THE STABILIZATION OF ATOMIC HYDROGEN : A NEW BOSE GAS

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NEW BOSE GAS

I. Silvera, J. Walraven

To cite this version:

I. Silvera, J. Walraven. THE STABILIZATION OF ATOMIC HYDROGEN : A NEW BOSE GAS.

Journal de Physique Colloques, 1980, 41 (C7), pp.C7-137-C7-146. �10.1051/jphyscol:1980722�. �jpa- 00220159�

JOURNAL DE PHYSIQUE CoZloque C 7 , suppl6ment au n o 7 , Tome 41, juiZZet 1980, page C7-137

THE STABILIZATION OF ATOMIC HYDROGEN : A NEW BOSE GAS

I.F. S i l v e r a and J.T.M. Walraven

Natumkundig Laboratorim der U n i v e r s i t e i t van Amsterdam, 2018 XE Amsterdam, The Netherlands

R@sume.- Dans l e s circonstances h a b i t u e l l e s , un gaz atomique d'hydrogene (H) e s t t r 6 s i n s t a b l e c a r il tend former par recombinaison des mol6cules dohydrogene (Hz). NOUS avons r e u s s i a s t a b i l i s e r un gaz d1hydrog@ne a f o r t e p o l a r i s a t i o n de s p i n (H+) a T = 300 mK dans des champsmagn6tiques a t t e i - gnant 10 Tesla, dans une c e l l u l e -3 p a r o i s recouvertes d l h @ l i u m s u p e r l f u i d e . Nous avons obtenu des densites atomiques de 1016 ~ m - ~ , e t observe que l e gaz H a une duree de v i e surprenante par sa longueur, mSme en champ magn@tique n u l . Nos r e s u l t a t s tendent a i n d i q u e r que Hs r e s t e sous forme gazeuse, sans se l i q u e f i e r ou se condenser s u r l e s surfaces de facon appreciable. On d i s c u t e l e s aspects cruciaux des techniques exp@rimentales pour s t a b i l i s e r Hs, a i n s i que quelques unes des p r o p r i @ t e s observees ou attendues de ce nouveau gaz de Bose.

Abstract.- Under normal circumstances a gas o f atomic hydrogen (H) i s h i g h l y u n s t a b l e w i t h respect t o recombination t o molecular hydrogen, H2. We have succeeded i n s t a b i l i z i n g a gas o f s p i n p o l a r i s e d hydrogen (H+) a t T = 300 mK i n magnetic f i e l d s up t o 10 Tesla i n a s u p e r f l u i d helium coated c e l l . D e n s i t i e s of a t l e a s t 1016atoms/cc have a l r e a d y been achieved. H i s found t o have a s u r p r i s i n g l y l o n g l i f e even i n zero magnetic f i e l d . Evidence p o i n t s t o H+ remaining i n t h e gaseous form and n o t l i q u i f y i n g o r condensing o u t on t h e surfaces t o any l a r g e e x t e n t . The c r u c i a l experimental t e c h n i - ques used t o s t a b i l i z e H+ w i l l be discussed as w e l l as some o f t h e observed p r o p e r t i e s and expecta- t i o n s o f t h i s new Bose gas.

I n t h e p a s t h a l f c e n t u r y low temperature physi- condensation and l i q u i f i e s . Below 2.17 K i t c i s t s have been f a s c i n a t e d by t h e u n r a v e l l i n g and becomes a s u p e r f l u i d . Since t h e e a r l y work o f e l u c i d a t i o n o f t h e many marvelous p r o p e r t i e s o f London / 4 / i t has been b e l i e v e d t h a t t h i s super- t h e quantum f l u i d s 4He and 3 H ~ . t h i s paper we f l u i d i t y i s i n t i m a t e l y r e l a t e d w i t h t h e pheno- s h a l l discuss o u r r e c e n t experiments i n making menon of Bose-Einstein condensation (BEC), i . e . new quantum f l u i d s : atomic hydrogen and t h e macroscopic p o p u l a t i o n o f t h e ground s t a t e deuterium /1 - 3/.

F i r s t many o f the p r o s p e c t i v e e x c i t i n g

a t a f i n i t e temperature. This i s most e a s i l y demonstrated f o r t h e weakly i n t e r a c t i n g Bose p r o p e r t i e s of these gases w i l l be b r i e f l y discussed. gas. However f o r helium a s e r i o u s problem We s h a l l then describe t h e techniques and d i f f i c u l t - a r i s e s i n t h e t h e o r e t i c a l analyses. I n t h e i e s i n v o l v e d i n producing t h e gases,and f i n a l l y l i q u i d s t a t e t h e mean He

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degeneracy. Although most o f t h e d i s c u s s i o n w i l l helium i s a s t r o n g l y i n t e r a c t i n g boson s u p e r f l u i d , be devoted t o atomic hydrogen, where d i f f e r e n c e s w i t h i n h e r e n t t h e o r e t i c a l d i f f i c u l t i e s . This occur, a p p r o p r i a t e comments w i l l be made about problem probably w i l l n o t e x i s t f o r a t o m i c

deuterium. hydrogen.

Since t h e m a j o r i t y o f t h e p a r t i c i p a n t s o f Atomic hydrogen (H) has been s t a b i l i z e d i n a t h i s conference come from a he1 ium background s p e c i a l s t a t e c a l l e d s p i n p o l a r i z e d hydrogen (H+) i t i s useful t o make some comparisons. /5/. I n t h i s s t a t e a l l hydrogen atoms i n t e r a c t

3

+

upon c o o l i n g a gas of 4 ~ e a t 1 atmosphel'e p a i r w i s e on t h e almost r e p u l s i v e x u p o t e n t i a l , pressure a t 4.2 K, i t becomes u n s t a b l e t o shown i n f i g . 1, and thus do n o t form bound s t a t e s .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980722

As discussed by Nosanow /6/, due t o t h e weak i n t e r - a c t i o n s and l i g h t mass, Hs w i l l n o t form a many- body bound s t a t e a t T = 0 K, i . e . as a r e s u l t of t h e l a r g e zero-point energy HI remains a gas t o T = 0 K. Hydrogen i s p r e d i c t e d t o have a s o l i d phase f o r pressures P 2 50 b a r . As a consequence, i g n o r i n g t h e problems o f recombination t o Hz, a t T % 0 K t h e d e n s i t y o f H+ can be v a r i e d almost a r b i t r a r i l y , so t h a t a t low d e n s i t i e s i t w i l l behave as a weakly i n t e r a c t i n g gas.

Since H has an e l e c t r o n s p i n o f 3 and a nuclear s p i n o f 3 i t i s a s p i n 1 or 0 p a r t i c l e , i . e . a com- p o s i t e boson. H+ w i l l thus enable a study o f t h e weakly i n t e r a c t i n g Bose gas and t h e r e l a t i o n between BEC and s u p e r f l u i d i t y . Since D+ has an e l e c t r o n s p i n

5 and n u c l e a r s p i n 1, i t i s a composite fermion. I t i s expected t h a t t h i s w i l l p r o v i d e an i d e a l system f o r t h e study o f s u p e r f l u i d i t y due t o f e r m i o n - p a i r i n g /7/. Since t h e mass o f D i s t w i c e t h a t o f H i t may be a l i q u i d a t T = 0 K, although t h e o r e t i c a l pre- d i c t i o n s have some u n c e r t a i n t y .

Dynamical p r o p e r t i e s o f H+ i n t h e Bose con- densation phase a r e p r e d i c t e d t o d i s p l a y many new phenomena. B e r l i n s k y /8/ has p r e d i c t e d an i n t e r e s t - i n g d e n s i t y - s p i n e x c i t a t i o n spectrum and S i g g i a and Ruckenstein /9/ have c o n j e c t u r e d t h a t t h e slow n u c l e a r r e l a x a t i o n r a t e enables t h e occurrence of two Bose condensates,distinguished by t h e n u c l e a r s p i n s t a t e s . They p r e d i c t t h a t coherent n u c l e a r r e l a x a t i o n occurs and may be observed as spontaneous emission o f rf r a d i a t i o n . S p a t i a l l o c a l i z a t i o n o f t h e condensate i n a magnetic f i e l d g r a d i e n t has been suggested as a c h a r a c t e r i s t i c o f t h e Bose con- densed gas a t low d e n s i t i e s where i n t e r a c t i o n s a r e unimportant /lo/. Some p o s s i b l e p r a c t i c a l a p p l i c a - t i o n s o f HS a r e as an improved maser f o r t i m e and frequency standards, a cryogenic r e f r i g e r a n t , and as an e x o t i c form o f chemical f u e l used as a r o c k e t p r o p e l l a n t . Although t h i s l a t t e r a p p l i c a t i o n seems somewhat remote a t present, one can imagine t h i s as a f u e l f o r f u t u r e space t r a v e l , w i t h space- ships g a t h e r i n g t h e i r f u e l w i t h huge c o l l e c t o r s as t h e y t r a v e l through i n t r a g a l a c t i c clouds of H.

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5

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_{- 1}

The s t a b l e form o f a gas o f hydrogen atoms i s w i t h a l l atoms p a i r w i s e bound i n t h e molecular form. T h i s i s t h e lowest energy s t a t e f o r t h e 1 ~ ' p o t e n t i a l of

9

f i g . 1. A gas o f H+ can g e t t o t h i s s t a t e by three- body recombination processes, H+ + Hs + X +

$

where X i s a t h i r d body, i n c l u d i n g surfaces, and t h e

*

I

- - = dn 3 K~ n + KK; n:

distance (10-~crn) d t

where Kv i s t h e volume recombination r a t e , K4 t h e Fig. 1 The i n t e r a t o m i c i n t e r a c t i o n p o t e n t i a l s f o r s u r f a c e r a t e and n_ t h e s u r f a c e coverage w i t h 6 = 1

1

+

s i n g l e t (dashed curve) and t h e t r i p l e t xu

9 o r 2. Since i n general ns ^2. n, we can w r i t e

( s o l i d curve) hydrogen as c a l c u l a t e d by Kolos and

Wolniewicz. The e f f e c t o f a magnet f i e l d i s shown K' n = K n. Kv i s known f o r t h e process

s s S

i n t h e i n s e t on a s c a l e which i s expanded by H + H

+

5

-

approximately 2000.

Kv = 1.2 x cm6/atom-s Dl/. w i t h a r a t e about

1/5 t h i s at about 1 K /12/. A t room temperature a d e n s i t y o f n % 1016 a t / c c would have a l i f e t i m e o f about 1 sec. The surface term i s l e s s w e l l known.

A t room temperature H can have many thousands o f bounces o f f o f a t e f l o n s u r f a c e b e f o r e recombining.

Metal surfaces have a p r o b a b i l i t y o f o r d e r one f o r recombination upon c o l l i s i o n . Since H w i l l have l o n g range a t t r a c t i v e i n t e r a c t i o n s w i t h a l l surfaces, a t temperatures low w i t h r e s p e c t t o t h e s u r f a c e a d s o r p t i o n energy, H w i l l condense, r a p i d l y b u i l d i n g up t h e s u r f a c e coverage and recombining due t o t h e second term i n eq. (1). I n s t a b i l i z i n g H+, t h i s i s t h e most i m p o r t a n t term t o c o n t r o l . With "normal" surfaces a t low temperatures t h e l i f e - t i m e o f a gas o f H+ i s o f t h e o r d e r o f tens o f microseconds. We have found t h a t by c o v e r i n g a l l surfaces w i t h a f i l m o f He, s u r f a c e recombination 4 i s s t r o n g l y suppressed, s i n c e €,/kg i s probably l e s s t h a n 1K /13/. The r a p i d recombination r a t e on helium f r e e surfaces provided us w i t h a s e n s i t i v e technique f o r d e t e c t i n g t h e presence o f t h e H+, as s h a l l be described.

Experimental S t a b i l i z a t i o n

of IF

Our experimental work on atomic hydrogen s t a r t e d i n 1972. A t t h a t t i m e we b e l i e v e d t h a t i t would be d i f f i c u l t t o c o l l e c t and c o n f i n e l a r g e q u a n t i t i e s o f s t a b l e atomic hydrogen and such s t u d i e s m i g h t b e s t be c a r r i e d o u t on surfaces. Atomic beams of H c o u l d be made w i t h a x i a l f l u x e s o f ^% 10'~/cm /sec 2 which corresponds t o about one monolayer/sec i f deposited on a substrate. Clean, we1 1 character- i z e d s u b s t r a t e surfaces o f closed s h e l l atoms o r molecules (Ar, Hz, N2 e t c . )

-

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be deposited o r grown i n s i t u o . I n t h i s case t h e hydrogen would be physisorbed and remain as e l e c t r i c a l l y n e u t r a l atoms. Because H i s a corn- posite boson, if i t was i n a s u f f i c i e n t l y mobile s t a t e on t h e surface, one c o u l d study t h e p o s s i b l e s u p e r f l u i d i t y of H f i l m s . To prevent t h e surface

recombination t h e deposited H would have t o be s p i n - p o l a r i z e d so t h a t atoms would interact via the non-binding 31: p o t e n t i a l o f f i g . 1. An apparatus was b u i l t t o p o l a r i z e a beam o f hydrogen and d 6 p o s i t t h i s H+ on a c o l d s u b s t r a t e (T ? 2 K) i n a moderate magnetic f i e l d . A f t e r a s u b s t a n t i a l b u i l d - u p p e r i o d experiments were performed, w i t h v e r y discouraging r e s u l t s . The H+ a p p a r e n t l y r a p i d l y d e p o l a r i z e d on t h e s u r f a c e followed by recombination o r d e s o r p t i o n /14/. A f t e r some c o n s i d e r a t i o n /15/ i t was decided t h a t t h e temperature and magnetic f i e l d were i n - a p p r o p r i a t e f o r s t a b i l i z i n g H. Furthermore we developed a r a t h e r negative p r o p e n s i t y toward t h e s u r f a c e due t o i t s c o n t i n u a l presence as t h e t h i r d body i n recombination processes. We decided t o l a y down t h e attempt t o s t a b i l i z e H on surfaces and b u i l d an apparatus f o r s t a b i l i z a t i o n o f a t h r e e dimensional gas. We f e l t t h a t t h e recombination processes c o u l d be b e t t e r c o n t r o l l e d i f we c o u l d prevent t h e H+ from condensing on t h e surfaces. A d e s c r i p t i o n o f t h i s approach and apparatus f o l l o w s .

I n o r d e r t o s t a b i l i z e H+

,

Experimental Techniques

The gas o f Hs was s t a b i l i z e d i n t h e apparatus shown i n f i g . 2. A hydrogen s t a b i l i z a t i o n c e l l (HSC) s i t s i n a solenoidal magnetic f i e l d o f maximum value 11 Tesla. The HSC can be cooled t o % 270 mK by a He evaporation r e f r i g e r a t o r . Atomic hydrogen 3 a r i s i n g from a room temperature microwave discharge i s guided i n t o t h e cryogenic environment by tef Ion l i n e d t u b i n g and, b e f o r e e n t e r i n g the HSC, i s cooled t o ^Q 4.2 K by c o n t a c t w i t h t h e H2 covered w a l l s o f a copper accomodator /16/.

Teflon

I ^- . .

_:

Room Ternpemture H Source

Fig. 2 The low temperature p a r t o f t h e apparatus used f o b s t a b i l i z i n g atomic hydrogen.

The s e p a r a t i o n o f t h e e l e c t r o n spin-up and s p i n - down s t a t e s i s performed by t h e magnetic f i e l d g r a d i e n t t h a t e x i s t s a t t h e entrance o f the sole- noid. The g r a d i e n t f i e l d e x e r t s a f o r c e on t h e atomic magnetic moments so t h a t t h e atoms in spin-up s t a t e s are r e p e l l e d and t h e spin-down s t a t e s a r e a t t r a c t e d i n t o t h e f i e l d center. Since t h e atoms a r e confined b y t h e guide tube, t h e spin-up atoms e i t h e r recombine on t h e w a l l s o r r e l a x t o spin-down and a r e drawn i n t o t h e f i e l d . The atoms i n t h e HSC come i n t o thermodynamic equi- l i b r i u m w i t h t h e c e l l w a l l s and a r e confined t o t h e f i e l d c e n t e r by t h e magnetic g r a d i e n t /lo/.

The atoms a r e prevented from condensing on t h e surfaces by covering a l l w a l l s w i t h a s a t u r a t e d f i l m o f He which i s a s u p e r f l u i d a t these low 4 temperatures. A l t h o u g h ' t h i s prevents w a l l recom- b i n a t i o n i t leads t o a s e r i o u s cryogenic problem:

due t o t h e f o u n t a i n e f f e c t , t h e f i l m f l o w s towards warmer regions, i n t h i s case t h e accomodator: The heat f l u x from t h e warmer regions o f t h e guide tube evaporates t h e f i l m ; a pressure g r a d i e n t d r i v e s t h e He gas back t o t h e c o l d e r HSC where i t con- 4 denses t o l i b e r a t e i t s heat o f condensation and warm t h e c e l l . To suppress t h i s h e a t i n g we b u i l t an i n t z r m e d i a t e He r e f r i g e r a t i o n stage c a l l e d a HEVAC. 3 The f l u x i n g 4 ~ e vapors condense o u t on t h e HEVAC;

r e s i d u a l f l u x i n g vapors a r e o f such l o w d e n s i t y t h a t they do n o t present a serious cryogenic problem.

The HEVAC which stands f o r h e l i u m vapor com- pressor serves a second r o l e . It i s a c t u a l l y a m i n i a t u r e vapor d i f f u s i o n pump, t h e f l u x i n g 4 ~ e

i m p a r t i n g i t s momentum t o t h e H gas and c o n f i n i n g i t t o t h e c e l l . It operates w i t h a compression cH ( l / c i s t h e p r o b a b i l i t y f o r a p a r t i c l e e n t e r i n g t h e

H

HEVAC t o escape) o f approximately 50.

With t h i s system t h e HSC can be loaded w i t h a gas o f H+ t h a t i s s t a b l e and c o n f i n e d f o r l o n g

periods o f time. The presence o f t h e gas was detected w i t h s p e c i a l l y developed bolometer d e t e c t - o r s made o f carbon composition from a Speer r e s i s t o r f o r which t h e r e s i s t a n c e drops r a p i d l y w i t h i n c r e a - s i n g temperature. Two such bolometers a r e suspended i n t h e HSC by f i n e w i r e s as shown i n f i g . 2. The idea i s t o s e l e c t i v e l y cause t h e H+ t o recombine and determine i t s presence by measuring t h e warming due t o t h e l i b e r a t e d recombination energy. Under normal c o n d i t i o n s the bolometers a r e covered by t h e f i l m o f He so t h a t t h e y a r e i n e r t w i t h respect t o 4 t h e HG gas. By passing a s u f f i c i e n t l y l a r g e c u r r e n t through a bolometer, t h e ohmic h e a t i n g w i l l cause t h e f i l m t o evaporate more r a p i d l y than i t can be replenished along t h e wires. When t h e surface i s c l e a n o f He, t h e H+ condenses and r a p i d l y recom- 4 bines. The surface o f t h e bolometer i s probably covered w i t h H2 which has an adsorption energy for H o f 38 K /17/, o r o t h e r molecules (02, N2, H20 e t c . ) which have even stronger a d s o r p t i o n energies. We expect t h a t f o r a gas o f H+ w i t h kT there w i l l be a p r o b a b i l i t y o f about 1 t h a t an atom t h a t c o l - l i d e s w i t h t h e surface w i l l s t i c k .

To determine t h e t i m e constant f o r recombina- t i o n o f t h e HG a f t e r " t r i g g e r i n g " by h e a t i n g t h e bolometer, we assume t h a t t h e r a t e l i m i t i n g process i s t h e thermal e f f u s i o n o f atoms t o t h e bolometer surface o f area Ab. Then s o l v i n g t h e equation dN/dt = $ nyAb where N i s t h e t o t a l number of atoms and 7 t h e average v e l o c i t y g i v e s N = N , e ~ p ( - t / ~ ) w i t h r = 4 Veff/vAb where Veff i s t h e e f f e c t i v e volume o f t h e gas H+ (16). T y p i c a l values o f

,

10

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When t h e atoms recombine t o Hz on t h e bolometer surface o n l y a f r a c t i o n o f t h e recombination energy i s d e l i v e r e d t o t h e bolometer /14/. Most l i k e l y t h e molecules desorb i n a h i g h l y e x c i t e d v i b r a t i o n - r o t a t i o n s t a t e , a l s o desorbing ground s t a t e H2

molecules from t h e f i r s t l a y e r s o f t h e bolometer under t h e helium. T h i s energy i s mostly adsorbed i n t h e w a l l s o f t h e c e l l ; p a r t o f i t i s probably blown o u t o f t h e HSC through t h e HEVAC. Although t h e bolometer i s an extremely s e n s i t i v e HG detector and can probably d e t e c t as l i t t l e as 10 atoms, 8 i t i s a h i g h l y n o n - l i n e a r d e t e c t o r , l e s s s u i t e d f o r d e n s i t y measurements o f the H+. To measure t h e d e n s i t y we a c t u a l l y measure t h e temperature r i s e of t h e HSC w i t h a (Speer) thermometer attached t o i t s - w a l l . This has a s l i g h t l y slower response than t h e bolometer and i s l e s s s e n s i t i v e , b u t w e l l matched t o our d e n s i t i e s . It can be c a l i b r a t e d w i t h e l e c t r i c a l heat pulses. It has t h e r a t h e r n i c e f e a t u r e t h a t i t s response, as monitored by t h e r e s i s t a n c e change o f t h e Speer r e s i s t o r , i s l i n e a r w i t h d e n s i t y . There a r e two shortcomings t o t h i s technique. F i r s t i t o n l y provides a lower bound t o t h e d e n s i t y since some o f the atoms o r a v a i l a b l e energy can escape o u t o f an open ended system. We s h a l l see the problem t h i s can c r e a t e a t h i g h e r d e n s i t i e s l a t e r . Second, i t i s a d e s t r u c t i v e tech- nique

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be a v i t a l l i n k i n t h e i n i t i a l s t a b i l i z a t i o n o f Hc. by being s t r u c k by recombined molecules t h a t desorb I t w i l l e v e n t u a l l y be replaced by n o n - d e s t r u c t i v e from t h e primary bolometer.

d e t e c t o r s f o r s t u d i e s a t h i g h d e n s i t i e s , b u t w i l l remain as an easy to operate diagnostic

t o o l .

When t r i g g e r e d t h e shape o f t h e h e a t i n g pulses

-

r

a r e o f some i n t e r e s t . I n f i g . 3 we show t h e response o f t h e c e l l thermometer f o r a low d e n s i t y o f H+.

2 _-

e %

P

-

1 . 8 1.2

.

T I M E ( S E C O N D S )

H SE Thermometer

f

-

I'

B = 6.0 tesla T = 2 7 0 m k

i f

Untrlggered Bolometer

HSC THERMOMETER

n

Fig. 3 The response o f t h e HSC thermometer and the bolometer used t o t r i g g e r t h e recombination o f hydrogen. The bolometer i s heated w i t h a c u r r e n t square wave. The v o l t a g e s a r e p r o p o r t i o n a l t o t h e resistances. Long a f t e r t h e H+ i s burned, t h e b o l o - meter approaches a lower v a l u e o f r e s i s t a n c e than b e f o r e t h e t r i g g e r i n g because t h e helium f i l m i s broken. The voltage of the thermometer has a zero of £ s e t .

1 I I I I

10 _{20 30}

1

Time (seconds)

n

I- +.,

m m

-

W (3 a

I- -I

> 0

I I I I

BOLOMETER

F i g . 4 Voltage responses o f t h e HSC thermometer and t h e secondary ( u n t r i g g e r e d ) bolometer. Due t o ohmic h e a t i n g a f t e r t h e t r i g g e r y n g , t h e HSC v o l t a g e remains low.

I I

Evidence f o r the gaseous n a t u r e comes from t h e ( n o n - q u a n t i t a t i v e ) thermal c o n d u c t i v i t y

I I

measurements. Furthermore time constants a r e i n

_

F i n a l l y experiments were performed i n which bolometers 1 and 2 were r a p i d l y s e q u e n t i a l l y heated.

Only t h e f i r s t bolometer heated r e s u l t e d i n a recombination s i g n a l . I f t h e H+ were predominantly i n an adsorbed s t a t e we would expect s i g n a l s from This was recorded on a f a s t response (100 Hz) s t r i p

both bolometers.

c h a r t recorder. I n f i g . 4 we show t h e response (on

a slow recorder a 5 Hz response) o f t h e secondary Measurements bolometer i n t h e c e l l , a f t e r t r i g g e r i n g by t h e o t h e r

I n f i g . 5 we show t h e r e s u l t s o f t h e f i r s t measure- bolometer. This bolometer r e c e i v e s i t s heat p r i m a r i l y

ments on H + / I / . At t h e time o f these observations I n t h e same f i g u r e we show t h e decay o f t h e most important questions were: c o u l d a gas o f H + t h e d e n s i t y i n zero magnetic f i e l d . This decay r a t e be s t a b i l i z e d and f o r how l o n g . I n these experiments c o u l d be f i t t o an exponential w i t h a t i m e constant t h e magnetic f i e l d was s e t t o 7 Tesla and the tempe- o f T 2 1.5 sec. T h i s decay i s a t t r i b u t e d t o thermal r a t u r e was 270 mK. The c e l l was f i l l e d f o r a c e r t a i n d i f f u s i o n o f t h e gas o u t o f t h e HSC. To c a l c u l a t e p e r i o d o f t i m e a t a f i x e d f i l l i n g f l u x and t h e d i s - t h i s t i m e constant we can again appeal t o simple charge was t u r n e d o f f . A f t e r w a i t i n g a s h o r t p e r i o d k i n e t i c theory,

of time, recombination o f t h e H was t r i g g e r e d . T h i s

-

-

n v ~

C.. ( 2 )

p e r i o d was c o n t i n u a l l y doubled u n t i l a w a i t t i m e o f n

Here K i s t h e Clausing f a c t o r o f t h e tube o f area 532 sec. A f t e r each t r i g g e r i n g t h e s i g n a l was unat-

A l e a d i n g from t h e HSC t o t h e HEVAC, n t h e d e n s i t y tenuated, t o w i t h i n experimental e r r o r . The con-

and cH t h e HEVAC compression. This leads t o a c l u s i o n t h a t c o u l d be drawn was t h a t t h e l i f e t i m e

time constant was much g r e a t e r than 532 sec. D e n s i t i e s o f o r d e r

r = 4 cHv/kVA 1014 a t / c c were s t a b i l i z e d , w i t h no e f f o r t exerted

a t t h a t time t o increase t h i s number. The r e s u l t s By measuring ^T one can determine cH 50 since a l l showed t h a t t h e main s t a b i l i z a t i o n was due t o sup- o t h e r f a c t o r s a r e reasonably w e l l known. When t h e pression o f surface recombination /19/ as t h e ex- magnetic f i e l d i s t u r n e d on we can replace pected volume recombination r a t e s would n o t be n(BH) = n(Bo)/cm which d e f i n e s t h e magnetic com- l i m i t i n g a t these d e n s i t i e s . pression c = expIu(Bo - BH)/kT} where Bois t h e

m

f i e l d s .

F i g . 5 The decay r a t e o f H f o r T = 270 mK w i t h mag- I n these measurements i t was shown t h a t a t n e t i c f i e l d B = 7 Tesfa and 0. ts i s t h e elapsed time

a f t e r l o a d i n g t h e c e l l t o d e n s i t y no. low d e n s i t i e s t h e c e l l loads up t o a s a t u r a t i o n f i e l d i n t h e HSC and BH t h a t i n t h e HEVAC / l o / .

With d e n s i t y no a t Bo we d e f i n e t h e e f f e c t i v e volume as veff = N/no. This then leads t o an expression f o r t h e t i m e constant i n magnetic f i e l d

= 4 c H cm v e f f / ~ V ~

m (4)

More r e c e n t l y we have c a r r i e d o u t more exten- s i v e measurements on t h e time dependence and t h e magnetic equation o f s t a t e o f H+. Samples o f H+

have been maintained f o r as long as 47 minutes b e f o r e t r i g g e r i n g . The decay i n a magnetic f i e l d was s t u d i e d a t d e n s i t i e s ~3 xl~14 a t / c c and found t o be exponential i n accordance w i t h t h e thermal d i f f u s i o n mechanism. The dependence o f eq. ( 4 ) r / /

I I

B=7Tesla --7 -- DECAY RATE O F H

> -

k -

-

w -

- P' nlneexp(-tsll.5)

z W

0 - B=O

-

- - - -

n W

'LJ -I

2

=

a

0 z - -

a b

-

0.001- ⁰ 1 1 2 I 3 I 1, I 5 I 6 7 I I 8 I

,

^v

TIME, t, (seconds) i s shown i n f i g . (68) f o r two d i f f e r e n t magnetic

I

- - -

-

- - -

-

= _-

- -

-

-

;

-

- -

4 TESLA. 0.39 K , o 8 TESLA, 0.37 K

no = IO~LATOMS~C

;?

observed, w i t h t h e time f o r t h e d e n s i t y t o h a l v e being o f order 20 minutes. A t these d e n s i t i e s t h e magnetic f i e l d i s c e r t a i n l y p l a y i n g an important r o l e i n reducing volume recombination ( i n zero f i e l d t h e time constant would be o f o r d e r 1 sec).

However t h e reduced l i f e t i m e s may be an i n d i c a t i o n o f t h e i n c r e a s i n g importance o f three-body recom- b i n a t i o n processes.

As a f i n a l p o i n t we discuss some i n t e r e s t i n g

2

1

I I 1 1 ^I I ^I

-

@

L TESLA. 0.39 K f o r a h i g h d e n s i t y t r i g g e r . The bolometer i s t r i g g e r e d by e x c i t i n g i t w i t h a square wave c u r r e n t

c 0 source; t h e thermometer i s powered w i t h a low l e v e l

0 100 200 300 LOO

TIME [SECJ ac c u r r e n t source, t h e v o l t a g e drops, p r o p o r t i o n a l Fig. 6 A. The d e n s i t y o f H as a f u n c t i o n o f t i m e t o t h e r e s i s t a n c e a r e monitored. The simple t h e o r y d u r i n g f i l l i n g o f t h e c e l l a t constant f l u x , f i e l d presented e a r l i e r p r e d i c t s a bolometer t i m e con- and temperature.

s t a n t independent o f d e n s i t y and the cell to

B. The decay o f i n i t i a l d e n s i t y no a t constant f i e l d

and temperature. ^{heat t o} higher temperatures for higher densities.

value t h a t can be r o u g h l y described by

where n e f f ( B 1 ) i s some e f f e c t i v e d e n s i t y d u r i n g loading, probably i n t h e t h r o a t o f t h e HEVAC. This i s shown i n f i g . (6A). A t h i g h e r d e n s i t i e s t h e r e a r e d e v i a t i o n s from t h i s such t h a t d e n s i t i e s lower than those p r e d i c t e d by eq. (5) a r e found. It i s n o t y e t c l e a r i f t h i s i s a fundamental l i m i t a t i o n o r a p r o - blem a r i s i n g from t h e c e l l design.

The h i g h e s t d e n s i t i e s we have achieved a r e

n > 1016 a t / c c a t 10.5 Tesla and T 2 500 mK. The _{3 2 1 0}

--

the r e f r i g e r a t i o n . As t h e f i l l i n g f l u x was increased F i g . 7 The response o f t h e HSC thermometer and t h e c e l l would warm up which reduces t h e compression bolometer f o r a h i g h density, n 2 1016 atoms/cc.

The bolometer i s heated w i t h a c u r r e n t square

(see eq. 5). We were forced t o work a t f i l l i n g fluxes wave which returns to zero before the burning is HSC THERMOMETER

I I I I

3 2 1 0

4

BOLOMETER

o f o r d e r 5

-

L50 mK

I 1

d e n s i t i e s d e v i a t i o n s from exponential decay a r e remains almost constant d u r i n g t h e b u r n i n g f o r approximately 2.4 sec.

3

I I

Instead t h e c e l l warms t o a c e r t a i n temperature and geometry, t h i s measurement technique becomes i n - remains constant u n t i l t h e HI i s completely burned. sensitive and can grossly underestimate the initial The time constant f o r b u r n i n g has been observed t o

be as l o n g a$ 2

-

follows. If t h e d e n s i t y i s above a c e r t a i n c r i t i c a l I n summary, we have discussed here t h e d i f f i - value, then a f t e r t r i g g e r i n g t h e c e l l heats UP t o

culties and the techniques used to stabilize H+.

a temperature:above t h a t o f t h e HEVAC-. The helium

film which towards regions now starts Experiments have a l s o been performed on D+. For un- f l o w i n g up i n t o t h e HSC and t h e vapors f l u x back t o determined reasons i t has n o t y e t been p o s s i b l e t o condense on t h e HEVAC. The H I i n t h e c e l l i s pumped

achieve densities of D I above s10I4 at/cc. H t has i n t o t h e r e g i o n between t h e HEVAC condenser and t h e

HSC. T h i s 5s a feedback c o n t r o l l e d process: t h e H, been stabilized to densities of at least 10 at/cc 16 l e a k s b a c k ' i n t o t h e HSC a t a constant r a t e P t o and perhaps as much as an order of magnitude higher m a i n t a i n t h e temperature o f t h e HSC constant u n t i l

At the higher densities the lifetimes appear to i t i s depleted. During t h i s time t h e H t can a l s o

l e a k o u t of t h e HEVAC and recombine i n warmer decrease, b u t t h i s has n o t y e t been s t u d i e d sys- regions, t h u s n o t c o n t r i b u t i n g t o t h e warming o f t e m a t i c a l l y . An increase o f d e n s i t y o f one t o two t h e c e l l . The t i m e r e q u i r e d t o e s t a b l i s h t h i s pro-

orders of magnitude does n o t seem t o be o u t of cess can be estimated from t h e bolometer temperature

-

observable.

i n g o f t h e c e l l b u t t h i s i s o n l y t h e lower l i m i t . We can g e t an i d e a f o r t h e l o s s o u t o f t h e HEVAC

from t h e f o l l o w i n g simple model. A f t e r t h e begin- References n i n g t r a n s i e n t , t h e decay o f t h e N H I atoms i n

t h e trapped volume can be c a l c u l a t e d from

Here N = NH + Nc where Nc i s t h e number o f atoms f l o w i n g t o t h e c e l l and corresponds t o our measured number o f atoms. NH i s t h e number l o s t o u t t h e HEVAC, K i s an e f f e c t i v e Clausing f a c t o r and V i s t h e volume o f t h e t r a p . The equation i s e a s i l y solved t o f i n d N = (No + T P ) e x p ( - t / ~ )

-

where No i s t h e i n i t i a l number o f atoms and

T = 4 c V / KVA. For an experimental burn time o f H

t = tb 2 2.5 sec we found Nc = p t b = 1016 atoms.

We f i n d No by s e t t i n g N = 0 o r No = r p l e x p ( t b / r ) - 1 1 The r e s u l t s are very s e n s i t i v e t o T . Using t h e most c o n s e r v a t i v e value, T = 1.5 sec, corresponding t o t h e measured value f o r atoms t o empty o u t o f t h e c e l l ( n o t t h e t r a p ) i n zero f i e l d , we f i n d

No

:

.

0 2 C

Thus f o r s h o r t burn times t h e measured value Nc i s l i n e a r l y dependent on t h e l e n g t h o f t h e HSC response pulse; however f o r h i 4 h d e n s i t i e s , i n t h e c u r r e n t

/1/ I.F. S i l v e r a and J.T.M. Walraven, Phys. Rev.

L e t t .

44,

/2/ J.T.ILl. Walraven and I.F. S i l v e r a , Phys. Rev.

L e t t .

9,

/3/ J.T.M. Walraven, I.F. S i l v e r a and A.P.M.

Matthey, submitted f o r p u b l i c a t i o n . /4/ F. London, Phys. Rev.

54,

/5/ Hs i s produced i n a magnetic f i e l d . The e l e c t r o n spins a r e p o l a r i z e d a n t i para1 1 e l

(down) w i t h r e s p e c t t o t h e f i e l d d i r e c t i o n , so i t seems more a p p r o p r i a t e t o use t h i s symbol r a t h e r than H+ which would correspond t o t h e h i g h e r energy s p i n l e v e l s .

/6/ L

.

.

.

/7/ A. J. Leggett, these proceedings.

/8/ A.J. B e r l i n s k y , Phys. Rev. L e t t .

3,

/9/ E.D. Siggia and A.E. Ruckenstein, p r e p r i n t and these proceedings.

/ l o / ^J.T.M. Walraven and I . F . S i l v e r a , these proceedings.

/11/ ^D.N. M i t c h e l l and R.J. LeRoy, J . Chem. Phys.

67, 1042 (1977).

-

/12/ W.N. Hardy, e t a l . , these p r o c e e d i n g s . /16/

1131 R.A. Guyer and M.D. M i l l e r , Phys. Rev. L e t t .

42, 1754 (1979); I.B. Mantz and D.O. Edwards, /17/

-

Phys. Rev.

208,

/14/ J.T.M. Walraven, E.R. E l i e l and I.F. S i l v e r a ,

Phys. L e t t .

e,

/15/ A.J. B e r l i n s k y , R . D . E t t e r s , V.V. Goldman and I.F. S l l v e r a , Phys. Rev. L e t t .

2,

I . F . S i l v e r a and J.T.M. Walraven, Phys. L e t t . 74A, 193 (1979).

-

S.B. Crampton, these proceedings.

I.F. S i l v e r a and V.V. Goldman, submitted f o r pub1 i c a t i o n .

We use t h e term s t a b i l i z a t i o n t o mean a very l a r g e increase o f t h e l i f e t i m e o f t h e gas as compared t o t h e l i f e t i m e i t would have i f no he1 ium f i l m , magnetic f i e l d o r low tempera- t u r e environment was used.