NEUTRON WAVE OPTICS STUDIED WITH ULTRACOLD NEUTRONS

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NEUTRON WAVE OPTICS STUDIED WITH ULTRACOLD NEUTRONS

A. Steyerl

To cite this version:

A. Steyerl. NEUTRON WAVE OPTICS STUDIED WITH ULTRACOLD NEUTRONS. Journal de

Physique Colloques, 1984, 45 (C3), pp.C3-255-C3-264. �10.1051/jphyscol:1984343�. �jpa-00224060�

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Colloque C3, suppl6ment a u n03, Tome 45, mars 1984 page C3-255

NEUTRON WAVE OPTICS STUDIED WITH ULTRACOLD NEUTRONS

A. Steyerl

F a k u l t d t fiir Physik, E 21, d e r Technischen U n i v e r s i t a t Miinchen, 8046 Garching, F.R .G.

Ri?sum$

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Dans l e s experiences d e c r i t e s on d6montre e t u t i l i s e l e s p r o p r i g t 6 s o n d u l a t o i r e s d e s n e u t r o n s aux longueurs d'onde d ' e n v i r o n 100 nm. On d i s c u t e l e s e f f e t s importants d e l a g r a v i t e s u r c e s n e u t r o n s

t r e s

l e n t s . Les c a r a c t g r i - s t i q u e s d e l a p a r a b o l e du v o l o n t permis l a c o n s t r u c t i o n d e nouveaux i n s t r u - ments d h a u t e r e s o l u t i o n e t d e systsmes o p t i q u e s .

A b s t r a c t - The paper r e p o r t s experiments demonstrating o r u t i l i z i n g t h e wave p r o p e r t i e s of n e u t r o n s w i t h wavelengths of about 100 nm. The s i g n i f i c a n t e f - f e c t s of g r a v i t y a r e d i s c u s s e d , and s p e c i a l f e a t u r e s of t h e f l i g h t p a r a b o l a have been used i n d e s i g n i n g h i g h - r e s o l u t i o n i n s t r u m e n t s and image-forming systems.

Due t o i t s z e r o e l e c t r i c charge, i t s l o n g l i f e t i m e , and i t s ready a v a i l a b i l i t y t h e f r e e n e u t r o n , of a l l known massive p a r t i c l e s , seems t o be t h e most s e n s i t i v e probe f o r p r e c i s e i n v e s t i g a t i o n s of t h e wave p r o p e r t i e s a t t r i b u t e d t o p a r t i c l e s i n motion I n t h e framework of quantum theory. I n t e r f e r e n c e phenomena a r e g e n e r a l l y regarded t o b e t h e " f i n g e r - p r i n t s " of t r a v e l l i n g waves, and t h e s e have been observed w i t h i n an enormous r e g i o n of neutron energy spanning 20 decades from 1012ev down t o 10-'ev.

The a s s o c i a t e d de B r o g l i e wavelengths range from l ~ - ~ n m t o 1 0 ~ n m , i . e . , from sub- n u c l e a r dimensions t o an almost macroscopic s c a l e . I n r e c e n t y e a r s a g r e a t number of papers have appeared r e p o r t i n g , o r s u g g e s t i n g , t h e u s e of n e u t r o n s f o r s p e c i f i c t e s t s of fundamental - and s t i l l c o n t r o v e r s i a l - i m p l i c a t i o n s of wave mechanics, l i k e w a v e - p a r t i c l e dualism, s u p e r p o s i t i o n , o r wave f u n c t i o n c o l l a p s e . The p r e s e n t paper d i s c u s s e s experiments i n v e s t i g a t i n g t h e o p t i c a l behaviour of u l t r a c o l d n e u t r o n s with wavelengths l y i n g a t t h e upper end of t h e spectrum mentioned above.

I - PECULIARITIES OF ULTRACOLD NEUTRONS

U l t r a c o l d n e l ~ t r o n s (UCN) move a t v e l o c i t i e s below -10 m / s and have e n e r g i e s of t h e o r d e r of l r 7 e v . A t t h e s e low e n e r g i e s t h e o r d i n a r y n u c l e a r , "electro-weak", and grav.. -iu f o r c e s experienced by any neutron g i v e r i s e t o a number of q u i t e e x t r a - ordina _' p znomena. Perhaps t h e most prominent of t h e s e i s t o t a l r e f l e c t i o n of t h e neutron wave a t t h e s u r f a c e of many s u b s t a n c e s , a t any a n g l e of incidence. T h i s phe- nomenon occurs f o r n e u t r o n e n e r g i e s l y i n g below t h e " o p t i c a l p o t e n t i a l " ( o r " s c a t - t e r i n g p o t e n t i a l " ) f o r t h e w a l l s u b s t a n c e ,

where N i s t h e number of atoms p e r cm3 and b t h e i r amplitude f o r c o h e r e n t s c a t t e r i n g of slow neutrons. For most s u b s t a n c e s , U i s p o s i t i v e and of t h e o r d e r of I O - ~ ~ V . Thus UCN w i t h E < U can be s t o r e d i n c l o s e d c a v i t i e s , t h e s o - c a l l e d "neutron b o t t l e s " , where t h e y t r a v e l t o and f r o between t h e w a l l s , rebounding from t h e r e many thou- sand times b e f o r e l o s s p r o c e s s e s become n o t i c e a b l e . This phenomenon had been pre- d i c t e d by Zel'dovich i n 1959 / I / .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984343

C3-256

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The s t o r y of experiments on UCN containment i n " b o t t l e s " i s l o n g , a n d i t m a y s u f f i c e t o mention t h a t i n t h e end long s t o r a g e l i f e t i m e s up t o a few hundred seconds have been r e p o r t e d /2,3/. These v a l u e s a r e reasonably c o n s i s t e n t w i t h e x p e c t a t i o n , a t

l e a s t f o r some of t h e w a l l m a t e r i a l s used. Although t h i s h i n d s i g h t s t a t e m e n t might appear t o b e merely g r a t i f y i n g , I t h i n k it h a s deeper i m p l i c a t i o n s : I t shows t h a t a p a r t i c l e behaving s o " c l a s s i c a l l y " i n a s e n s e - i t moves s o slowly t h a t it can r i s e only s e v e r a l metres a g a i n s t t h e e a r t h ' s g r a v i t a t i o n a l f i e l d b e f o r e f a l l i n g back down l i k e a pebble

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a t t h e same time e x h i b i t s u t t e r l y " u n c l a s s i c a l " f e a t u r e s : I t under- goes t o t a l r e f l e c t i o n a t t h e w a l l a s a consequence of m u l t i p l e c o h e r e n t s c a t t e r i n g of t h e neutron wave f u n c t i o n f r o m t h e w a l l atoms, i n such a p e r f e c t manner t h a t it s u r v i v e s , s a y , 10' s u c c e s s i v e r e f l e c t i o n s . Moreover, t h e observed t i n y l o s s proba- b i l i t y p e r r e f l e c t i o n conforms t o t h e c a l c u l a t e d p r o b a b i l i t y of " r e a c t i o n s " of t h e wave a s i t t u n n e l s a s h o r t d i s t a n c e i n t o t h e medium and i s s u b j e c t t o t h e p o s s i b i l - i t y of b e i n g absorbed i n t o a nucleus o r of undergoing i n e l a s t i c s c a t t e r i n g by t h e t h e r m a l l y a c t i v a t e d w a l l atoms. I n t h i s s e n s e UCN containment experiments may b e ranked among t h e key experiments demonstrating t h e fundamental wave n a t u r e of m a t t e r Yet, t h e i n f o r m a t i o n on p a r t i c l e wave behaviour t o be gained from s t o r a g e experiments seems t o be l i m i t e d f o r two r e a s o n s : F i r s t l y , t h e d e t a i l s of t h e s i n g l e r e f l e c t i o n p r o c e s s a r e b l u r r e d by averaging o v e r a g r e a t number of e v e n t s , measuring only one i n t e g r a l parameter: t h e s u r v i v a l r a t e a s a f u n c t i o n of s t o r a g e time. Secondly, t h e r e s u l t s may be

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and indeed have f o r a long time been - obscured by u n c e r t a i n t i e s i n w a l l s u r f a c e c o n d i t i o n s l i k e hydrogen c o n t e n t .

Before proceeding t o a d i s c u s s i o n of more s p e c i f i c experiments on UCN o p t i c s , l e t me p o i n t o u t t h a t i n a d d i t i o n t o t h e n u c l e a r i n t e r a c t i o n , which g i v e s r i s e t o t h e s c a t - t e r i n g p o t e n t i a l , two f u r t h e r i n t e r a c t i o n s of e q u a l importance t o UCN behaviour have t o be considered: The g r a v i t a t i o n a l f o r c e and t h e magnetic i n t e r a c t i o n . T h e i r magni- tudes a r e : mNg Z eV p e r metre of v e r t i c a l r i s e , and H~ E 6 x l o m 8 e v / t e s l a , r e - s p e c t i v e l y . The magnetic f o r c e h a s been used f o r UCN-confinement i n a magnetic s t o r - age r i n g /4/, and g r a v i t a t i o n a l e f f e c t s have, e . g . , been s t u d i e d and a p p l i e d exten- s i v e l y i n t h e experiments d i s c u s s e d below. The t h r e e i n t e r a c t i o n s mentioned

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and o t h e r s l i k e t h e p a r i t y v i o l a t i n g (3.3)-type i n t e r a c t i o n

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may be i n c o r p o r a t e d i n a s p a t i a l l y v a r i a b l e index of r e f r a c t i o n ,

E d e n o t e s t h e k i n e t i c energy a t an ( a r b i t r a r y ) p o i n t i n s p a c e where t h e p o t e n t i a l egergy i s s e t e q u a l t o zero. The p o s i t i v e ( n e g a t i v e ) s i g n of t h e magnetic term r e - f e r s t o n e u t r o n s p i n o r i e n t a t i o n p a r a l l e l ( a n t i p a r a l l e l ) t o t h e magnetic f i e l d

2.

The magnetic i n t e r a c t i o n may u s u a l l y be i n c l u d e d i n t h i s simple form s i n c e f o r UCN, due t o t h e i r low v e l o c i t y , t h e a d i a b a t i c c o n d i t i o n i s s a t i s f i e d e x c e p t i n s p e c i f i c s i t u a t i o n s .

I1

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GRAVITATIONAL EFFECTS ON UCN OPTICS

A s a consequence of t h e e a r t h ' s g r a v i t a t i o n a l p o t e n t i a l even empty s p a c e , i n t h e ab- sence of magnetic f i e l d s , a c t s a s a r e f r a c t i v e medium w i t h a s p a t i a l l y v a r i a b l e i n - dex of r e f r a c t i o n . T h e r e f o r e , t h e g e o m e t r i c a l o p t i c s of UCN i s c h a r a c t e r i z e d by c u r v i l i n e a r r a y s .

I t i s s t r a i g h t f o r w a r d t o show t h a t t h e curved r a y s c a l c u l a t e d from Fermat's p r i n - c i p l e c o i n c i d e w i t h t h e c l a s s i c a l t r a j e c t o r i e s of a p a r t i c l e exposed t o t h e same f o r c e f i e l d . Indeed, f o r ( n o n r e l a t i v i s t i c ) m a t t e r waves, Fermat's c o n d i t i o n of s t a - t i o n a r i t y of t h e a c t i o n i n t e g r a l ,

B+ -+

A / k - d s = 0 A

can be w r i t t e n i n t h e a l t e r n a t i v e ways:

B B

A / n 2 d t = 0 o r A / T d t = 0.

A A

But t h e l a t t e r form i s e q u i v a l e n t ( e - g . / 5 / ) t o t h e a c t i o n p r i n c i p l e of n o n r e l a t i - v i s t i c c l a s s i c a l mechanics,

t~

6

3

L d t = O , t~

q.e.d. The symbols used above s t a n d f o r

A, B - s t a r t i n g and end p o i n t of a p a t h with p a t h element d g = d t

= (6/m )

2

d t ;

3,

^{tB -} s t a r t i g g and a r r i v a l time;

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k i n e t i c energy;

L

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Lagrange f u n c t i o n ;

6 - a r b i t r a r y v a r i a t i o n w i t h t t k e p t f i x e d ;

A - v a r i a t i o n such t h a t A, 3 a r e k e p t f i x e d and energy ^{A' B} i s conserved a t any p o i n t of t h e p a t h .

I t should b e emphasized t h a t t h u s t h e c l a s s i c a l t r a j e c t o r y f o l l o w s from a phase con- s i d e r a t i o n f o r t h e wave f i e l d , and b e l i e v i n g i n t h e wave n a t u r e of m a t t e r a t a l l t h e r e seems t o be no way even of a r r i v i n g a t t h e " f a l l i n g neutron" w i t h o u t due r e - gard t o t h e wave phase. We a l s o n o t e t h a t , i n c o n t r a s t t o l i g h t o p t i c s , n o t t h e t r a v e l time i s an extremum f o r m a t t e r waves b u t t h e i n t e r g r a l over n 2 d t .

A l t e r n a t i v e l y , t h e c l a s s i c a l f l i g h t p a r a b o l a i n t h e presence of t h e g r a v i t a t i o n a l f i e l d a l s o f o l l o w s d i r e c t l y from t h e Schrodinger e q u a t i o n , u s i n g t h e Newtonian po- t e n t i a l and applying E h r e n f e s t ' s theorem. These r e s u l t s a r e v a l i d f o r any f o r c e s de- r i v a b l e from a p o t e n t i a l .

I t seems worth-while mentioning an anomaly i n t h e behaviour of t h e wave phase which i s w e l l known i n l i g h t o p t i c s : On t r a n s i t i o n t h r o u g h a " c a t a s t r o p h i c region"

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v i z . , of a r e g i o n i n space where a s i n g u l a r i t y of i n t e n s i t y should occur i n t h e framework of r a y o p t i c s - wave o p t i c s p r e d i c t s t h e d i s a p p e a r a n c e of t r u e s i n g u l a r i t i e s and t h e occurrence of phase changes: by T f o r a t r u e f o c a l p o i n t , and by n/2 f o r a c a u s t i c s u r f a c e . For n e u t r o n s , g r a v i t y i n t r o d u c e s a c a u s t i c s u r f a c e a t t h e "bounding p a r a - b o l o i d " of b a l l i s t i c s , i . e . , a t t h e envelope of a l l f l i g h t p a r a b o l a s p o s s i b l e w i t h a given i n i t i a l v e l o c i t y . Thus we e x p e c t a phase change by s/2 t o occur a s a neutron touches t h i s s u r f a c e . Berry h a s p o i n t e d o u t /6/ t h a t an i n t e r e s t i n g d i f f r a c t i o n p a t - t e r n should b e e s t a b l i s h e d n e a r t h e c a u s t i c which might b e o b s e r v a b l e w i t h mono- e n e r g e t i c UCN emerging from a narrow h o l e . The f r i n g e spacing i s of o r d e r (h2/$g)113

2 0.03 mm, and t h e p a t t e r n can be i n t e r p r e t e d s e m i - q u a n t i t a t i v e l y a s a r i s i n g from t h e i n t e r f e r e n c e of t h e two p a r a b o l i c " r a y s " a b l e t o r e a c h a given p o i n t i n t e r n a l t o t h e c a u s t i c : one o f them touches t h e c a u s t i c s u r f a c e on i t s way and t h e o t h e r does n o t .

Another q u i t e amusing e f f e c t of g r a v i t y on t h e UCN wave f i e l d h a s been p o i n t e d o u t by Luschikov and Frank /7/: For n e u t r o n s " s l i d i n g " on a f l a t m i r r o r p l a t e d i s c r e t e bound s t a t e s

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"bound" o n l y w i t h r e s p e c t t o t h e c o o r d i n a t e normal t o t h e s u r f a c e - a r e p o s s i b l e w i t h e n e r g i e s of o r d e r (mNg2h2 )

*

1 0 - l 2 eV. N e i t h e r of t h e s e e f f e c t s h a s a p p a r e n t l y been observed a s y e t .

I n c o n t r a s t t o t h e e f f e c t s mentioned above i t i s v e r y e a s y t o observe t h e s t r o n g cur- v a t u r e of UCN beams p r o p a g a t i n g i n t h e g r a v i t a t i o n a l f i e l d . We have used s p e c i a l p r o p e r t i e s of t h e f l i g h t p a r a b o l a f o r " g r a v i t y f o c u s i n g " i n novel h i g h - r e s o l u t i o n neutron i n s t r u m e n t s .

111.1 - G r a v i t y Spectrometer

The g r a v i t a t i o n a l f i e l d i s an extremely d i s p e r s i v e "medium" f o r UCN. Thus t h e energy, E , of a UCN may b e determined very p r e c i s e l y by measuring t h e maximum r e a c h , R

,

of i t s f l i g h t p a r a b o l a . Numerically, t h e r e a c h d i s p e r s i o n i s given by: R /E m = 2/mYTg ^f

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Monochromator

A\

Fig. 1

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Scheme of t h e g r a v i t y s p e c t r o m e t e r NESSIE, where t h e p r i n c i p l e of reach a n a l y s i s i s a p p l i e d f o r p r e c i s e energy s e l e c t i o n .

2 cm/neV. Lying on t h e c a u s t i c s u r f a c e t h e p o i n t s of maximum reach o f f e r t h e advan- t a g e of h i g h b r i l l i a n c e - a r a t h e r d i v e r g e n t i n i t i a l beam i s focused t h e r e . The UCN g r a v i t y s p e c t r o m e t e r NESSIE (NEutronen-Schwerkraft-SpektrometrIE) i s based on t h i s p r i n c i p l e . A s shown i n Fig. 1 , both t h e monochromator and t h e a n a l y s e r employ reach focusing. Ample use i s made a l s o of a d d i t i o n a l f o c u s i n g t e c h n i q u e s , l i k e t h e a p p l i - c a t i o n of e l l i p t i c a l m i r r o r s i n t h e a n a l y s e r and of two s p e c i a l l y shaped m i r r o r s provided i n f r o n t of t h e sample. Thus wide beam divergences can be used, and t h i s i s a p r e r e q u i s i t e f o r t h e p o s s i b i l i t y of f u l l e x p l o i t a t i o n of a methodical a s p e c t p o i n t e d o u t by Maier-Leibnitz / 8 / : I n h i g h - r e s o l u t i o n q u a s i - e l a s t i c neutron s c a t - t e r i n g t h e u s a b l e volumes i n phase space, and hence t h e i n t e n s i t y , i n c r e a s e quadrat- i c a l l y with wavelength. This advantage made it p o s s i b l e t o demonstrate t h e "world- b e s t " r e s o l u t i o n

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a f u l l width a t h a l f maximum of 17 neV f o r a n e l a s t i c s c a t t e r i n g l i n e and t h e p o s s i b i l i t y of measuring a d i f f u s i v e broadening by a few neV /9/ - a t a small r e a c t o r l i k e t h e FRM with i t s thermal f l u x of only 2 x l ~ ~ ~ c m - ~ s - ~ . ( T h i s r e s o l u t i o n i s only comparable t o t h a t o b t a i n e d a t t h e spin-echo spectrometer i n - s t a l l e d a t t h e high-flux r e a c t o r a t Grenoble.) Within t h e c o n t e x t of neutron o p t i c s it seems worth mentioning t h a t t h e r e s o l u t i o n measured i n NESSIE e x a c t l y checks w i t h t h e e x p e c t a t i o n which was based on curved-ray o p t i c s , assuming i d e a l m i r r o r geome- t r i e s . Recently a d i f f e r e n t scheme of UCN g r a v i t y spectrometer has been proposed by Utsuro and Kawabata

/lo/.

111.2

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G r a v i t y D i f f r a c t o m e t e r

Another f e a t u r e of g r a v i t y h a s been u t i l i z e d i n t h e " g r a v i t y d i f f r a c t o m e t e r " /11,12/:

The g r a v i t a t i o n a l p o t e n t i a l d e p e n d s ' o n l y on t h e v e r t i c a l h e i g h t , z. Thus t h e f a l l h e i g h t i s a p r e c i s e measure of t h e change of " v e r t i c a l energy" of a n e u t r o n , i . e . , of t h e k i n e t i c energy corresponding t o t h e v e r t i c a l component of v e l o c i t y . Q u a n t i t a t i v e - l y , AZ/AE = l / m g

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1 cm/neV. I n t h e g r a v i t y d i f f r a c t o m e t e r sketched i n Fig. 2 t h e

" v e r t i c a l energ?" of UCN i n c i d e n t on a h o r i z o n t a l sample i s p r e c i s e l y d e f i n e d by t h e f a l l h e i g h t from t h e e n t r a n c e s l i t t o t h e sample. A good "neutron economy" i s a g a i n ensured by e x p l o i t i n g a s p e c i a l p r o p e r t y of t h e f l i g h t p r a b o l a : The maximum h e i g h t i s s t a t i o n a r y and t h e r e f o r e t h e e n t r a n c e s l i t i s imaged o n t o t h e e x i t s l i t . From t h e

Vacuum Vessel (p:~~-3 m m ~ g )

UCN Scurce (From "Neutron Turbine")

Fig. 2

-

Scheme of t h e g r a v i t y d i f f r a c t o m e t e r . The e n t r a n c e s l i t i s imaged o n t o t h e e x i t s l i t .

chosen s l i t width of 2 cm a " v e r t i c a l " r e s o l u t i o n of 2 neV i s deduced, and t h i s was confirmed by experiment.

I V

-

WAVE OPTICAL EXPERIMENTS

The high r e s o l u t i o n provided by t h e g r a v i t y d i f f r a c t o m e t e r h a s been e x p l o i t e d i n a s e r i e s of experiments aimed a t e l u c i d a t i n g t h e wave p r o p e r t i e s of p a r t i c l e s w i t h wavelengths approaching macroscopic dimensions.

IV.l

-

Mirror R e f l e c t i o n

I n a simple b u t c r u c i a l a p p l i c a t i o n we s t u d i e d t h e f e a t u r e s of UCN t o t a l r e f l e c t i o n from a f l a t m i r r o r /11/. Fig. 3 shows t h e d a t a f o r a g l a s s p l a t e , p l o t t e d v s , t h e h e i g h t of f a l l . The d a t a p o i n t s e x h i b i t t h e expected s t e e p edge a t t h e c r i t i c a l h e i g h t of f a l l which i s determined by t h e l i m i t f o r t o t a l r e f l e c t i o n . However, t h e measured s l o p e i s c o n s i d e r a b l y s t e e p e r t h a n c a l c u l a t e d f o r a s t e p - f u n c t i o n poten- t i a l ( a ) , i . e . a s h a r p t r a n s i t i o n from t h e vacuum t o t h e b u l k g l a s s . A p o t e n t i a l d i s t r i b u t i o n smoothed by t h e e f f e c t of contamination i n t h e i n d i c a t e d manner ( b )

,

on t h e o t h e r hand, p r o v i d e s a n adequate r e p r e s e n t a t i o n of t h e d a t a . T h i s o b s e r v a t i o n was c o n s i d e r e d t o b e a s t r o n g evidence of s u r p r i s i n g l y l a r g e q u a n t i t i e s of hydroge- nous s u b s t a n c e s a t t h e w a l l s u r f a c e a s being t h e main source of t h e high UCN l o s s e s from " b o t t l e s " observed i n t h e e a r l y containment experiments. T h i s had been surmised from t h e v e r y beginning, b u t c e r t a i n t y was gained only from c a r e f u l s u r f a c e a n a l y s e s /13,14/ and t h e d i r e c t demonstration by Mampe, Ageron, and Gahler / 3 / , of t h e connec- t i o n between s u r f a c e c l e a n i n g by glow d i s c h a r g e and t h e UCN s t o r a g e l i f e t i m e s . IV.2 - Wave I n t e r f e r e n c e a t a Thin Film

The o b s e r v a t i o n of UCN wave i n t e r f e r e n c e a t a t h i n f i l m h a s been r e p o r t e d f i r s t i n /15/. Fig. 4 shows t h e h i g h - r e s o l u t i o n d a t a o b t a i n e d a t t h e g r a v i t y d i f f r a c t o m e t e r , u s i n g a t h i n g o l d f i l m evaporated on g l a s s / I t / . On t h e b a s i s of t h e one-dimensional Schrijdinger e q u a t i o n t h e observed f r i n g e p a t t e r n can be w e l l e x p l a i n e d . The t h i c k n e s s v a l u e of (268

*

^{6 )} nm f i t t e d t o t h e d a t a a g r e e s w i t h a l i g h t - o p t i c a l measurement.

J O U R N A L

DE

PHYSIQUE

Primary Intensity

-C

---

F a l l tielsht - cm f a l l H e i g h t - c m

Fig. 3 - R e f l e c t e d i n t e n s i t y v s neutron Fig. 4 - I n t e r f e r e n c e p a t t e r n f o r UCN f a l l h e i g h t f o r a g l a s s sample. The d a t a r e f l e c t i o n from a t h i n g o l d f i l m on g l a s s . p o i n t s a r e compared t o c a l c u l a t i o n s f o r The s o l i d curve 2 i s a c a l c u l a t i o n w i t h a ) a s t e p - f u n t i o n p o t e n t i a l d i s t r i b u t i o n , an a d j u s t e d f i l m t h i c k n e s s .

and b ) a smoothed p o t e n t i a l a s a model f o r a hydrogenous s u r f a c e f i l m with a g r a d u a l change i n composition.

IV.3 - Neutron Resonances i n More Complex S t r a t i f i e d Systems

An e x t e n s i o n of t h e t h i n - f i l m experiments t o more complex s t r a t i f i e d systems was undertaken mainly i n view o f t h e p o s s i b i l i t y t o i n v e s t i g a t e quasi-bound s t a t e s of t h e neutron i n m a t t e r . That long-lived resonances of t h e n e u t r o n wave c o u l d a r i s e from t h e c o l l e c t i v e i n t e r a c t i o n with t h e atoms h a s been p o i n t e d o u t by Kagan /16/ and S e r e g i n /17/. The l a t t e r a u t h o r proposed t o t r a p UCN i n a s y n t h e t i c p o t e n t i a l w e l l c r e a t e d by a sequence of t h r e e f i l m s , such t h a t a medium w i t h low s c a t t e r i n g poten- t i a l ( l i k e aluminium) i s sandwiched between two l a y e r s of a s u b s t a n c e with high s c a t t e r i n g p o t e n t i a l ( l i k e c o p p e r ) . For UCN, such an arrangement r e p r e s e n t s two m i r - r o r s s e p a r a t e d by a gap. Thus i t resembles an o p t i c a l Fabry-Perot i n t e r f e r o m e t e r . The t r a n s m i s s i o n and r e f l e c t i o n behaviour of t h i s system i s c h a r a c t e r i z e d by resonances and can be analysed i n t h e same way a s i n l i g h t o p t i c s /18/. Fig. 5 shows t h e grav- i t y d i f f r a c t o m e t e r d a t a /19/ f o r r e f l e c t i o n from a t a r g e t with t h e f o l l o w i n g f i l m sequence d e p o s i t e d on g l a s s : Cu (24 nm)

,

^~l (86 nm)

,

^{C u} (24 nm)

,

and a s a p r o t e c t i o n from o x i d a t i o n , A 1 (10 nm). The corresponding p o t e n t i a l d i s t r i b u t i o n i s i n d i c a t e d i n t h e i n s e t . The pronounced r e f l e c t i v i t y minimum observed is due t o t h e resonance of o r d e r n = 1, which i s c h a r a c t e r i z e d by an approximate matching of gap width and neu- t r o n wavelength h

.

^{Here i s} t h e wavelength corresponding t o t h e p e r p e n d i c u l a r component of neutFon wavevector i n t h e aluminium r e g i o n . Again t h e d a t a a r e w e l l r e p r e s e n t e d by t h e simple t h e o r y , and t h e l i f e t i m e of

-lo-'

s deduced from t h e measured l i n e w i d t h s u g g e s t s t h a t t h e n e u t r o n s have made about f o u r round t r i p s on t h e average w i t h i n t h e sandwich.

IV.4

-

Tunneling S p l i t t i n g f o r Two Coupled Resonators

Suppose, a system of two coupled r e s o n a t o r s f o r t h e neutron wave i s c r e a t e d by a l a y - e r sequence Cu-Al-Cu-Al-Cu ( a s shown i n t h e i n s e t diagram of Fig. 6 ) . The r e s o n a t o r s a r e "tuned", i . e . symmetrical w i t h equal w e l l widths and e q u a l l a t e r a l b a r r i e r widths.

Then t h e waves i n t h e two w e l l s a r e coupled by t h e p o s s i b i l i t y of t u n n e l i n g through t h e c e n t r a l b a r r i e r . We know from quantum mechanics t h a t t h e n t h e s i n g l e - r e s o n a t o r s t a t e s s p l i t i n t o two each, and t h e s e a r e c h a r a c t e r i z e d by a symmetric and antisym- m e t r i c wavefunction, r e s p e c t i v e l y .

These p r e d i c t i o n s a r e borne o u t by t h e experimental UCN t r a n s m i s s i o n d a t a /18/ d i s - p l a y e d i n Fig. 6 f o r a sample with t h e i n d i c a t e d l a y e r sequence. The s p l i t t i n g of t h e (n = 0) - resonance by 6.3 neV i s w e l l r e s o l v e d . The observed r e d u c t i o n i n r e s - onance amplitude may be a t t r i b u t e d mainly t o d i f f u s e s c a t t e r i n g from t h e s l i g h t l y rough s u r f a c e s and i n t e r f a c e s between t h e l a y e r s .

IV.5

-

Neutron Tunneling Through a System of Many B a r r i e r s

If t h e above system of two coupled r e s o n a t o r s i s extended t o t h e c a s e of many (M) i d e n t i c a l coupled r e s o n a t o r s , we e x p e c t a s p l i t t i n g of t h e s i n g l e - r e s o n a t o r l e v e l s i n t o M l i n e s each, and f o r M - m , t h e appearance of t r a n s m i s s i o n bands /20/. These bands may a c c u r i n t h e energy r e g i o n below t h e l i m i t of t o t a l r e f l e c t i o n f o r t h e b a r r i e r s u b s t a n c e , and i n t e r e s t i n g l y , even below t h e mean s c a t t e r i n g p o t e n t i a l of t h e composite f i l m s t r u c t u r e . They a r e complementary t o t h e more f a m ~ l i a r r e f l e c t i o n bands c h a r a c t e r i z i n g Bragg r e f l e c t i o n .

We have r e c e n t l y i n v e s t i g a t e d - n o t i n t h e g r a v i t y d i f f r a c t o m e t e r b u t u s i n a u n w l a r - i z e d 3.93

W

n e u t r o n s from a Ge ( I l l ) monochromator, i n c i d e n t a t g l a n c l n g a n g l e

-

^{t h e}

c h a r a c t e r i s t i c s of t h e "anomalous" t r a n s m i s s i o n bands i n an Fe-Ge

-

m u l t i b i l a y e r system ( S t e i n h a u s e r , S t e y e r l , and Malik, t o be p u b l i s h e d ) . The sample c o n s i s t e d of 10 b i l a y e r s of Fe (15 nm) and Ge (16 nm), sandwiched between a d d i t i o n a l " a n t i r e f l e c - t i o n " l a y e r s of s u i t a b l e t h i c k n e s s e s . For one s p i n s t a t e , Fe r e p r e s e n t s t h e b a r r i e r r e g i o n w i t h high p o t e n t i a l while t h e p o t e n t i a l f o r t h e i n t e r v e n i n g Ge l a y e r s i s low.

This f i l m sequence was evaporated on g l a s s . The sample was mounted on a (8-20) d r i v e and m a g n e t i c a l l y s a t u r a t e d i n a p a r a l l e l f i e l d up t o 0.2 t e s l a .

Fig. 7 shows t h e r e f l e c t i o n d a t a taken w i t h t h i s m u l t i l a y e r sample, a s compared t o t h e i n t e n s i t y r e f l e c t e d by a sample w i t h a s i n g l e Fe f i l m (60 nm) d e p o s i t e d on g l a s s . For t h e geometry chosen t h e r e f l e c t e d i n t e n s i t y i s p r o p o r t i o n a l t o t h e r e f l e c t i v i t y and t o t h e a n g l e of i n c i d e n c e , 8. The Fe d a t a c l e a r l y e x h i b i t t h e two r e f l e c t i o n edges f o r t h e two s p i n c o n f i g u r a t i o n s . I n t h e m u l t i l a y e r sample t h e r e f l e c t i v i t y n e a r t h e upper edge i s almost f u l l y suppressed due t o t h e appearance of t h e ( n = 0)

-

resonance i n t h e Ge w e l l s . The s o l i d l i n e r e p r e s e n t s an a t t e m p t a t a q u a n t i t a t i v e i n t e r p r e t a t i o n , which h a s t o t a k e i n t o account d i f f u s i o n and t h e development of Fe-Ge compounds a t t h e i n t e r f a c e s .

Fig. 5

-

I n t e n s i t y r e f l e c t e d from a sample F i g . 6 - Level s p l i t t i n g observed i n with t h e i n d i c a t e d l a y e r sequence which UCN t r a n s m i s s i o n through a coupled- corresponds t o a double-hump p o t e n t i a l . r e s o n a t o r p o t e n t i a l c r e a t e d by t h e The narrow minimum i s due t o t h e ( n = 1 )

-

l a y e r sequence i n d i c a t e d i n t h e i n s e t resonance s t a t e i n t h i s s y n t h e t i c poten- diagram

t i a l d i s t r i b u t i o n .

JOURNAL

DE

PHYSIQUE

- f ^Fe-Ge

Fig. 7 - Comparison of reflected intensity for a magnetized Fe film (60 nm) on glass with the data for an Fe(15 nm)

-

Ge(16 nm) - multibilayer sample. The pronounced re- flectivity dip observed with the multilayer sample near the upper limit for total reflection is due to coupled resonances. The energy scale is for the perpendicular component of motion.

- .-

^C U

^c-

E

\

-

ln

4.0

1v.6 - Diffraction from a Ruled Grating

Fe

A11 the above experiments are very well described by the one-dimensional Schrodinger equation. As a two-dimensional object we investigated a ruled reflection grating /11,12/. We used a grating with 1200 grooves per mm, "blazed" for first-order dif- fraction. It was installed vertically in the gravity diffractometer at the position indicated in Fig. 2. In the process of diffraction the neutron receives a well-de- fined momentum transfer, hm/d, parallel to the surface (d - groove spacing, m - order of diffraction). The resulting change in height of the secondary flight parab- ola up to the exit slit may be scanned by a vertical slit displacement. The inten- sity profiles measured in this way show several clearly separated orders of diffrac- tion as shown in Fig. 8. The linewidths may be fully explained by the instrumental resolution.

01

. '

^I

-20 -10 0 10 20

Relative Slit Position i n cm

A

Fig. 8 - Several orders of diffraction from a ruled grating, scanned by vertical displacement of the exit slit in the gravity diffractometer.

,0,

1

u) C 0 -

a d

.-

c

- -

.c

2

I

Resonance

*/ . . ^.&*

O'

-io b

1b 2b 3'0 4b 50 @[min]

We have, very t e n t a t i v e l y , i n t e r p r e t e d t h e absence of a d e t e c t a b l e l i n e broadening i n terms of a lower l i m i t f o r t h e " i n t r i n s i c coherence l e n g t h f o r t h e n e u t r o n wave t r a i n " . Such a h y p o t h e t i c a l l i m i t - beyond t h o s e determined by t h e i n s t r u m e n t a l r e s o - l u t i o n and t h e f i n i t e neutron l i f e t i m e - does n o t e x i s t i n quantum mechanics, and I do n o t know which m o d i f i c a t i o n s i n t h e t h e o r y might be r e q u i r e d t o account f o r a s p e c u l a t i v e "coherence l e n g t h " . N o n l i n e a r i t i e s , a s proposed by de B r o g l i e /21/ o r B i a l y n i c k i - B i r u l a and Mycielski /22/ would r e q u i r e d r a s t i c r e v i s i o n s i n our p r e s e n t views of quantum phenomena. Thus, l a c k i n g a c l e a r model even our i n t e r p r e t a t i o n of t h e absence of l i n e broadening i n terms of a lower l i m i t f o r t h e "coherence l e n g t h "

might be q u e s t i o n a b l e , because even t h i s i n t e r p r e t a t i o n may depend on t h e model.

Therefore t h e v a l u e of

.-J

0.1 mm d e r i v e d from t h e minimum number of c o h e r e n t l y i l l u m i - n a t e d grooves n e c e s s a r y f o r t h e observed l i n e w i d t h , o n t h e b a s i s of t h e l i n e a r t h e o r y , should be taken only a s a guide number. I n c i d e n t a l l y , t h e p r e s e n t experiment i s sen- s i t i v e n e i t h e r p u r e l y t o t h e l o n g i t u d i n a l nor t h e t r a n s v e r s e coherence l e n g t h , b u t s i n c e t h e n e u t r o n s impinge on t h e g r a t i n g a t an a n g l e of . - ' 4 5 O , t h e wave coherence i s probed i n a d i r e c t i o n halfway between l o n g i t u d i n a l and t r a n s v e r s a l . For t h e s p e c i - f i c , l o g a r i t h m i c , n o n l i n e a r i t y p r o osed i n / 2 2 / t h e above v a l u e would correspond t o a l i m i t f o r t h e c o n s t a n t b of 10-1' ev, s i m i l a r t o t h e value r e c e n t l y r e p o r t e d by GShler e t a l . /23/ and 100 times lower t h a n t h e l i m i t given by S h u l l e t a l . /24/.

V - IMAGE FORMATION WITH ULTRACOLD NEUTRONS

A s a l a s t example of UCN o p t i c s I should l i k e t o d i s c u s s b r i e f l y t h e p o s s i b i l i t y of image formation and t h e p r o s p e c t s of a neutron microscope. The main i n c e n t i v e f o r work on t h e development of a neutron microscope a r i s e s from t h e i n t e r e s t i n explor- i n g t h e i n f o r m a t i o n t o be gained from t h e c o n t r a s t i n m a t t e r a s "seen" by n e u t r o n s

-

which i s q u i t e d i f f e r e n t from t h a t with l i c h t o r e l e c t r o n s , and which i s a d j u s t a b l e by proton-deuteron exchange. For thermal o r c o l d n e u t r o n s , however, no s a t i s f a c t o r y focusing systems a r e a v a i l a b l e , and it i s only with UCN, due t o t h e i r p r o p e r t y of being r e f l e c t e d a t l a r g e a n g l e s , t h a t high m a g n i f i c a t i o n s a t t o l e r a b l e a b e r r a t i o n s appear a t t a i n a b l e . A s a m o d i f i c a t i o n from l i g h t o p t i c s , t h e s t r o n g c u r v a t u r e of UCN beams due t o g r a v i t y i n t r o d u c e s chromatic a b e r r a t i o n s which r e q u i r e compensation.

Glass

Optical Axis

Fig. 9

-

Scheme of t h e "zone m i r r o r " which F i g . 10 - Set-up of a "neutron micro- p r o v i d e s achromatic imaging with UCN scope". Chromatic a b e r r a t i o n s a r e com-

p e n s a t e d i n a s p e c i a l m i r r o r system.

C3-264

JOURNAL D E PHYSIQUE

A p o s s i b i l i t y of compensating gravity-induced a b e r r a t i o n s c o n s i s t s i n " c r o s s i n g " a concave m i r r o r w i t h a Fresnel-zone p l a t e t o o b t a i n a r e f l e c t i n g "zone m i r r o r " /25/, a s sketched i n Fig. 9. T h i s d e v i c e can be designed s o a s t o d i f f r a c t t h e UCN i n t e n - s i t y i n c i d e n t from a p o i n t o b j e c t i n t o a s i n g l e image p o i n t . The zone m i r r o r t h e n e x h i b i t s much t h e same p r o p e r t i e s a s a l e n s o r concave m i r r o r i n l i g h t o p t i c s . T h i s has been demonstrated i n an experiment a t t h e Grenoble r e a c t o r where we o b t a i n e d s h a r p images o f an o b j e c t s l i t w i t h m a g n i f i c a t i o n s up t o s i x /26/. I n a l a t e r e x p e r i - men: image formation a t m a g n i f i c a t i o n 1 was a l s o r e p o r t e d by Klein e t a l . /27/ u s i n g 20 A n e u t r o n s . Kashukeev and Chikov have observed an unmagnified two-dimensional image w i t h UCN, u s i n g a c y l i n d r i c a l m i r r o r /28/.

A t p r e s e n t we a r e t e s t i n g , a t t h e Grenoble r e a c t o r , a two-mirror system a s shown i n Fig. 10. I n t h i s i n s t r u m e n t t h e chromatic a b e r r a t i o n s of t h e f i r s t , p a r a b o l i c , m i r - r o r a r e compensated by t h o s e of a second, s p h e r i c a l , m i r r o r . T h i s i s p o s s i b l e i f t h e n e u t r o n s , a f t e r r e f l e c t i o n from t h e p a r a b o l i c m i r r o r , a r e allowed t o p a s s t h e high- e s t p o i n t of t h e i r f l i g h t p a r a b o l a b e f o r e f a l l i n g down on t h e second m i r r o r . The p r e s e n t d e s i g n admits o f a m a g n i f i c a t i o n o f 50, b u t i n p r i n c i p l e m a g n i f i c a t i o n s up t o l o 4 should be p o s s i b l e . I t can be shown t h a t under c e r t a i n c o n d i t i o n s t h e i n t e r - mediary ( v i r t u a l ) image a l s o shows an i n t e r e s t i n g f e a t u r e : The image d i s t a n c e i s a- chromatic t o a l l o r d e r s , w h i l e t h e l a t e r a l chromatic a b e r r a t i o n i s k e p t w i t h i n t o l - e r a b l e l i m i t s . A modified scheme of t h e two-mirror system i n c l u d e s t h e p o s s i b i l i t y of u s i n g m u l t i l a y e r m i r r o r s , which r e f l e c t two t o t h r e e t i m e s f a s t e r n e u t r o n s t h a n o r d i n a r y m i r r o r s , and t h i s could h e l p t o i n c r e a s e t h e a v a i l a b l e beam i n t e n s i t y /29/.

The r e s e a r c h of t h e Garching group c o n t a i n e d i n t h i s review was supported by t h e German Bundesministerium f i i r Forschung und Technologie.

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1 ZEL'DOVICH Ya.B., Sov. Phys. JETP

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(1959) 1389.

2 KOSVINTSEV Yu.Yu. e t a l . , Sov. Phys. JETP L e t t .

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(1978) 153.

3 MAMPE W . , AGERON P., and G-LER R., Z . Physik B

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Condensed M a t t e r

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(1981) 1 . 4 K ~ ~ G L E R K . - J . , PAUL W . , and TRINKS U . , Phys. L e t t . 7 2 (1978) 422.

5 WLDSTEIN H . , " C l a s s i c a l Mechanics", Addison-Wesley, London, 1959.

6 BERRY M . V . , J. Phys. A

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