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MAGNETIC RESONANCE STUDIES OF ATOMIC HYDROGEN GAS AT LOW TEMPERATURES
W. Hardy, M. Morrow, R. Jochemsen, B. Statt, P. Kubik, R. Marsolais, A.
Berlinsky, A. Landesman
To cite this version:
W. Hardy, M. Morrow, R. Jochemsen, B. Statt, P. Kubik, et al.. MAGNETIC RESONANCE STUD-
IES OF ATOMIC HYDROGEN GAS AT LOW TEMPERATURES. Journal de Physique Colloques,
1980, 41 (C7), pp.C7-157-C7-160. �10.1051/jphyscol:1980725�. �jpa-00220162�
JOURNAL DE PHYSIQUE CoZloque C7, suppZe'ment au n o 7 , Tome 41, juiZZet 1980, Page C 7 - 1 5 7
MAGNETIC R E S O N A N C E S T U D I E S OF A T O M I C HYDROGEN G A S A T LOW T E M P E R A T U R E S W.N. Hardy, M. Morrow, R. Jochemsen, B.W. S t a t t , P.R. Kubik, R.M. Marsolais, A.J. B e r l i n s k y and A. ~andesman"
Department o f Physics, U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B.C. Canada V6T 1W5 ' s e r v i c e de Physique du S o l i d e e t de RQsonance Magne'tique, CEA, Orme des Merisiers,
B.P. n o 2, 91190 Gif-sur-Yvette, France.
Resume
.-
En u t i 1 is a n t une decharge p u l see 1 basse temperature dans une c e l l u l e s c e l l ee contenant H2 e t '+He nous sommes parvenus 3 accumuler du gaz d'hydrogene atomique sous f a i b l e d e n s i t e (Q 1012ato- mes p a r cm3) pour des durees de 1 'o r d r e d'une heure en champ magnetique nu1 e t 1 T = 1 K. Nous avons u t i l i s e l a resonance magnetique pulsee appliqu@e 2 l a t r a n s i t i o n h y p e r f i n e 1 1420 MHz pour @ t u d i e r un c e r t a i n nombre de p r o p r i 6 t e s du gaz t e l l e s que l e taux de recombinaison H+
H+
4He + H2+
4He, l e s taux de r e l a x a t i o n de 1 'hydrogene par @change de spin, l e c o e f f i c i e n t de d i f f u s i o n de H dans l e gaz de 4He e t l e deplacement de l a frequence h y p e r f i n e p a r l e gaz tampon de 4He en f o n c t i o n de l a pression. Nous discutons i c i l ' u t i l i s a t i o n des deplacements de l a frequence h y p e r f i n e comme sonde du p o t e n t i e l H-He e t comme moyen de determiner l 1 @ n e r g i e de l i a i s o n de l ' a t o m e H s u r l e l i q u i d e d'helium.Abstract.- Using a pulsed low temperature discharge i n a closed c e l l c o n t a i n i n g Hz and '+He, we have been a b l e t o s t o r e a low d e n s i t y (Q 1012 atoms/cc) gas o f atomic hydrogen f o r p e r i o d s o f order one hour i n zero magnetic f i e l d and T = 1 K. Pulsed magnetic resonance a t t h e 1420 MHz h y p e r f i n e t r a n - s i t i o n has been used t o study a number o f t h e p r o p e r t i e s o f t h e gas, i n c l u d i n g t h e recombination r a t e H
+
H+
'+He + Hz+
'+He, t h e hydrogen spin-exchange r e l a x a t i o n r a t e s , t h e d i f f u s i o n c o e f f i c i e n t o f H i n '+He gas and t h e pressure s h i f t o f t h e h y p e r f i n e frequency due t o t h e '+He buffer gas. Here we discuss t h e a p p l i c a t i o n o f h y p e r f i n e frequency s h i f t s as a probe o f t h e H-He p o t e n t i a l , and as a means f o r determining t h e b i n d i n g energy o f H on l i q u i d helium.Previous magnetic resonance s t u d i e s o f atomic H gas a t low temperatures were performed under non- e q u i l i b r i u m c o n d i t i o n s , where e i t h e r f l o w condi- tions") o r s t r o n g i n t e r a c t i o n s w i t h the (hydrogen coated) w a l l s ( 2 ) l i m i t e d the atom l i f e t i m e s t o a t most a few tens o f m i l l i s e c o n d s . ~ e c e n t l y ( ~ ) we have developed a technique t o produce and c o n f i n e a low d e n s i t y atomic H gas i n
zero
magneticfield
t h a t can be s t u d i e d v i a pulsed magnetic resonance a t t h e 1420 MHz (F=O + F=l
,
MF=O) h y p e r f i n e t r a n s - i t i o n f o r periods o f up t o an hour, A pulsed r . f . discharge i n a closed b u l b c o n t a i n i n g a small amount o f H2 and '+He creates atom d e n s i t i e s o f o r d e r 0.5 x 1013/cc t h a t decay r a t h e r s l o w l y due t o t h e i n e r t n e s s o f the 1 iq u i d 4He f i l m c o a t i n g t h e w a l l s . I t has been demonstrated t h a t t h e atoms recombine v i a the t h r e e body process H + H + '+He + H2 + 4He where the '+He i s an atom i n t h e r e l a t i v e l y dense 4He vapour(n
Q 1018/ccHe
near 1K). The r a t e constant was measured t o be
0.28 x 10-32 cm6/sec a t l K , which i s not very d i f f e r e n t from t h e room temperature value (4) 0.7 x 10-32 cmG/sec. I n a d d i t i o n , using spin echo techniques t h e cross-section, QD, f o r d i f f u s i o n o f H i n '+He has been determined t o be 20 k 1 0 A a t 1K. Glhen combined w i t h the atomic
s c a t t e r i n g data o f Toennies e t a1. ( 5 ) , t h i s value o f QD suggests t h a t a b e t t e r value f o r the w e l l depth o f t h e H-He p o t e n t i a l i s 0.6 meV ( a 7 ~ ) , somewhat deeper than t h a t obtained from t h e s c a t t e r i n g data alone. ble have a l s o made measure- ments o f t h e s p i n - l a t t i c e r e l a x a t i o n time T1 and shown i t t o be dominated by t h e e l e c t r o n spin- exchange process t h a t occurs i n H-H c o l l i s i o n s . The spin-exchange cross-section, d e f i n e d as l/Tl = o e x n H "here
i
i s the average r e l a t i v e0
v e l o c i t y o f t h e H atoms, was found t o be 0.6 A2 a t 1.1K which i s very c l o s e t o t h e value 0.55 0 A2
c a l c u l a t e d by B e r l i n s k y and Shizgal
.
(6)Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980725
JOURNAL DE P H Y S I Q U E
I n t h i s paper we w i l l concentrate on another aspect o f t h e resonance work, namely t h e s h i f t o f t h e h y p e r f i n e frequency due t o i n t e r a c t i o n s o f t h e H atoms w i t h each other, w i t h 4 ~ e atoms and w i t h t h e w a l l s . Fig. 1 shows t h e h y p e r f i n e f r e - quency as measured f r o m t h e f r e e i n d u c t i o n decay as a f u n c t i o n o f t h e 4He atom d e n s i t y . An accur- a t e l y l i n e a r s h i f t i s observed, even though t h e change i n '+He d e n s i t y i s obtained by v a r y i n g T ( f r o m about 1 t o 1.3K). The zero d e n s i t y i n t e r - c e p t i s 1,420,405,760.1 Hz which i s about 0.8 Hz a b o ~ e t h e f r e e atom v a l u e ( 7 ) when c o r r e c t e d f o r our r e s i d u a l f i e l d o f 53 mG. This discrepancy could be due t o a s l i g h t t e m ~ e r a t u r e dependence of t h e pressure s h i f t o r perhaps an e r r o r i n t h e c a l i b r a t i o n o f our frequency counter. The
r e s o l u t i o n o f t h e measurements was very high, of order 0.01 Hz i n f a v o r a b l e cases, because o f t h e l o n g f r e e i n d u c t i o n decay times (0.2 + 2 sec).
n ,
, (lo'* crn-3)
Fig. 1 : P l o t o f measured h y p e r f i n e frequency f minus a constant, fo = 1 420 405 000 Hz, versus t h e d e n s i t y o f t h e h e l i u m vapour nHe.
Except f o r s i t u a t i o n s where a f i e l d g r a d i e n t was a p p l i e d , t h e decay was dominated by r a d i a t i o n damping
,
i n which energy l o s t t o t h e resonator by t h e precessing spins causes t h e f r e e i n d u c t i o n s i g n a l t o damp out. A t l o n g times t h e decay i syQdW0
exponential w i t h
-
=- -
where y i s t h e7
e f f e c t i v e gyromagnetic r a t i o f o r t h e t r a n s i t i o n ( c l o s e t o y e i n t h e present case),
Q
t h e q u a l i t y f a c t o r o f t h e resonator, a t h e f i l l i n g f a c t o r and Mo the i n i t i a l magnetization. Thus one expects l / ~ = n H H ' which i s what i s observed. However, t h e r e i s another transverse r e l a x a t i o n process t h a t i s a l s o p r o p o r t i o n a l t o nH, namely s p i n exchange. By a n a l y z i n g t h e shape o f t h e decays we c o u l d show t h a t (1/T2)spin exchange c o n t r i - butes about 20% t o t h e decay. When we compare t h e T2 so obtained w i t h t h e p r e v i o u s l y measured TI, one gets rough agreement w i t h t h e t h e o r e t i c a l r e s u l t : T2 = 2T1 f o r spin-exchange r e l a x a t i o n .Spin-exchange c o l l i s i o n s a l s o produce a frequency
shift
o f t h e h y p e r f i n e resonance.Experimentally, no dependence o f t h e h y p e r f i n e
frequency on H atom d e n s i t y up t o c 1 x 1 0 ~ ~ / c m ~ was observed. B e r l i n s k y and Shizgal p r e d i c t (6 ) avSE x 0.045 Hz a t n H = 1012/cm3 and T=lK. With c a r e f u l temperature r e g u l a t i o n t o keep t h e &He vapor d e n s i t y and hence t h e '+He pressure s h i f t constant, such a s h i f t c o u l d perhaps be measured i n t h e present apparatus.
To summarize, our r e s u l t s f o r t h e h y p e r f i n e frequency a r e c o n s i s t e n t w i t h no w a l l o r spin- exchange s h i f t a t t h e l e v e l o f .L 0.1 Hz, b u t show a '+tie b u l k pressure s h i f t o f -11.83 x 1 0 - l 8 Hz cm3. The s h i f t i s o p p o s i t e i n s i g n and about 16 times s m a l l e r than t h e room temperature s h i f t a t e q u i v a l e n t densi t i e s ( 7 ) . T h i s i s r e a d i l y under- standable i n terms o f t h e t h e o r e t i c a l r e s u l t s o f Davison and ~ i e w ( * ) . The h y p e r f i n e s h i f t
c a l c u l a t e d as a f u n c t i o n o f separation o f the 4He and H atoms, i s found t o be n e g a t i v e a t l a r g e distances, and p o s i t i v e and r i s i n g r a p i d l y a t s h o r t e r distances. A t low temperatures t h e c o l l i s i o n s sample predominantly t h e negative, l o n g range p a r t o f t h e s h i f t . A c a l c u l a t i o n o f t h e zero temperature l i m i t o f t h e frequency s h i f t u s i n g t h e r e s u l t s o f Ref.(8) and a zero energy s c a t t e r i n g wave f u n c t i o n c a l c u l a t e d from a syn- t h e t i c p o t e n t i a l w i t h a w e l l depth o f 0.6 meV (9)
,
gave a pressure s h i f t o f about -25 x 1 0 - l 8
Hz
cm3, which i s i n t h e d i r e c t i o n one would expect. A complete c a l c u l a t i o n w i t h a p p r o p r i a t e thermal averaging w i l l be forthcoming. We have a l s o used Davison and L i e w ' s work(8) t o estimate t h e w a l l s h i f t f o r an H atom i n t h e ( s i n g l e ) bound s t a t e associated w i t h t h e l i q u i d '+He surface. Using a s i n g l e p a r t i c l e wave f u n c t i o n f o r t h e H atom p o s i t i o n , d e r i v e d from a simple model o f t h e '+He s u r f a c e ( l O ) , t h e s h i f t i s found t o be .L -30x103Hz.One can combine t h i s r e s u l t w i t h t h e experimental b u l k pressure s h i f t t o estimate t h e temperature dependence o f t h e h y p e r f i n e frequency o f atomic H gas c o n f i n e d i n a he1 ium coated bulb. F i g u r e 2 shows -Av vs 1/T f o r several values o f Eb, t h e b i n d i n g energy f o r t h e surface s t a t e .
There a r e two important i m p l i c a t i o n s o f t h e r e s u l t o f Fig. 2. F i r s t , w i t h r e g a r d t o t h e use o f atomic H confined a t low temperatures as t h e b a s i s f o r an improved frequency standard, one can see t h a t t h e b e s t p l a c e t o operate such a system i s a t t h e minimum o f t h e pressure s h i f t . To t h e e x t e n t t h a t t h e p o s i t i o n o f t h e minimum changes very l i t t l e w i t h Eb, t h e optimal temperature o f o p e r a t i o n can already be estimated t o be about 0.5K, and t h e s h i f t w i l l be o f o r d e r 10
mHz
f o r a 10 cm diameter bulb. To o b t a i n a reproduce- a b i l i t y o f 1 i nlo1'+,
one would need t o know t h e surface area t o % 0.14%.Fig. 2 : Predicted h y p e r f i n e frequency s h i f t ver- sus temperature f o r
H
gas c o n f i n e d i n a '+He coated b u l b o f 10 cm diameter. The h i g h tempera- t u r e p a r t (T 2 1K) i s d e r i v e d d i r e c t l y from experiment, whereas t h e low temperature p a r ti n v o l v e s a t h e o r e t i c a l estimate o f the w a l l s h i f t i n t h e bound surface s t a t e .
The second i m p l i c a t i o n i s t h a t a measurement o f t h e low temperature behaviour o f A V w i l l d i r e c t l y y i e l d t h e value o f Eb, a q u a n t i t y o f c r u c i a l importance i n spin-aligned H experiments.
I f t h e t o t a l surface area o f t h e helium surface i s known, one can a l s o determine t h e w a l l s h i f t associated w i t h t h e surface s t a t e . Together these numbers should p r o v i d e a r a t h e r s t r i n g e n t t e s t o f t h e t h e o r i e s f o r t h e bound s t a t e .
The present work demonstrates t h e h i g h sensi- t i v i t y and v e r s a t i l i t y o f z e r o f i e l d magnetic resonance f o r s t u d i e s o f atomic H gas. I n p a r t i - c u l a r , i t i s an i d e a l probe f o r measuring t h e i n t e r a c t i o n of H atoms w i t h a l i q u i d helium s u r - face. The methods can be extended t o D w i t h some
JOURNAL DE PHYSIQUE
l o s s i n s e n s i t i v i t y ( ~ ~ ' 3 2 7 MHz), and t o T w i t h some i n c r e a s e i n danger. O f c o u r s e t h e most i n t e r e s t i n g r e s u l t s have t o a w a i t a l o w e r temper- a t u r e c r y o s t a t , which i s i n p r e p a r a t i o n . Lower temperatures w i l l a l s o a l l o w a s t u d y o f t h e i n t e r - a c t i o n s between t h e hydrogens and 3He.
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The p o t e n t i a l i s a c o m b i n a t i o n o f an expon- e n t i a l r e p u l s i v e p a r t (R. Gengenbach, Ch.
Hahn and J.P. Toennies, Phys. Rev.
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3063 (1976)), smoothly j o i n e d t o g e t h e r b y a Lennard-Jones w e l l w i t h a d e p t h o f 0.6 meV.T h i s a p p r o x i m a t i o n t r e a t s t h e h e l i u m as a h y p o t h e t i c a l s t a t i c s o l i d a t t h e d e n s i t y o f t h e l i q u i d .
