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Production and diffusion of muonium in powdered silica Marshall, Glen Murray 1976

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PRODUCTION AND DIFFUSION OF MUONIUM IN POWDERED SILICA by GLEN MURRAY MARSHALL B.Sc , M c G i l l U n i v e r s i t y , 1974 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Physics) We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December, 1976 © Glen Murray Marshall, 1976 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , 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 s t u d y . 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 o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Depar tment o r 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 o r 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 . Depar tment o f Phvsics The U n i v e r s i t y o f B r i t i s h C o l u m b i a 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date (W^ICSL .Zl. /<? 7/i 6 - i -ABSTRACT The f i r s t d i r e c t observation of the atomic state of the muon (muonium) i n a f i n e l y powdered sample of SiC^ ( s i l i c a ) i s reported, with evidence of muonium d i f f u s i o n into a vacuum. The formation technique, f i r s t used i n the study of the positron atomic state (positronium), has been extended and modified to s u i t the p a r t i c u l a r requirements of a beam of surface muons presently a v a i l a b l e at TRIUMF. Some emphasis i s placed on a des-c r i p t i o n of the muon beam, i t s operation, and the problems inherent i n the successful use of these low energy, nearly monokinetic,polarized part-i c l e s . The basic method of MSR (muonium spin rotation) as i t applies to the experimental circumstances i s reviewed. The use of powder targets of t h i s kind i s examined i n the context of possible experiments i n weak i n -teractions, d i f f u s i o n studies, and gas chemistry. - i i -TABLE OF CONTENTS I. Introduction I I . Related Phenomena A. Experimental Problem B. Other Experiments I I I . The Positronium Analogy A. Pioneering Powder Experiments B. Techniques of Orthopositronium Observation 1. Angular c o r r e l a t i o n 2. Lifetime 3. Gamma spectrum analysis C. Testing the Powder Samples 1. Experimental design 2. Data analysis 3. Results IV. The TRIUMF Experiment A. The Source of Muons 1. General 2. The TRIUMF M9 channel 3. Surface muons 4. Detection of low energy muons 5. Tuning f o r surface muons B. The MSR Time Spectrum 1. Rotation 2. Relaxation 3. Spectral form 4. T y p i c a l muonium and muon spectra C. Apparatus 1. Precession cart 2. E l e c t r o n i c s and data c o l l e c t i o n D. Muonium i n S i l i c a Powder 1. Quenching technique 2. Results V. Evaluation; D i f f u s i o n of Muonium into a Vacuum A. Q u a l i t i v e Assessment B. Quantitative Consequences of the Observed Muonium Asymmetry C. Applications i n Future Experiments 1. F e a s i b i l i t y of an antimuonium experiment 2. D i f f u s i o n studies 3. Chemistry of gases VI. Bibliography - i i i -L I S T OF TABLES T i t l e Page I . L e p t o n Number A s s i g n m e n t Scheme 2a I I . A d d i t i v e Muon Number A s s i g n m e n t Scheme 2b I I I . M u l t i p l i c a t i v e Muon Number A s s i g n m e n t Scheme 2b I V . P o s i t r o n i u m E x p e r i m e n t a l R e s u l t s 13a V . Muonium E x p e r i m e n t a l R e s u l t s 24a - i v -LIST OF FIGURES T i t l e Page 1. Positronium A n n i h i l a t i o n 10a 2. Positronium A n n i h i l a t i o n i n Quartz Powder 12a 3. M9 Beam Schematic 15a 4. Surface Muon Range Curve 17a 5. Positron Energy Spectrum and Asymmetry Parameter 18a 6. H e l i c i t i e s i n T T + -»• u + -> e + Becay 18b 7. Muonium i n Fused Quartz (4.2 Gauss) 20a 8. Asymmetry of Muons i n Carbon Tetrachloride (75 Gauss) 20b 9. Muon Precession i n Copper (75 Gauss) 20c 10. Precession Apparatus 21a 11. MSR E l e c t r o n i c s and Logic 22a 12. Muonium i n S i l i c a Powder at 10 ^ Torr (2.5 Gauss) 24b 13. Muonium i n S i l i c a Powder at 0.05 Torr (2.5 Gauss) 24c 14. Muonium i n S i l i c a Powder at 0.15 Torr (2.5 Gauss) 24d 15. Muonium i n S i l i c a Powder at 0.40 Torr (2.5 Gauss) 24e 16. Relaxation Rate as a Function of Oxygen Pressure 26a - V -ACKNOWLEDGEMENT Upon p r e s e n t a t i o n o f t h i s t h e s i s , I w o u l d l i k e t o t h a n k t h o s e who have a s s i s t e d i n t h e r e s e a r c h and p r e p a r a t i o n b e h i n d i t . I n p a r t i c u l a r , I am g r a t e f u l t o D r . J . B . W a r r e n f o r h i s s u g g e s t i o n s r e g a r d i n g t h e e x p e r i m e n t a l t e c h n i q u e s and h i s a d v i c e i n t h e w r i t i n g o f t h e t e x t ; t o t h e e n t i r e TRIUMF MSR G r o u p , whose t i m e and e f f o r t have c r e a t e d a f i n e MSR f a c i l i t y ; and t o M r . Geo rge C l a r k , f o r h i s t a l e n t s i n t h e d e s i g n and c o n s t r u c t i o n o f t h e h a r d w a r e n e c e s s a r y f o r a s u c c e s s f u l e x p e r i m e n t . I. Introduction With the advent of the so-called meson f a c t o r i e s , the use of the muon as a t o o l f o r in v e s t i g a t i n g properties of materials and d e t a i l s of i n t e r a c t i o n s becomes a p r a c t i c a l , i l l u m i n a t i n g p u r s u i t . Such a t t r i b u t e s as long l i f e -time (^2.2 usee), magnetic moment, asymmetric decay, and p o i n t - l i k e s t r u c -ture coupled with the a v a i l a b i l i t y of highly polarized beams make the muon spin research (uSR) method (and MSR, i t s muonium counterpart) unique, a l -though not without analogue, i n studying some properties of a v a r i e t y of s o l i d s , l i q u i d s , and gases. Muonium (u +e , denoted also as M) i s often regarded conceptually as a l i g h t isotope of atomic hydrogen, of mass about one-ninth that of the heavier atom. Since the muon i s s t i l l heavier than the electron by over 200 times, the atomic s i z e i s not appreciably d i f f e r e n t from hydrogen, i n contrast to positronium, where the mass of the p o s i t i v e p a r t i c l e i s the same as that of the electron. Positronium was at one time considered as a l i g h t isotope of hydrogen, but due to large s i z e (twice the Bohr radius) and mass d i f f e r e n c e s , the v a l i d i t y of t h i s approach i s f a r from u n i v e r s a l . Positronium phenomena are i n general d i f f i c u l t to i n t e r p r e t v i s - a - v i s i t s int e r a c t i o n s with a mediumiinaanypphase. One of the more successful treatments of these phenomena has been the determination of positronium d i f f u s i o n constants by stopping positrons i n f i n e l y powdered samples of MgO, A^O^, and Si02> (Brandt and Paulin, 1968) In p r i n c i p l e , the MSR (muonium spin rotation) method enables the same type of experiment to be performed with muons. Moreover, a powder may provide muonium i n vacuum, enabling further experiments on th i s system. I I . R e l a t e d Phenomena The muon has l o n g been r e g a r d e d as a heavy e l e c t r o n b e c a u s e i t does n o t i n t e r a c t s t r o n g l y w i t h n u c l e a r m a t t e r . T h i s i s a b a s i c q u a l i t y o f t h e l e p t o n f a m i l y , w h i c h a l s o i n c l u d e s n e u t r i n o s and a n t i n e u t r i n o s . I t was n o t u n t i l more r e c e n t l y t h a t t h e e x i s t e n c e o f two t y p e s o f n e u t r i n o - a n t i n e u t r i n o p a i r s was e s t a b l i s h e d (Danby e t a l , 1 9 6 2 ) , now r e f e r r e d t o as e l e c t r o n (v , v ) and muon (v , v ) n e u t r i n o s . e e y u The i n d i v i d u a l i d e n t i t y o f t h e muon has s i n c e b e e n more f i r m l y u n d e r l i n e d by t h e need f o r a s e p a r a t e c o n s e r v a t i o n l a w f o r what i s t e rmed ar. muon (o r m uon ic l e p t o n ) number , i n a d d i t i o n t o a l e p t o n c o n s e r v a t i o n l a w . F o r i n s t a n c e , p r o c e s s e s s u c h as t h e f o l l o w i n g a r e n o t o b s e r v e d : + + u e + y + + . - • + y -> e + e + e + + y + A ->• e + A z z v g + n ->- y + p E a c h r e a c t i o n i s a l l o w e d by c o n s e r v a t i o n o f t o t a l l e p t o n number ZZ^ ( s e e T a b l e I ) . The p h y s i c a l f o r b i d d e n n a t u r e becomes e v i d e n t o n l y when t h e c o n s e r v a t i o n o f t h e sum o f muon number ( T a b l e I I ) i s i n v o k e d . I n t e rms o f a p p l i c a b i l i t y , h o w e v e r , t h e a d d i t i v e r u l e i s n o t u n i q u e . I n f a c t , a l e s s r e s t r i c t i v e l a w by w h i c h t h e p r o d u c t o f a d i f f e r e n t s e t o f muon numbers must be c o n s e r v e d a s w i t h p a r i t y , i s c o n s i s t e n t w i t h o b s e r v a -t i o n ( s e e T a b l e I I I ) : a l s o , i f s u c h a l a w were shown t o be o b e y e d , i t w o u l d have r a m i f i c a t i o n s i n t h e t h e o r y o f weak i n t e r a c t i o n s , s i n c e e i t h e r scheme, a d d i t i v e o r m u l t i p l i c a t i v e , c a n be deduced by a s s u m i n g d i f f e r e n t t r a n s f o r m a t i o n p r o p e r t i e s o f t h e n e u t r i n o f i e l d . - 2a -Particle Lepton Number +1 + e , v e - i +i ' P + ' \ - i Hadrons 00 TABLE I. LEPTON NUMBER ASSIGNMENT SCHEME - 2b -Particle iVluon Number e , v e - i + e , v e +1 +i Hadrons o TABLE I I . ADDITIVE MUON NUMBER ASSIGNMENT SCHEME Particle Muon Number + ~ . Vl V • - i + e e +i Hadrons 0 T A B L E I I I I . M U L T I P L I C A T I V E MUON NUMBER ASSIGNMENT SCHEME - 3 -In order to test muon number conservation, one could look f o r the decay: + + -y -> e + v ++ v (1) e y The usual p o s i t i v e muon decay involves v and \> and i s allowed under e u botheschemes, whereas (1) i s consistent only with the m u l t i p l i c a t i v e law. Experimentally, detection of neutrinos i s d i f f i c u l t at best, and observation of the a l t e r n a t i v e y + decay mode i s somewhat imp r a c t i c a l as a test of conserved quantities (Eichten et a l , 1973). Another t e s t , which i n the past has not been possible f o r reasons which w i l l be explained s h o r t l y , i s to search for the conversion of muonium into what i s termed as antimuonium (y e +, or M): y + e ->- y + e -In an additive scheme, t h i s i n t e r a c t i o n i s not allowed since E£ i s -2 y for ||and +2 for M (Table I I ) . Since II Jl i s -1 for both M and M (Table I I I ) , the conversion i s consistent with the m u l t i p l i c a t i v e scheme. Obviously, the observation of M i n a system i n i t i a l l y prepared i n the M state would i n d i c a t e that the more general p a r i t y - l i k e conservation law better describes lepton behavior. It would also i n d i c a t e the existence of a neutral lepton current i n the weak i n t e r a c t i o n Hamiltonian (Feinberg and Weinberg, 1961). On the other hand, i f no M i s observed, one can only set some upper lim-i t s . By postulating a s p e c i f i c form for the possible M-M i n t e r a c t i o n , such as: H = v l V A ( l + Y 5 ) V y Y A ( l + Y 5 H e + H ' C ' ( 2 ) where G i s the M-M coupling constant, the conversion rate can be c a l c u l -ated i n terms of G/G^. Since G^, the usual vector coupling constant, i s known very accurately from beta decay, an estimate of G can be extracted. - 4 -The probability of this interaction is (Feinberg and Weinberg, 1961), in the absence of external f i e l d s : P(M*M) = 2.5 x 10" 5 ( J ) 2 ( 3 ) v Thus, assuming the validity of the interaction (2) , and assuming that the multiplicative law does describe nature's selectivity, one can set an upper limit on the coupling constant G. - 5 -A. The Experimental Problem According to such c a l c u l a t i o n s , i t would seem that an antimuonium exper-iment i s straightforward, but such i s not the case. One must prepare muonium from a beam of muons thermalized i n the presence of an electron don-or, i n a chemical r e a c t i o n of the form: u + + X -* u +e~ + X + (4) As shown by Feinberg and Weinberg, the conversion process i s d r a s t i c a l l y altered i n the presence of matter, which, from (4), i s a necessary con-d i t i o n f o r the i n i t i a l formation. S p e c i f i c a l l y , the presence of electromagnetic f i e l d s breaks the energy degeneracy of the M and M states by an amount A, thus reducing the prob-a b i l i t y of conversion. I t i s estimated that unless A «3xl0 ^eV, the i n t e r a c t i o n (2) would be quenched beyond observation i n the l i f e t i m e of muonium. It i s further estimated that the lowest order contributions to 3 A w i l l be of order E , and to lowest order i n gradients: A « E '• "V(E2) g For E<<10 v o l t s per centimetre, A i s i n s i g n i f i c a n t . The l o n g i t u d i n a l magnetic f i e l d must be kept to <Q01 gauss, however, i n order that the IS (F,F z)=(l,±1) states are not s p l i t so much that the conversion i s completely quenched. For muonium i n a gas, the conversion p r o b a b i l i t y must be m u l t i p l i e d by the inverse of the c o l l i s i o n rate to take into account the environmental e f f e c t on A. At reasonable moderator p r e s s u r e s , ( f l Torr) t h i s e f f e c t i s great enough to place the experiment beyond f e a s i b i l i t y . - 6 -B. Previous Experiments The i n t e r e s t i n a muonium conversion experiment i s not new; i n f a c t , at least three attempts, using d i s s i m i l a r techniques, have been made. None has met with success. They have served only i n emphasizing the major d i f f -i c u l t y , that of producing the muonium i n c o l l i s i o n l e s s space or high vacuum. Each has used a d i f f e r e n t muon moderator - electron donor combination. The f i r s t attempt (Amato e t a l , 1968) r e l i e d on argon gas at atmospheric pressure to stop the muons and supply the electrons. A search f o r the c h a r a c t e r i s t i c argon muonic K X-ray was made, since there should be a a high u capture rate i n an argon-antimuonium c o l l i s i o n . The r e s u l t of the experiment was consistent with zero, and the lowest upper l i m i t that could be established f o r the M-M coupling constant was G < 58000^. The muonium c o l l i s i o n rate severely r e s t r i c t e d the p r o b a b i l i t y of conversion. Another experiment (Hofer et a l , 1972) has met with no greater success. A beam of pions at 39.5 MeV/c momentum was allowed to decay i n f l i g h t i n a magnetic f i e l d p a r a l l e l to the beam. Some backward emitted muons should then have energies <10 keV. Thes slow p a r t i c l e s would follow a long h e l i c a l path due to the f i e l d and could form muonium i n a c o l l i s i o n with an argon atom of the low pressure gas environment. The uncharged system would have a r a d i a l v e l o c i t y component and could be detected i n a d i r e c -t i o n perpendicular to the beam. However, no s i g n a l a t t r i b u t a b l e to t h i s process has yet been reported. The t h i r d technique (Kendall, 1972) used a 24 MeV/c 100% pol a r i z e d muon beam stopping i n t h i n platinum f o i l s heated to %1500CC. Muons d i f f u s i n g to the f o i l surface were expected to form muonium and escape into the - 7 -vacuum environment. Again, an i n s i g n i f i c a n t amount of muonium was de-tected (Bowen et a l , 1973). Other s i m i l a r experiments are i n progress at the meson f a c i l i t i e s . For instance, LAMPF has received proposals f or testing muon behavior i n t h i n gold f o i l s . Several neutrino experiments are also planned there to check lepton conservation from another approach. Yet another experiment i s de-signed to investigate muon conservation laws using u capture i n n u c l e i with subsequent electron emission. - 8 -I I I . The Positronium Analogy Since hydrogen, muonium, and positronium atoms are a l l hydrogen-like sys-tems, one would expect some s i m i l a r i t y i n behavior i n a given environment, the main differences a r i s i n g from s i z e and (reduced) mass e f f e c t s . How-ever, high f l u x muon sources i n the form of meson factory beamlines have been only recently a v a i l a b l e , and studies of p o s i t i v e muon behavior are not yet as extensive as those of positrons. Compact sources of isotopes 22 58 64 such as Na, Co, and Cu have long been used to provide positrons i n a wide range of experiments (West, 1973). The unrav e l l i n g of the complex behavior of positronium (Ps) has been slowly advancing, and i t seems rea-sonable to make comparisons and seek information from analogous Ps studies i n the f i r s t stages of a muonium experimental program. - 9 -A. Pioneering Powder Experiments The f i r s t experiments i n which positrons were in j e c t e d into f i n e l y pow-dered i n s u l a t o r samples showed (Paulin and Ambrosino, 1968) that positronium was produced i n the powder grains and could d i f f u s e out to a n n i h i l a t e i n the intergranular vacuum. The exact formation process i s s t i l l not as w e l l understood as, for example, Ps formation i n i n e r t gases, but the r e s u l t was c l e a r : a positron, on slowing i n the s o l i d , could d i f f u s e and leave the granule i n the form of positronium. This positronium a n n i h i l a t e s to three y - r a y s with the longer T q=140 nsec l i f e t i m e of the t r i p l e t ortho-positronium (o-Ps) state, whereas two shorter l i f e t i m e components, both observed i n bulk samples, a r i s e from a n n i h i l a t i o n within the granules. The shorter l i f e t i m e s i n d i c a t e two gamma decay; the f i r s t (T - 0.4 nsec) due to i n - f l i g h t as well as s i n g l e t parapositronium (p-Ps) a n n i h i l a t i o n , the second((T . , „ - 2 nsec) due to p l c k o f f of electrons from the pic k o f f medium by the bound positron i n o-Ps. These l i f e t i m e s are shorter than the average time taken to d i f f u s e into the vacuum. Shortly a f t e r the discovery of t h i s e f f e c t , i t was applied to the prob-lem of determining the d i f f u s i o n rate of o-Ps i n i n s u l a t i n g s o l i d s such as Si02> Al^O^, and MgO. More recently the vacuum l i f e t i m e of o-Ps was measured with great accuracy using t h i s d i f f u s i o n (Gidley et a l , 1975), and the r e s u l t s obtained showed some discrepancy with the t h e o r e t i c a l pre-d i c t i o n s of quantum electrodynamics. Thus the technique has proven worthwhile i n more than one branch of physics. - 10 -B. Techniques of Orthopositronium Observation There are three basic approaches to positronium i n v e s t i g a t i o n s , each with s l i g h t l y d i f f e r e n t applications.(West, 1973). They are b r i e f l y described here i n the context of how tifrey can and have been applied i n the studies of i n s u l a t i n g powders. (Fig. 1) 1. Angular c o r r e l a t i o n A parapositronium atom at res t w i l l decay into two y-rays emitted at 180° to conserve momentum, thus the coincidence rate of two we l l collimated detectors as a function of angular displacement can show sharp peaking about t h i s angle. In bulk samples t h i s e f f e c t i s smeared due to the zero-point energy of the atom. In a f i n e l y powdered i n s u l a t o r , injected p o s i -trons w i l l form both o-Ps and p-Ps, but due to th e i r much longer l i f e t i m e the o-Ps atoms d i f f u s e much f a r t h e r . This i s manifested i n the appearance of a sharp angular c o r r e l a t i o n peak as the powder s i z e i s reduced to < 100 A when the sample i s i n vacuum i n a strong magnetic f i e l d . The f i e l d mixes the m=0 substates of o-Ps and p-Ps, and leads to two gamma an n i l a t i o n i n the vacuum, where the zero-point energy i s small.(Steldt and Varlashkin, 1972). 2. Lifetime In some isotopes the formation of the beta decay positroniiLeaves the nuc-leus i n an excited state which promptly ( < 10 ^  sec) emits a gamma ray of s p e c i f i c energy, as i n the process: 2 2 2 2 „ * , + . Na -y Ne* + e + v e 22 22 Ne* -» N e + y (1.28 MeV) - 10a -P O S I T R O N I U M A N N I H I L A T I O N P a r a p o s i t r o n i u m ( Sq) t w o q u a n t u m a n n i h i l a t i o n t ^ 0 . 1 2 n s e c P p - P s i n v a c u u m Angular correlation 10 0 10 Angle between photons (mrad) T o Lifetime spectrum t . , Cf. ^ 2 nsec pickoff _L 25 t (nsec) 50 Orthopositronium ( S^) three quantum annihilation! T 'i- 140 nsec o Gamma energy spectrum normal p-Ps component - U I significant o-Ps component J I 200 400 Energy (keV) 600 FIGURE 1 - 11 -By s t a r t i n g a clock with the 1.28 MeV s i g n a l and stopping i t with the de-te c t i o n of a gamma of 511 keV or l e s s , one can determine the l i f e t i m e of the positron. Up to three medium-dependent l i f e t i m e s have been observed (Paulin and Ambrosino, 1968) i n powdered i n s u l a t o r s , corresponding to the d i f f e r e n t a n n i h i l a t i o n processes previously mentioned. The strength of the l i f e t i m e component due to pick o f f of the positron i n o-Ps i s found to decrease as p a r t i c l e s i z e i s decreased, which can be explained i n terms of the d i f f u s i o n of o-Ps into the void between p a r t i c l e s . A d i f f u s i o n model, assuming uniform positronium thermalization i n spher i c a l powder p a r t i c l e s followed by a random walk, was used to describe the data. The assumption of aejectionn of the atom into the vacuum at the p a r t i c l e surface was i n -cluded. A f i t of the pick o f f component strength as a function of p a r t i c l e radius yielded the d i f f u s i o n constant D f o r positronium i n each of SiC^, A1 20 3, and MgO. 3. Gamma spectrum analysis While p-Ps a n n i h i l a t i o n leads to two gamma rays of 511 keV each, o-Ps must decay to three gammas (or at le a s t an odd number greater than one) whose energy spectrum i s continuous up to a maximum of 511 keV. By care-f u l comparison of two spectra taken under i d e n t i c a l conditions (except f o r those designed to enhance the three gamma process) one can discern a f i l -l i n g i n of the v a l l e y region between the usual 511 keV peak and i t s Compton scat t e r i n g edge at about 341 keV. The .511 keV peak i s correspondingly r e -duced. This i s observable i n spectra from positrons i n j e c t e d into powders held i n a i r and i n vacuum, since three gamma a n n i h i l a t i o n i s quenched i n the presence of oxygen molecules due to spin.exchange. - 12 -C. Testing the Powder Samples In order to assess the s u i t a b i l i t y of a p a r t i c u l a r sample of powder, the method of spe c t r a l analysis was used. Although quantitative i n t e r p r e t a t i o n i s d i f f i c u l t with t h i s technique, a difference i n the p a r t i c l e s i z e a f f e c t s the f r a c t i o n of positrons a n n i h i l a t i n g as o-Ps, which i s i n agreement with the model of positronium d i f f u s i o n . 1. Experimental design The apparatus used for the positron segment of the experiment consisted of a four inch diameter by three inch c y l i n d r i c a l Nal(Tl) c r y s t a l mounted on an RCA XP1140 photomultiplier tube with i t s associated e l e c t r o n i c s , a pre-amplifier and pulse shaping a m p l i f i e r , and a Victoreen PIP 400 multichannel 22 analyzer f o r pulse height a n a l y s i s . A Na source was deposited on a t h i n f l a t aluminum disk which could be submerged i n a powder sample and held at —6 a pressure of 10 Torr by a d i f f u s i o n pumping system. The source and pow-der were enclosed by glass i n order to make the powder v i s i b l e while pump-ing on i t , as i t had a tendency to " b o i l " into the vacuum pump. 2. Data analysis Approximately 20 runs of about 30 minutes each were made on various powder samples, both i n a i r and i n vacuum. The data were analyzed i n the f o l -lowing way: contents of each of four sets (valley (V), a n n i h i l a t i o n peak z (A), background (B), and prompt peak (P) ) of f i v e channels apiece were separately t o t a l l e d (see F i g . 2)- The background due to the 1.28 MeV Comp-ton scattered events (B) was subtracted from both the v a l l e y channels and the a n n i h i l a t i o n peak. These values were then normalized to the prompt 40 30 H O 'TO K3 2 0 1=1 O u 10 0 POSITRONIUM ANNIHILATION IN QUARTZ POWDER xn air 0 i n vacuum 40 60 CHANNEL NUMBER •••• 80 100 - 13 -1.28 MeV peak and comparison was made between runs i n a i r and i n vacuum (as w e l l as a run i n vacuum baked-out at 200 C). The r e s u l t s are ta b u l -ated i n Table IV.. I t should be emphasized that the fi g u r e "per cent e f f e c t " i s not to be construed as a measure of the amount of t r i p l e t positronium i n vacuo, but i s f o r purposes of comparison between samples only. This f i g u r e i s derived from the reduction i n the strength of the a n n i h i l a t i o n peak, since the v a l l e y region i s much more prone to error from background and increased e f f i c i e n c y at the lower energies. Obviously, the three gamma component can grow only at the expense of the two gamma 511 keV peak. 3. Results As expected, the per-cent e f f e c t i s largest f or the power of smallest grain s i z e used, the 70 A diameter s i l i c a (Cab-0-Sil EH5) sample. It was smallest for a sample of lar g e r , low-purity (^96%) magnesiumooxide granules, which i s i n agreement with other experiments using MgO. We have placed emphasis on the study of s i l i c a powders f o r two reasons: f i r s t l y , very f i n e , pure Si02 powder samples are commercially a v a i l a b l e at no cost; secondly, the behavior of muons and muonium i n fused quartz i s w e ll established (Miyasishcheva et a l , 1968, and Gurevich et a l , 1971) and such behavior i s a probable condition f o r the observation of muonium i n vacuum. This w i l l be c l a r i f i e d i n the chapters on the experiment at TRIUMF. POWDER MATERIAL SIZE AIR V-B P AIR A-B P VACUUM V-B P VACUUM A-B P PER CENT EFFECT S i 0 2 (Aerosil) 1.1541.003 5.7001.012 1.297±.004 5.4981.011 3.510.4 SiO| (Aerosil) baked out 1.154±.003 5.7001.012 1.3181.003 5.4801.009 3.910.4 S i 0 2 (Cab-O-Sil) 70 A 1.1531.003 5.578±.Q11 1.349±.004 5.302+.01.1 4.910.4 S i 0 2 (Cab-O-Sil) 140 A 1.1131.003 5.617±.010 1.2851.004 5.4341.011 3.310.4 MgO (impure) 1.116±.003 5.5031.009 1.375+.003 5.422+.010 1.510.4 : TABLE IV. POSITRONIUM EXPERIMENTAL RESULTS - 14 -I V . The TRIUMF E x p e r i m e n t The s t u d y o f muonium and i t s b e h a v i o r i n a powdered i n s u l a t o r t a r g e t i s s i m i l a r t o t h a t o f p o s i t r o n i u m i n t h a t one c a n t r a c e t h e l i f e h i s t o r y o f t h e F = 1 s t a t e . T h e r e t h e s i m i l a r i t y e n d s , f o r t h e muonium atom p r o d u c e s no a n n i h i l a t i o n q u a n t a . One i n s t e a d o b s e r v e s t r a n s i t i o n s among t h e F = 1 s u b s t a t e s o f t h e a tom, i n t h e f o r m o f t h e p o l a r i z a t i o n o f t h e muons i n t h e s e s u b s t a t e s . T r a n s i t i o n s i n v o l v i n g t h e F = 0 s t a t e o c c u r a t a f r e -quency t o o h i g h t o be o b s e r v e d . The t i m e dependence o f t h e p o l a r i z a t i o n p r o v i d e s i n f o r m a t i o n on t h e e n v i r o n m e n t o f muonium, w h i c h i s t h e b a s i c i d e a o f MSR. The TRIUMF i n s t a l l a t i o n p r o v i d e s beams o f h i g h l y p o l a r i z e d p o s i t i v e muons , a p r e r e q u i s i t e f o r an MSR ( o r u + S R ) e x p e r i m e n t . - 15 -A. The Source of Muons 1. General —8 The dominant mode of p o s i t i v e pion decay, with l i f e t i m e T ^ 2.6 x 10 sec i s : TT + +£ru+ + v i i . The r e s u l t i n g muons can be c o l l e c t e d to form a beam. The pions are i n turn produced by i r r a d i a t i o n of a target with an intense, well-focussed proton beam. TRIUMF produces such a beam at 500 MeV, u t i l i z i n g f o r pion production a reaction such as: ^Be^ (p, T r +)^Be^. The conventional mode of beamline operation i s to c o l l e c t muons from i n - f l i g h t pion decay. The decay can take place either near the production target, producing so-called cloud muons, or i n the beam l i n e , i n which case either the forward or backward (with respect to beam d i r e c t i o n ) decay muons are selected by subsequent momentum ana l y s i s . Each process leads to a d i f f e r e n t set of beam properties such as f l u x , momentum, p r o f i l e , and contamination (proton, pion, and po s i t r o n ) . 2. The TRIUMF M9 channel The M9 channel i s a multipurpose low energy and stopping^pion ,or muon beam l i n e , designed and b u i l t by the U n i v e r s i t y of V i c t o r i a contingent at TRIUMF. It consists, f o r our purposes, of seven magnetic elements, which focus p a r t i c l e s , emitted from the production target i n a s o l i d angle of ^60 m i l l i s t e r a d i a n s at 135° to the proton beam, onto the target of i n t e r e s t . Two of the elements are 45° bending dipoles, the remaining f i v e being ten inch quadrupole lenses, arranged symmetrically about the midpoint as shown i n F i g . 3 . P a r t i c l e s produced i n the proton target are focussed to a beam spot which i s e s s e n t i a l l y a 45° plane p r o j e c t i o n of the target. - 16 -3. Surface muons Conventional modes of muon production are not compatible with good focussing c h a r a c t e r i s t i c s , since the muons do not come d i r e c t l y from the proton target. There are, however, a large number of pions that decay at rest close to the skin of the target, producing muons which can be sharply focussed by a beam l i n e ( E i f e r et a l , 1976). A beam of these muons has c e r t a i n other properties which can be advan-tageous. The p o l a r i z a t i o n i s high (> 95%), the momentum i s well defined (a maximum of 29 MeV/c), and the range i s short (148 mg/cm^ CH^), making i t i d e a l f or MSR studies i n low density materials such as gases and powders. One would expect protons, pions, and positrons of 29 MeV/c to contaminate such a beam, but only the positrons are present at the muon target. The protons do not pass throught the t h i n (2 m i l mylar) window at the beam pipe e x i t . Only about 0.3% of the pions remain due to decay during a time of f l i g h t of about s i x mean l i f e t i m e s , and these have a range of the order of one-third that of the muons. The positrons, on the other hand, haveaaarafcher i l l - d e f i n e d range VL00 times greater than the muons, and do not stop i n a low density target. 4. Detection of low energy muons The short muon range necessitates the use of a very t h i n counter system, since one must i d e n t i f y the time at which the muon enters the target by passing i t through a s c i n t i l l a t o r . The system used consisted of a s i n g l e four inch square sheet of 15 m i l (40 mg/cm2) NE102 p l a s t i c s c i n t i l l a t o r . Light c o l l e c t i o n was f a c i l i t a t e d - 17 -by a wedge shaped a l u m i n i z e d m y l a r s h e a t h s u p p o r t e d i n a l u c i t e f rame w h i c h r e f l e c t e d l i g h t f r o m t h e s c i n t i l l a t o r t o w a r d s t h e w i d e r end o f t h e wedge , where i t was g u i d e d v i a t h e u s u a l l u c i t e l i g h t g u i d e s t o a n RCA8575 p h o t o m u l t i p f l i i e r . A s e c o n d s h e a t h o f 0.3 m i l a luminum f o i l p r o v i d e d a l i g h t t i g h t w r a p p i n g . Due t o much l o w e r e n e r g y d e p o s i t i o n by 29 M e V / c e l e c t r o n s i n c o m p a r i s o n w i t h muons , t h e p h o t o m u l t i p l i e r h i g h v o l t a g e and s i g n a l d i s c r i m i n a t i o n l e v e l s c a n be a d j u s t e d so as t o p r o v i d e a c l e a n muon t r i g g e r w i t h h i g h e f f i c i e n c y and good t i m e r e s o l u t i o n . 5. T u n i n g f o r s u r f a c e muons The M9 c h a n n e l was i n i t i a l l y a d j u s t e d f o r s u r f a c e muons by s c a l i n g t h e b e n d i n g magnet c u r r e n t s down by t h e momentum r a t i o , s i n c e i t was known t h a t h y s t e r e s i s e f f e c t s were s m a l l . W i t h a l l q u a d r u p o l e s o f f , t h e c o u n t i n g r a t e i n t h e muon d e t e c t o r was m a x i m i z e d by f i n e a d j u s t m e n t o f t h e b e n d i n g m a g n e t s . The q u a d r u p o l e s were t h e n t u r n e d on t o t h e a p p r o x i m a t e ( s c a l e d ) s e t t i n g s , and f i n e a d j u s t m e n t s were made by an i t e r a t i v e p r o c e s s , a g a i n by m a x i m i z i n g t h e r a t e . F l u x e s as h i g h as 5 x 10^ p o s i t i v e muons p e r s e c o n d were a c h i e v e d i n t h e f o u r i n c h s q u a r e s c i n t i l l a t o r , a t one m i c r o a m p e r e p r o t o n c u r r e n t . I n o r d e r t o i d e n t i f y t h e muons u n a m b i g u o u s l y , an i n t e g r a l r a n g e c u r v e was measured by s c a l i n g t h e muon c o u n t e r as a f u n c t i o n o f t h i c k n e s s o f m y l a r a b s o r b e r a t t h e beam p i p e e x i t . The c u r v e i s shown i n F i g . 4 . A muon p r e c e s s i o n c u r v e i n c o p p e r p r o v e d t h a t t h e p a r t i c l e s were muons r a t h e r t h a n p i o n s . Beam p r o f i l e s were measured i n a s u b s e q u e n t e x p e r i -m e n t , and s h o w e d , t h e muon s p o t t o be r o u g h l y e l l i p t i c a l i n s h a p e , t h r e e i n c h e s w i d e by two i n c h e s h i g h . <7 aanoia CO Q 1 J. i - 18 -B. The MSR Time Spectrum The MSR technique i s based on two i n t r i n s i c q u a l i t i e s of the muon, i t s asymmetric decay and i t s magnetic moment. Due to maximal p a r i t y v i o l a t i o n i n the process y + -* e + + V g + -v (Emax = 52.8 MeV) , the positrons are emitted with an angular d i s t r i b u t i o n 1 + a cos0, where 6 i s the angle between the positron d i r e c t i o n of f l i g h t and the y + spin ( i n the y + r e s t frame) at the instant.of decay. The asymmetry parameter a i s a function of the decay positron energy E (Fig. 5): a = ijW ~ 1 , w = E/52.8 MeV. 3 - 2w This asymmetric behavior provides a method of observing the rot a t i o n s of the spin magnetic moments of a time ensemble of muons i n a transverse magnetic f i e l d . ( F i g. 6) 1. Rotation In contrast with y +SR, where the r o t a t i o n of free muons i s observed, MSR 3 i s the r o t a t i o n (and relaxation) of the S- state (F = 1) of the muonium i z atom. Here the muon spin i s coupled to that of the electron by the hyperfine i n t e r a c t i o n . The magnetic moment of the system gives r i s e to Larmor precession i n low magnetic f i e l d s , at the frequency u> , where: M CO = ig(ci) + 03 ) ^  -103u M y e y The factor of one-half i s due to the precession of a spin one state, rather than spin one-half, since the i n d i v i d u a l magnetic moments depend on the charge-to-mass r a t i o , co ^ - 207 co , and the sense of r o t a t i o n f o r muonium ° e y i s opposite to that of a free muon. Numerically, |CO^/B| ^ 2TT:1.394 MHz/gauss, fo r B § 50 gauss. In higher f i e l d s , Zeeman couplings cause a s p l i t i n - 18a -POSITRON ENERGY SPECTRUM AND ASYMMETRY PARAMETER _ 0 4 L 1 1 1 1 -1- 1 i I i I ' 0.0 0.2 0.4 0.6 0.8 1.0 w = E/Emax FIGURE 5 » - i g -frequency (Gurevich et a l , 1971, and Brewer et a l , 1974) and a beat phenomenon i s observed. 2. Relaxation The average of the muon decay asymmetry's' over a l l possible positron energies i s one-third, but i n p r a c t i c e one does not detect a l l positrons with the same e f f i c i e n c y . Moreover, a l l muons do not form t r i p l e t ( F z = 1) muonium and the beam may not be 100% p o l a r i z e d , which leads to a reduction i n the observed asymmetry. Therefore, we do not measure a ' d i r e c t l y , but a more subtle quantity A q , the experimental asymmetry at the time the t r i p l e t muonium atoms form i n the transverse f i e l d . It i s the time evolution of the experimental asymmetry A that has spawned another meaning f o r the MSR acronym, Muonium Spin Relaxation; the r e l a x a t i o n of the spin due to depolarizing e f f e c t s of various kinds provides valuable information on the environment of the M-^atom. Applied f i e l d inhomogeneity, random l o c a l f i e l d s , and chemical reactions are sources of r e l a x a t i o n . C o l l i s i o n s with paramagnetic molecules such as O2 lead to an exponential decay of the asymmetry at a rate proport t i o n a l to the p r o b a b i l i t y of c o l l i s i o n s , that i s , the gas pressure. This r e s u l t can be summarized: A (t) = A Q expJ-t/T^)• The quantity T2 i s c a l l e d the r e l a x a t i o n time. 3. Spectral form O v e r a l l , the form of the muoniumm decay time spectrum i s : N ($;>) = N Q { e _ T / T | l + A 0 e " t / T 2 cos (ugt + <f>)(|! + B} The parameter T = 2.2uusec i s the muon l i f e t i m e . The phase cf> depends - 20 -on positron telescope geometry and the d i f f e r e n c e between the time of formation of muonium and the experimental t = 0 (usually small). i s a normalization factor while B takes into account the background, assumed to be constant.T 4. T y p i c a l muonium and muon spectra A t y p i c a l muonium spin r o t a t i o n spectrum obtained using a fused quartz precession target i s displayed i n F i g . 7. In F i g . 8, a p l o t of the asymmetry as a function of time i s shown for muons i n a l i q u i d carbon t e t r a c h l o r i d e target (obtained by f o l d i n g out the background and exponential decay). Both of these were obtained i n a conventional muon beam. F i g . 9sshows the precession of surface muons at TRIUMF i n a copper target. Both muon spectra were taken with the applied transverse f i e l d of 75 gauss, while the muonium spectrum was at 4.2 gauss. With a large free muon component, one should assume a l i n e a r time dependence for B(Fleming et a l , 1976). - 20a -FIGURE 7 ASYMMETRY OF MUONS I N CARBON TETRACHLORIDE (75 GAUSS) M Q a w t— UJ >— CO ( X 1 h 0 -.1 -.2 h -.3 -.75 -.25 .25 .75 1.25 1.75 2.25 2.75 3.25 3.75 4.25 O TIME (MICRQSEC) TIME IMICROSEC) - 21 -C. Apparatus 1. Precession cart The technique of MSR was applied to search f o r the formation and d i f f u s i o n of Muonium i n s i l i c a powders. The main components of the apparatus as shown i n F i g . 10 are; the t h i n defining counter, two positron telescopes, Helmholtz precession c o i l s , and a target vacuum chamber with a d i f f u s i o n pump and support assembly. The use of a wheeled precession cart makes the apparatus portable and the geometry reproducible. The two positron ttelescopes view the muon stopping region i n a d i r e c t i o n perpendicular to both the beam d i r e c t i o n and the applied transverse f i e l d . Each telescope consists of three 8" x 16" x V p l a s t i c counters, one near the target and two fa r t h e r away, separated by 2" of graphite degrader to reduce scattered positron background and discriminate against low energy (and hence negative asymmetry) decay positrons. A l l counters use RCA 8575R photomultipliers. The telescopes were designed and b u i l t by the U n i v e r s i t y of Arizona group at Lawrence Berkeley Laboratory, as were the precession c o i l s , and have been modified for use at TRIUMF. The c o i l s themselves are dual Helmholtz type, the extra set of c o i l s enhancing the f i e l d uniformity. A deviation of less than +0.1% over a volume of 400 cubic centimetres minimizes d e p o l a r i z a t i o n due to f i e l d inhomogeneity. The maximum f i e l d a v a i l a b l e i s over 75 gauss, s u f f i c i e n t f o r both muonium and muon precession studies. The vacuum chamber i n which the target i s supported consisted of a glass cylinder 6 inches i n diameter and 15% inches long, with brass and aluminum flanges on each end supporting mylar windows. The upstream (5 mil) - 22 -window allowed muons (and positrons) into the target while the down-stream (10 mil) one allowed p a r a s i t i c use of the positrons behind our apparatus. Our e n t i r e experiment did not present enough mass to the beam to scatter positrons appreciably. Two ports on the upper and lower sides 6f the cylinder provided, r e s p e c t i v e l y , a l i n e to the vacuum pump and a connection through two c l o s e l y spaced needle valves to an oxygen supply. The powder i t s e l f was put i n a wire-supported mylar v e s s e l with a 0.25 m i l aluminized mylar face to allow muons into the target. It was open at the top to permit the i n t e r s t i c e s to be evacuated. This was done by means of a d i f f u s i o n pump with a cold trap. Pressure was measured with a UBC-NP-12 type i o n i z a t i o n gauge for high vacuum and a P i r a n i gauge for lower vacuum. 2. E l e c t r o n i c s and data c o l l e c t i o n Signals from the photomultiplier bases i n the experimental area were fed v i a 100 foot cables to the e l e c t r o n i c s configuration shown i n F i g . 11. The stopping muon l o g i c i s v i r t u a l l y nonexistent i n t h i s configuration f o r two reasons. F i r s t , the clean, noiseless s i g n a l from the muon counter eliminates need f or a coincidence to define the incoming p a r t i c l e . Secondly, the i n e f f i c i e n c y of electron counting i n the t h i n p l a s t i c makes an electron veto counter unnecessary. No muons have s u f f i c i e n t energy to pass completely through the target v e s s e l . Start and stop signals from one telescope were fed to an Ortec 437A time-to-amplitude converter coupled to a Tracor-Northern pulse height analyzer MSR ELECTRONICS AND LOGIC - 23 -and punched on paper tape. Time histograms from stop signals i n both telescopes were accumulated simultaneously with a PDP-11/40 using an EG&GTDC100 time d i g i t i z e r connected v i a CAMAC and an MBD-11 programmable branch d r i v e r . These histograms were recorded on magnetic tape. D. Muonium i n S i l i c a Powder 1. Quenching technique The vacuum system on the precession cart was assembled the day before the run at TRIUMF. A sample of 70 A diameter s i l i c a powder i d e n t i c a l to that used i n the most successful positronium study was inserted. The —6 system was pumped at 10 Torr f o r four hours to remove impurities (eg. hydroxyl groups, siloxane, water) from the granule surfaces. It -2 was kept overnight at ^ 2 x 10 Torr u n t i l an hour before the f i r s t run, when d i f f u s i o n pumping was resumed. The pressure f o r that run was —6 'VLO Torr. The transverse magnetic f i e l d applied i n t h i s and subsequent runs was 2.5 gauss. Oxygen was then introduced, at a pressure of 0.4-H- 0.05 Torr, f o r the second run, i n order to check whether dep o l a r i z a t i o n (or "quenching") would take place. The high vacuum run was repeated with better s t a t i s t i c s , followed by two runs at 0.05 + 0.005 Torr and 0.15 + 0.02 Torr oxygen pressure. Another high vaccum run, a run with a low pressure xenon atmosphere, and a run at high vacuum with a mylar s h i e l d on the in s i d e surface of the glass v e s s e l , followed the i n i t i a l runs. If muons form muonium i n a powdered sample as they are known to do i n bulk quartz ,,precession at the muonium frequency w i l l be apparent. If - 24 -they do not reach the powder surface, the addition of a small component of oxygen to the target w i l l have l i t t l e e f f e c t . I f , however, there i s fa s t d i f f u s i o n to the surface, the paramagnetic oxygen molecules w i l l depolarize the muonium and quench the precession at that frequency. Moreover, i f the powder acts as an i n e r t moderator ( e s s e n t i a l l y a dense ine r t gas) the dependence of the r e l a x a t i o n rate, , on the oxygen p a r t i a l pressure could be s i m i l a r to the r e s u l t from the gas chemistry of muonium (Garner et a l , to be published). The addition of xenon, on the other hand, should increase the muonium formation p r o b a b i l i t y , since i t i s known that small admixtures of xenon i n other i n e r t gases enhances the muonium formation p r o b a b i l i t y , with no depolarizing e f f e c t . To ensure that the glass walls of the v e s s e l were not responsible f o r the muonium present, they were shielded with mylar sh o r t l y before the end of the s h i f t . 2. Results Analysis of the time histograms obtained was done off l i n e on the IBM 370/168 at the UBC Computing Centre. The data were f i t t e d to the form (5) by the routine VARMIT, and the r e s u l t s obtained are summarized i n Table Vi. Plots iofimsome of the data and the best f i t s are shown i n Figures 12 - 15. The plo t s show a clear trend i n the r e l a x a t i o n of the precession s i g n a l as a function of oxygen pressure; d e p o l a r i z a t i o n i s taking place. t This was observed i n a p r i o r run at TRIUMF, and has been observed elsewhere Oiiiyasishcheva et a l , 1968, and Gurevich et a l , 1971). RUN EVENTS(10 3) STANDARD DEVIATIONS A o T 2 (ysec) FIELD (gauss) PRESSURE (Torr) COMMENTS 1 34 -0.13 0.071(6) 9(6) 2.49 l O " 6 Low s t a t i s t i c s 2 • 132 -1.22 0.06(1) 0.3(1) 2.48 0.4,O2 3 77 +0.95 0.091(7) 8(5) 2.48 l O " 6 4 100 -0.39 0.060(3) 2.0(3) 2.48 0.05 0 2 5 16 -0.21 0.09(2) 0.9(3) 2.58 0.15 0 2 Low s t a t i s t i c s 6 112 -1.20 0.082(4) 6(2) 2.49 l O " 6 7 31 +0,26 0.19(2) 0.28(5) 2.56 ^1 Xenon Probable 0 2 contam-in a t i o n 8 23 +0.48 0.093(7) 12(4) 2.44 l O " 6 Mylar s h i e l d used TABLE V. MUONIUM EXPERIMENTAL RESULTS -500 1 1 1 1 1 1 1 1 i i i I -.75 -.25 .25 .75 1.25 1.75 2.25 2.75 3.25 3.75 4.25 TIME (MICROSEC) TIME (MICRQSEC) TIME (MICR05EC) - 25 -V. Evaluation; D i f f u s i o n of Muonium into a Vacuum The presence of muonium de p o l a r i z a t i o n when oxygen i s added i n small amounts to the target chamber constitutes evidence f o r the d i f f u s i o n the atom i n the s i l i c a granules. - 26 -A. Q u a l i t a t i v e Assessment The extent of the d i f f u s i o n i n the powder i s not well defined i n our experiment. The argument can be made that a muonium atom would depolarize i n the powder granule i f i t d i f f u s e d to the surface and interacted there with adsorbed oxygen. Adsorption of oxygen c e r t a i n l y takes place on the powder surface, r e s u l t i n g i n the formation of a siloxane group (Cabot Corporation, 1976) but there are several f a c t s contradicting t h i s as a depolarizing mechanism. The l i n e a r dependence of the r e l a x a t i o n rate, T^ "*", on the oxygen pressure (Fig. 16) supports the contention that muonium i s f i n d i n g the void and depolarizing there. Secondly, adsorbed oxygen does not have the paramagnetic (depolarizing) character of the gaseous atom. T h i r d l y , the positronium r e s u l t s demonstrate that a n n i h i l a t i o n takes place i n the vacuum, and muonium, being a neutral atom, should behave i n a s i m i l a r fashion at the s o l i d -vacuum i n t e r f a c e . In other words, i f the atom gets to the surface, the p o t e n t i a l b a r r i e r i i s such that i t should escape to the v o i d . It w i l l remain there, since the thermal energy i s small i n comparison with t y p i c a l b a r r i e r potentials at the surface of a s o l i d . B. - 27 -B. Quantitative Consequences of the Muonium Asymmetry Some idea of the amount of muonium present i n vacuum can be extracted i f one i s prepared to make a few reasonable assumptions. From the evidence of f a s t d i f f u s i o n just given, i t i s p l a u s i b l e that a l l the muonium formed eventually finds the vo i d , since the mean l i f e t i m e (2.2 usee) i s long compared to the r e l a x a t i o n time of 0.3 ysec. However, i n the powder target, the p r o b a b i l i t y of muonium formation i s not one, but i s reduced. This p r o b a b i l i t y can be estimated by analysis of the muonium asymmetry, which i s ^ 0.08 on the average for our experiment (excluding the Xenon run, where formation i s enhanced due to the presence of.a donor gas). With our experimental arrangement, the maximum observable asymmetry ( i e . , with no de p o l a r i z a t i o n present) i s of the order of 0.4 f o r a muon s i g n a l . This i s reduced by one-half f o r muonium since i n the atomic state, only the t r i p l e t precession i s recorded. Therefore, roughly 40% of the muons injected decay as muonium i n the p a r t i c l e i n t e r s t i c e s . - 28 -C. Applications i n Future Experiments 1. F e a s i b i l i t y of an antimuonium experiment With t h i s information the p o s s i b i l i t y of attempting an antimuonium conversion experiment at TRIUMF can be c r i t i c a l l y examined. For one microampere of proton current on the production target, t y p i c a l surface 4 4 muon stop rates are of the order of 4 x 10 per sec, of which ^1.6 x 10 decay as muonium i n vacuum. If c o l l i s i o n s with the powder p a r t i c l e s have l i t t l e e f f e c t - on-the degeneracy of the M-M states, one can expect the conversion p r o b a b i l i t y of 2.5 x 10 to hold i n the absence of external f i e l d s , so that ^.4 conversions take place i n one second. Experimentally, t h i s i s not p r o h i b i t i v e l y small. There are two possible methods for detecting the conversion. The most sure i s the observation of a f a s t electron from negative muon decay, which requires magnetic analysis to d i f f e r e n t i a t e the electron from the vast positron background due to normal p o s i t i v e muon decays. Sol i d angle considerations imply the necessity of a rather large fancy device such as a spark chamber. A somewhat easier approach i s the search for muonic X-rays i n the target material. The p r o b a b i l i t y of breakup of antimuonium i s high i n dense materials, and should be high i n the powder environment. Taking into account a 10% detector e f f i c i e n c y f o r , say, the s i l i c o n muonic Ka X-ray at 400 keV, and a s o l i d angle of 5%, the o v e r a l l p r o b a b i l i t y of observing antimuonium i n t h i s way i s ^ 0.5%. This gives an expected event rate f o r an experiment of t h i s kind performed -3 at TRIUMF of ^ 2 x 10 per sec, or 'W events per hour. At 100 microamperes - 29 -proton current, t h i s i s 700 per hour. It i s obvious that background (such as positron a n n i h i l a t i o n radiation) i n the X-ray measurements w i l l be a problem. Hopefully, t h i s can be reduced to a t o l e r a b l e l e v e l : possibly the assumptions made are pessimistic ones. If not, the more complex, f a s t electron detection system w i l l be required. 2. D i f f u s i o n studies Another i n t e r e s t i n g , though very s p e c i f i c , u t i l i z a t i o n of the powder technique i s i n the i n v e s t i g a t i o n of the d i f f u s i o n rate of atomic muonium i n s i l i c a which i n t h i s instance may be considered as a l i g h t isotope of hydrogen. If a target of s u i t a b l e p a r t i c l e s i z e i s used (that i s , such that the average muonium d i f f u s i o n time to the p a r t i c l e surface i s about one microsecond), the time dependence of the asymmetry should have two components; one represents d i f f u s i o n , the other the (fast) r e l a x a t i o n due to the low pressure oxygen environment. Such experiments w i l l soon be undertaken at TRIUMF to elucidate the nature of the processes undergone by a muon i n the powder target, and to investigate the e f f e c t of surface i n t e r a c t i o n s on the muonium atom. 3. Chemistry of gases One of the major e f f o r t s of the TRIUMF MSR group i s the study of the chemical reactions of muonium atoms injec t e d i n t o a gas. The usualy method i s to stop the muons i n an argon moderator, which supplies electrons necessary to muonium formation. Trace amounts of reactants are added to t h i s moderator, and information on the reactions of muonium i s drawn from the decay spectrum shape (relaxation, phase, e t c . ) . However, since - 30 -the gas mixture of the ta r g e t i s at 1^ atmosphere, the muons stop over a very l a r g e volume, h i n d e r i n g p r e c i s e measurements. Moreover, the moderator i t s e l f may play some r o l e i n the r e a c t i o n s . Both of these problems might be l a r g e l y a l l e v i a t e d w i t h the use of a powdered moderator. This avenue i s c u r r e n t l y being explored at TRIUMF. - 31 -VI. Bibliography Amato, J . J . , P. Crane, V.W. Hughes, J.E. Rothberg, and P.A. Thompson, 1968, Phys. Rev. L e t t . 2_1, 1709. Bowen, T., K.R. Kendall, K.J. N i e l d , and A.E. P i f e r , 1973, Lawrence Berkeley Laboratory Internal Report. Brandt, W. , and R. Paulin, 1968, Phys. Rev. L e t t . 2l_, 193. Brewer, J.H., D.G. Fleming, K.M. Crowe, R.F. Johnson, B.D. Patterson, A.M. P o r t i s , F.N. Gygax, and A. Schenck, 1974, Physica Sc r i p t a 1_1, 144. Cabot Corporation, Cab-0-Sil Properties and functions, 1976. Danby, G., J-M. G a i l l a r d , K. Goulianos, L.M. Lederman, N. Mistry, M. Schwartz, and J . Steinberger, 1962, Phys. Rev. L e t t . 9., 36. Eichten, T., H. Deden, F.J. Hasert, W. Krenz, J . Von Krogh, D. Lanske, J. Morfin, H. Weerts, G. Bertrand-Coremans, J . Sacton, W. Van Doninck, P. V i l a i n , D.C. Cundy, D. Haidt, M. J a f f r e , G. Kalb-f l e i s c h , S. N a t a l i , P. Musset, J.B.M. Patti s o n , D.H. Perkins, A. P u l l i a , A. Rousset, W. Venus, H. Wachsmuth, V. Brisson, B. Degrange, M. Haguenauer, L. Kluberg, U. Nguyen-Khac, P. Petiau, E. B e l l o t t i , S. Bonetti, D. C a v a l l i , C. Conta, E. F i o r i n i , C. F r a n z i n e t t i , M. R o l l i e r , B. Aubert, L.M. Chounet, P. Heusse, A.M. Lutz, J.P. V i a l l e , F.W. Bullock, M.J. Esten, T.W. Jones, J . McKenzie, G. Myatt, and J.L. P i n f o l d , 1973, Physics L e t t e r s 46B, 281. Feinberg, G., and S. Weinberg, 1961, Phys. Rev. 123, 1439. Fleming, D.G., J.H. Brewer, D.M. Garner, A.E. P i f e r , T. Bowen, D.A. D e l i s e , and K.M. Crowe, 1976, J . Chem. Phys. 64, 1281. Garner, D.M., J.H. Brewer, G. Clark, D.G. Fleming, G.M. Marshall, and J.B. Warren, to be published. Gidley, D.W., P.W. Zitzewitz, K.A. Marko, and A. Rich, 1976, Phys. Rev. L e t t . 21, 729. Gurevich, I.I., I.G. Ivanter, E.A. Meleshko, B.A. N i k o l ' s k i i , V.S. Roganov, V.I. Selivanov, V.P. Smilga, B.V. Sokolov, and V.D. Shestakov, 1971, JETP 33, 253. Hofer, H., K. Borer, P. Jenni, P. LeCoultre, P.G. S e i l e r , and P. Wolff, 1972, CERN research proposal. Kendall, K.R., 1972, Ph.D. t h e s i s , U n i v e r s i t y of Arizona. - 32 -Miyashcheva, G.G., Yu.V. Obukhov, V.S. Roganov, and V.G. F i r s o v , 1968, JETP,26.» 298. Paulin, R. , and G. Ambrosino, 1968, J . de Phys. 29_, 263. P i f e r , A.E., T. Bowen, and K.R. Kendall, 1976, Nucl. Inst, and Meth. 135, 39. St e l d t , F.R., and P.G. Varlashkin, 1972, Phys. Rev. B5_, 4265. West, R.N., 1973, Advances i n Physics 22, 263. 

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