied with the amount of current through the heater purifier. This indicated that the gas was in thermal equilibrium with the chamber walls. The combined error in the density is therefore' of the order of 3fo. The deviations from the perfect gas laws in helium i s negligible (^2$) compared with the uncertainty in the density result. 3.6.5 E/D The error in S/D, as obtained by combining the error in E and D, is of the order of 4.5?£. At 40 volts/cm-amagat, this coxresponds to an error of - 1.8 volts/cm-amagat. 3.6.6 Gas Composition Both the effect of impurities on the annihilation rate and estimate of the impurity levels have been discussed previously (Sections 1.3.3.1, 2.3.2, 3.2.3 and Appendices A and B). 50 3.7 Recommendations for Future Work Because of the importance of accurate experimental knowledge of the electric field dependence of the direct annihilation rate of positrons in helium, the only situation amenable to both experimental and theoretical analysis, the experiments indicating electric field dependent effects, which are described in this thesis for the first time, should be- amplified and the precision improved. The direct annihilation rate should be measured over a greater density range and over a greater range of E/D. Both of these measurements would possibly require seme redesign of the experimental chamber to reduce wall annihilation and sparking of the electric field. The ortho-positronium lifetime should be measured with greater accuracy. This could be accomplished by running the 0.51 gamma single-channel analyser in the ortho-enhanced (valley region) setting. This would require a longer running time since the "slov/" coincidence rate is reduced. An- important measurement in helium would be the measurement of the number of ortho-positronium decays. This would provide a check of the effect of an electric field on positronium formation. One method of investigating this would use a maximum likelihood spectrum analysis that involves total counts and lifetime, parameters that are correlated to a much less degree than the parameters I ?jnd"C now used. This would possibly reduce the error to acceptable limits. The present technique that computes I^ endseparately has a large error associated with the product I^T,.. Such a measurement would also allow a direct estimation 51 to be made of the percentage of positrons; forming positronium. This measurement should be done i n conjunction with a val ley-to-peak measure-ment i n order to ensure that i f there i s a positronium increase with increased e l e c t r i c f i e l d i t i s observed i n both cases. As indicated by the present resu l t s the measurement should be carr ied out with provis ion for' an E/D of greater than 40 volts/cm-amagat. The most important part of any future helium experiments should be s t r i c t attent ion to gas p u r i t y . As indicated by the present work, impurities can affect r e su l t s s ign i f i cant ly . . One: improvement might be the use of cryogenic pumping to reduce ba:ckstreaming while evacuating the chamber and outgassing the chamber by heating under vacuum. In addi t ion , a thermocouple w i l l be aff ixed to the p u r i f i e r so that the ef fect ive temperature of the t i tanium i s known. Analysis of the ,gas for trace impurities should be performed both before and after the experiment, although th i s i s d i f f i c u l t because of the lack of analysing f a c i l i t i e s and the problem of at ta ining a "pure" sample. 52 CHAPTER FOUR CONCLUSIONS The d i r e c t ann ih i la t ion rate of positrons i n helium was measured as a function of e l e c t r i c f i e l d . The posi tron l i fet ime was found to increase with increas ing e l e c t r i c f i e l d s igni fy ing an annih i la t ion rate which decreases with increasing v e l o c i t y . This i s i n agreement with r e s u l t s obtained i n the other noble gases. The zero f i e l d d i rec t annih i la t ion rate was found to be i n good agreement with the resul ts of previous workers. Over the density range invest igated no deviat ion from a l inear density dependence was detected. The value of Z „ „ , obtained from these measurements, was 3.628 - .041. e i i V l t h the free ortho-positronium annih i la t ion rate assumed to be 7.2 x 10^ sec ^ the ortho-positronium quenching rate i n helium was found to be (0.0991 - .0067) x 10 sec amagat which i s i n good agreement 18 with previous r e s u l t s . Valley-to—peak ra t io s taken at the same time as the l i f e t ime measure-ments disagreed with previous resul ts but agreement with former workers was attained with gas concluded, on the basis of annih i la t ion rate re su l t s , to be contaminated. Using the lower l i m i t obtained for the value of E/D at which a s i gn i f i cant increase in positronium formation takes place, 2 a lower l i m i t of .1357Ta i s obtained for the scattering cross-sect ion o at 17.7 ev. T h i s i s s i g n i f i c a n t l y higher than the previous result of . 2 35 .023TTaQ obtained by Teutch and Hughes. The experimental resul ts were compared with the predict ions of 2 10 several current theories by means of a d i f fus ion analys i s . ' Only 53 the recent ca lculat ions of Dra.chraan (1968) give good agreement with the r e s u l t s . The p u r i t y of the gas was found to be of great importance for accurate determination of annih i la t ion rates and for accurate estimation of the e l e c t r i c f i e l d dependence of positronium formation. 54 REFERENCES 1 Massey, H .S .V. , "Positron Annihi lat ion" (Proceedings of the Conference on Pos i tron A n n i h i l a t i o n held at Vayne State Univers i ty , De tro i t , Michigan, 1965- A . T . Stewart and L . O . R o e l l i g , ed.) Academic Press, N.Y. £ 1 9 6 5 ) . 2 Orth , P . K . R . , F h . D . Thesis , Univers i ty of B r i t i s h Columbia. (Unpublished) (1966). 3 Falk,,, W.R. , and Jones, G . , Can. J . Phys. 42, 1751 (1964). 4 Tao, S . J * , B e l l , J . , and Green, J . H . , Proc. Phys. Soc. (London) 83, 453 (1964)). 5 Paul , , D . A . L . , Proc . Phys. Soc. (London) 84, 563 (1964). 6 0smonJ; P . E . , Phys. Rev. 138, B216 (1965). 7 R o e l l i g , L . C , and K e l l y , T . M . , Phys. Rev. Letters 15., 746 (1965). 8 Orth,, P . H . R . , and Jones, G . , to be published. 9 M i l l e r , , D . B . , Orth , P . H . R . , and Jones, G . , Phys. Letters 27A, 649 (1968). 10 F a l k , ¥ . R . , Ph .D. Thesis , Univers i ty of B r i t i s h Columbia. (Unpublished) (1965). 11 Green, J . , and Lee, J . , "Positronium Chemistry" Academic Press, N . I . (1964). 12 F r a s e r , P . A . , "Advances i n Atomic and Molecular Physics" V o l . 4 Academic Press , N.Y. (1968). 13 Mackl ia , P . A . , Lidofsky, L . J . , and Wu, C . S . , Phys. Rev. 78, 318 (1950). 14 Gerhart , J . B . , Carlson, B . C . , and Sherr, R . , Phys. Rev. 94, 917 (1954). 15 Kendall, , II .V. , and Deutsch, M . , Phys. Rev. 93, 932 (1954). 16 Tao,, S . J . , Green, J . H . , and Ce l i tans , G . T . , Phys. Soc. 81, 1091 (1963). 17 Jauch, J . M . , and Rohr l i ck , F . , "The Theory of Photons and Electrons" Chapv 12 A d d i s o n - ¥ e s l e y (1955). 18' Duff,,. B . G . , and Heymann, F . F . , Proc. Roy. Soc. (London) A270, 517 (1962). 19 Gold'anskii , ¥ . 1 . , "Positron Annihi la t ion" (Proceedings of the Conference on Pos i t ron A n n i h i l a t i o n held at Wayne State Univers i ty , De tro i t , Michigan, 1965. A . T . Stewart and L . O . R o e l l i g , ed.) Academic Press, N.Y. (1965). 20'; Khare, K . C , ¥ a l l a c e , P . R . , Bach, G . G . , and Chodos, A . , Can. J . Phys. 42, 1522 (1964). 21 Drachman, R . J . , (1968), private communication. 22 Drachman, R . J . , Phys. Rev. 173, 190 (1968). 23- Massey, H . S . ¥ . , and Moussa, A . H . A . , (1966), private communication with P . A . F r a s e r from reference 12. 55 24 Drachman, 'R.J . , Phys. Rev. 144, 25 (1966). 25 Kraidy , M . , and Fraser , P . A . , "V International Conference on the Physics of Electronic and Atomic C o l l i s i o n s , Leningrad, U . S . S . R . , 1967: Abstracts of Papers" ( I . P . Flaks and E . S . Solovyov, ed.) pp. 110-113. 26 F a l k , W.R., Jones, G . , and Orth, P . H . R . , Phys. Rev. Letters 14, 447 (1965). 27 Mobley, R . M . , "Methods of Experimental Physics: V o l . 4, part B" Academic Press, N.Y. (1967). 28 Stout, V . L . , and Gibbons, M . D . , J . A . P . 26, 1488 (1955). 29 M i l l e r , D . B . , M.A.Sc . Thesis , Univers i ty of B r i t i s h Columbia. (Unpublished) (1967). 30 Green, R . E . , and B e l l , R . E . , Can. J . Phys. 36, 1684 (1958). 31 Jones, G . , and Fa lk , W.R., Nucl . Ins tr . and Methods 37, 22 (1965). 32 F a l k , V . R . , Jones, G . , end Orth, P . H . R . , Nucl . Ins tr . and Methods 33, 345 (1965). 33 Orth, P . H . R . , and Jones, G . , to be published. 34 Harder, S . , Hughes, V . ¥ . , Wu, C . S . , and Bennet, ¥ . , Phys. Rev. 103,-1258 (1956) 35 Teutsch, W.B. , and Hughes, V . W . , Phys. Rev. 103, 1266 (1956). 36 Paul , D . A . L . , and Sa in t -P ierre , L . , Phys. Rev. Letters 11_, 493 (1963). 56 APPENDIX A EFFECT OF IMPURITIES ON. POSITRONIUM FORMATION A.1 Positronium Formation . A rough ca lcu la t ion can indicate the magnitude of the effect of trace impurit ies with low positronium formation thresholds on positronium formation. Ve assume the impurity has a positronium formation cross-sect ion approximately one-tenth as large as the scattering cross-sect ion. (No deta i led estimates are avai lable but for eas i ly polar ized atoms or molecules the positronium formation cross-sect ion Is theore t i ca l l y expected to be s i g n i f i c a n t l y lower than the scattering cross-sect ion.) We also assume that the scatter ing cross-sections for helium and the impurit ies are CF £ 307n Imp o then we can calculate the number of c o l l i s i o n s per second between a posi tron and an atom c o l l i s i o n s / s e c = N., CTT v + n. 0~~ v lie He 1 1 where N ^ = atoms/unit volume of helium N^ = atoms/unit volume of impurities ^ = scatter ing cross-sect ion for helium ne 0*^  = scatter ing cross-sect ion for impurit ies I f we assume n^@"^«. ^ j j e 0 ^ e "then the number of c o l l i s i o n s per second i s c o l l i s i o n s / s e c = ^ j e ^ j e v = 2.76 x 10 1 0 CT D He II6 O 2 V and are constant for a l l v e l o c i t i e s a 57 where i s units of "IT a 2 He o D i s density i n amagats and the ra t io of t o t a l c o l l i s i o n s to c o l l i s i o n s with an impurity i s t o t a l number of c o l l i s i o n s N t r <5\. v He He c o l l i s i o n s with impurity ni^V v NHe. ._-2 = —— x 10 n. x Now for helium .7 x 'lO'^'.D sec * (Section 3.3.1) y i e l d i n g a mean l i f e ,-6 -6 sec am .7 D D ~> 10 ~ 1.43 x 10"" -1 Therefore the number of c o l l i s i o n s i n the mean l i fe t ime T i s given by T- c o l l i s i o n s = 2.76 x 101Q0L D x 1 , 4 3 x I 0 " 6 ne n sec D = 3.95 x 10 4C; i e For our assumed value of the e las t i c scattering cross-sect ion i n rr 2 He of .37/ a the number of c o l l i s i o n s i n mean l i fe t ime i s approximately 10 4 . For an impurity l eve l of 10 ppm n. l Therefore t o t a l number of c o l l i s i o n s /\ . ^ Q3 ( c o l l i s i o n s with impurity Hence a 10 ppm impurity would have a. very appreciable effect since a posi tron h i t s ten atoms of an impurity i n i t s l i fet ime and i f the formation cross-sect ion i s one-tenth of the scattering cross-sect ion i t is; almost cer ta in to form positronium. 58 Even an impurity l eve l of 1 ppm would cause 10$ of the positrons to form positronium since each positron would h i t an impurity i n i t s l i f e t i m e . Since the number of positrons i n i t i a l l y forming positronium i n helium i s estimated at 30$^ th i s would be an appreciable ef fect , that i s a 23$ increase . The actual increase noted was of the order of 10$. T h i s corresponds to a 4$ decrease i n the free posi tron population which,- on the basis of the assumptions involved here, would correspond to an impurity l e v e l of approximately .4 ppm. This e f fect would probably be greatly reduced for a neon impurity 2 which has a lower scatter ing cross-sect ion than 30TTa o . Neon i s expected to be the Eiajor impurity (Aj>pendix B) . A.2 Annihi lat ion. Rates The e f fect of impurity levels of the order of that considered i n A . I on the d i r e c t l i f e t ime of positrons i n helium can be shown to be 4 neg l i g ib l e for impurity atoms with ? 10 . I f we consider = 2.02 x 10 5 D' Z » = 2.01 x IO 5 D" Z e f f M where I f = d i rec t annih i la t ion rate D = density and 1 denotes helium "denotes impurity (for 10 ppm impurity leve l ) £ - = 1 0 5 D" then the densi ty then D-D' "> 5 D " A " = 2.01 x K T ~ Z 10 5 eff 59 and i f Z eff • = 3.6 (Section 3.3*1) where combining then Ai = 2.01 x 10 3.6 + Eehce a Z eff " of the order of 10 would be needed to produce a few percent e f fect . Pew atoms have values of Z „ th i s large except the effect of most impurit ies present at leve ls less than 100 ppm to have a neg l ig ib le effect on the d i rec t annih i la t ion ra te . There might be an effect on the d irec t annih i la t ion rate due to increased positronium formation i f t h i s provides a s ign i f i cant al ternate channel through which positrons can annih i la te . For a 10$ effect (corresponding to a 4$ decrease i n the free positron population) the number annih i la t ing through d irec t annihi lat ions drops from 70$ to 66$ - about a 5$ e f fec t . Since the s t a t i s t i c a l accuracy of the d irec t ann ih i la t ion rate i s about 5$ th i s effect i s barely detectable. for some large polyatomic molecules. 36 One would expect therefore that 60 APPENDIX B CALCULATION OP INITIAL GAS PURITY The chamber was f i l l e d with helium by a method of successive flushings as indicated i n Chapter Two. The pressures attained were as follows Gas Used I n i t i a l Pressure ( p . s . i . a . ) F i n a l Pressure ( p . s . i . a Commercial 99.995^ 14.7 425 pure 40 469 -from Canada 15 415 L i q u i d A i r 40 520 Matheson 99.9997$ 30 615 u l tra-pure 30 815 After the las t f i l l i n g the pressure dropped i n twelve hours to 770 p . s . i . a . B . I Pur i ty Leve l The assumption made i n th i s ca lculat ion i s that the gas reached equi l ibrium and that the impurit ies i n the helium were evenly d i s tr ibuted i n a ra t io proportional to the p a r t i a l pressure. Since the volume was constant the pressure i s a measure of the amount of gas contained. I n i t i a l Pressure ( p . s . i . a . ) F i n a l Pressure ( p . s . i . a . ) Impurity Level 14.7 1:1 14.7 425 14.7:425 = 1:11 40 469 1:300 15 415 1:8300 40 520 1:10500 = 1:10' This i s the l eve l of the impurity i n the commercial gas and hence further flushings with th i s gas are of no further benef i t . Using the Matheson ul tra-pure gas we get 61 I n i t i a l Pressure ( p . s . i . a . ) F i n a l Pressure ( p . s . i . a . ) Impurity Level 30 615 (I:10 4 )(30:615). = 1:2 x IO 5 30 815 1:5 x 10 The t h e o r e t i c a l impurity l eve l i s now below the l eve l of the u l t r a -pure gas. Matheson gives the impurity l eve l of the lo t from which the gas used was taken as Impurity ppm co2 0.0 ° 2 ° ' 3 H 2 0.0 Ne 9.2 Guaranteed 10 ppm excluding neon. Ar 0.0 H 2 0 1.4 CH. . 0 . 0 4 A conservative estimate of the i n i t i a l pur i ty level of the gas i s therefore 5 ppm excluding neon and 10 ppm including neon. This ca lcu la t ion does not take into account outgassing from the chamber wa l l s . 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

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"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0103738/manifest

Comment

Related Items