THE INTEREST OF SPIN DEPENDENT NEUTRON NUCLEAR SCATTERING AMPLITUDES

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THE INTEREST OF SPIN DEPENDENT NEUTRON NUCLEAR SCATTERING AMPLITUDES

A. Abragam, G. Bacchella, J. Coustham, H. Glattli, M. Fourmond, A.

Malinovski, P. Meriel, M. Pinot, P. Roubeau

To cite this version:

A. Abragam, G. Bacchella, J. Coustham, H. Glattli, M. Fourmond, et al.. THE INTEREST OF

SPIN DEPENDENT NEUTRON NUCLEAR SCATTERING AMPLITUDES. Journal de Physique

Colloques, 1982, 43 (C7), pp.C7-373-C7-381. �10.1051/jphyscol:1982753�. �jpa-00222360�

THE INTEREST OF SPIN DEPENDENT NEUTRON NUCLEAR SCATTERING AMPLITUDES

A-. Abragam*, G.L. B a c c h e l l a , J . Coustham*, H. G l a t t l i , M. Fourmond , A. M a l i n o v s k i * * , P. M e r i e l * , M. P i n o t * and P . Roubeau*

*CEN-Saalay, DPhSKM, 91191 Gif-our-Yvette Cedex, France

* Institute of Physios, Bulgarian Academy of Sciences, Sofia, Bulgaria

Résume* : On expose les méthodes au moyen desquelles les amplitudes de d i f f u s i o n de neutrons dépendant du s p i n nucle'aire peuvent ê t r e mesure'es,et ce qui a e'té f a i t , à ce j o u r , pour les de'terminer. On d i s c u t e e n f i n de l ' i n t é r ê t de t e l l e s mesures.

Abstract : A review i s given of the methods by which the spin dependent neutron s c a t t e r i n g amplitudes can be measured, and of what has been made, up t o now,to obtain them. The i n t e r e s t of such measurements i s discussed.

The i n t e r a c t i o n between an atom and a thermal neutron may be expressed by a s c a t t e r i n g amplitude o p e r a t o r ? * which contains t h r e e main terms

(1) &>= b + 2 mL. T + 2 B T.T

The f i r s t and t h i r d terms take account of the i n t e r a c t i o n between the neutron and the atomic nucleus. The f i r s t one, b , i s the i s o t r o p i c nuclear s c a t t e r i n g amplitude. The t h i r d expresses the i n t e r a c t i o n between the n e u t r o n , c a r r y i n g a spin s, and the n u c l e u s , c a r r y i n g a spin I .

The w e l l known second term corresponds to the d i p o l a r i n t e r a c t i o n between the e l e c t r o n i c magnetic moment of the atom, and the magnetic moment of the neutron ( v i a i t s spin s ) . Mj_denotes the component of M normal t o the s c a t t e r i n g v e c t o r K .

Let us n o t e , i n passing, the formal analoay between the two l a s t terms (except f o r the s u b s c r i p t _L , but the d i f f e r e n c e disappears i f M i s o r i e n t e d along a f i e l d normal t o K). However, they correspond t o q u i t e d i f f e r e n t i n t e r a c t i o n s : the second t e r m , as said b e f o r e , i s r e l a t e d t o a magnetic d i p o l a r i n t e r a c t i o n between the e l e c t r o n i c and the neutron magnetic moments. The same k i n d of i n t e r - a c t i o n e x i s t s , of course,between nuclear and neutron magnetic moments.

But nuclear moments are so weak - r o u g h l y 2000 times less than e l e c t r o n i c ones-that the corresponding term has been purposely omitted i n Jo . Such a d i p o l a r

i n t e r a c t i o n has nothing t o do w i t h the t h i r d term i n ( 1 ) , w h i c h , l i k e b, r e s u l t s from strong nuclear i n t e r a c t i o n s . We then r e t a i n only the analogy between the l a s t two terms of -M , keeping i n mind t h a t t h i s analogy i s purely f o r m a l . This w i l l be used l a t e r .

Coming back now t o the f i r s t and t h i r d terms, l e t us r e c a l l t h a t they may be expressed as a f u n c t i o n of b+and b_ . These are the nuclear s c a t t e r i n g a m p l i -

-* ->

tudes corresponding t o the s c a t t e r i n g processes i n wich I and s couple i n the channels I + | and I - j - r e s p e c t i v e l y . One has :

b = ( I + l ) b . + l b - a n d B = bt- b .

21+1 21+1

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982753

JOURNAL DE PHYSIQUE

If t h e nuclear s c a t t e r i n a arnpli tude b i s now well known f o r a number of nuclei, t h i s was not t h e case, u n t i l r e c e n t l y , f o r b+and b-

.

For t o get them,we need t o know not only t h e value of b

,

but a l s o t h a t of B , t h e s o c a l l e d s p i n depen- dent s c a t t e r i n g amplitude. And very few B values were known 10 years ago. We may then ask t h r e e questions

l o )

How can we measure t h e s e B values?

2 " ) What has been done up t o now t o measure them?

3") What i s t h e i n t e r e s t of such measurements?

I

-

The p r i n c i p l e s of B measurements

They may be found from t h e expression of t h e s c a t t e r i n g c r o s s - s e c t i o n i n an experiment where neutrons f a l l on a c r y s t a l with atoms of non z e r o nuclear spin.

This problem has been solved t h e o r e t i c a l l y i n t h e most general c a s e by BLUME and SCHERMER, f i f t e e n years aqo, i n a s e r i e s of t h r e e papers L21C"3

.

Nevertheless, f o r our purpose, i t w i l l be s u f f i c i e n t t o consider t h e very simple case of a c r y s t a l b u i l t of i d e n t i c a l atoms of only one nuclear s p e c i e s with non zero nuclear s p i n , without any e l e c t r o n i c maqnetic moment, t h i s c r y s t a l having only one atom p e r u n i t c e l l . Under such conditions, t h e s c a t t e r e d i n t e n s i t y w i l l be :

a) f o r a p a r t coherently s c a t t e r e d i n Bragg peaks, with an i n t e n s i t y proportional t o t h e modulus square of t h e s t r u c t u r e amplitude whose expression i s

+ -+

P and n being t h e p o l a r i z a t i o n of nuclei and neutrons r e s p e c t i v e l y . b) f o r another p a r t incoherently s c a t t e r e d with a spin-incoherent s c a t - t e r i n g c r o s s - s e c t i o n p e r atom :

From t h e s e two expressions, i t i s easy t o get t h o s e corresponding t o t h e d i f f e r e n t combinations of nuclear and neutron p o l a r i z a t i o n s , asshown i n t a b l e I .

TABLE I

The ways t o obtain B appear then c l e a r l y :

we can measure t h e incoherent s c a t t e r i n g c r o s s s e c t i o n ( l a s t column of t a b l e I ) . B u t one o b t a i n s [BI and t h e u n c e r t a i n t y about the sign remains. Moreover, i n t h e past, a c c u r a t e determination of spin-incoherent s c a t t e r i ng c r o s s s e c t ions were d i f f i c u l t , except when t h i s c r o s s - s e c t i o n i s very l a r g e . Such was t h e c a s e f o r

Nuclear p o l a r i z a t i o n

o

0

4

P

-+

P

& ( d i f f u s e s c a t t e r i n g ) B ~ I ( I + I )

B ~ I ( I + I ) - B 2 I 2 P 2 2 2 2 2"

B ~ I ( I + I ) - B I P -B 1P.n Neutron

p o l a r i z a t i o n

o

-+ n

o

4 n

~'(Bragcj peaks) b

b 2 + ~ 2 ~ 2 ~ 2

b 2 + ~ 2 ~ 2 ~ 2 + 2 b ~ ~ 7 . ;

TABLE I 1

The u n c e r t a i n t y o n t h e s i g n o f B was r e s o l v e d f o r A H f r o m t h e o r e t i c a l p r e d i c - t i o n s a c c o r d i n g t o which t h e s c a t t e r i nu p - o s s - s e c t i o n o f o r t h o h y d r o q e n s h o u l d be 40 t i m e s t h a t o f parahydrogen i f B was p o s i t i v e , and o f t h e same o r d e r o f maqnitude i f B was n&ativeL4'

.

The experimentZ51 gave 30, l e a d i n g w i t h c e r - t a i n t y t o a p o s i t i v e v a l u e o f B.

From t a b l e I, a n o t h e r method c o u l d be t o measure, w i t h u n p o l a r i z e d neutrons, b u t p o l a r i z e d n u c l e i , t h e i n t e n s i t y v a r i a t i o n o f a B r a g q peak a g a i n s t n u c l e a r p o l a r i z a t i o n . But once more, t h e s i g n o f B remains unknown, and t h e s e n s i t i v i t y remains poor, s i g n a l b e i n g p r o p o r t i o n a l t o t h e square o f a p o l a r i z a t i o n o f t e n smal I.

N u c l e u s ( 6 i n c

The b e s t and t h e most s e n s i t i v e method i s , o b v i o u s l y , and by f a r , t o u s e p o l a - r i z e d n e u t r o n s and p o l a r i z e d n u c l e i . The f l i p p i n g r a t i o I + / I - o f a B r a g g r e f l e c - t i o n t u r n s t h e n o u t t o be

I

--- --- 2

IH

5 1 ~

which, i f P i s small, as i s o f t e n t h e case, i s p r a c t i c a l l y b a r n

79.6

5.0

+ - b2+2b B I Pn BIPn

I - b2-2b BIPn

# -

b I B l

10-12cm

2.90

Compared t o t h e o t h e r methods, t h e s e n s i t i v i t y i s s t r o n g l y enhanced b y t h e f a c t t h a t t h e s i q n a l i s now p r o p o r t i o n a l t o P,rather t h a n P ,and one g e t s t h e s i g n 2 o f B, t h e s i g n a l b e i n g a l s o p r o p o r t i o n a l t o B, r a t h e r t h a n B . 2

2 0 . 1 6

---

T h e r e f o r e i t i s n o t s u r p r i s i n g t h a t , i n t h e e a r l y days o f B measurements, use has been made o f t h i s method. However, t w e n t y y e a r s ago, a p p r e c i a b l e n u c l e a r p o l a r i z a t i o n s were n o t easy t o o e t . Indeed, t h e p o l a r i z a t i o n o f n u c l e i o f s p i n I and m a g n e t i c moment i n a f i e l d H, and i n t h e r m a l e q u i l i b r i u m a t t e m p e r a t u r e T i s g i v e n b y

0.56 I B I I 10-12cm

1.45

3,

b e i n g t h e B r i l l o u i n f u n c t i o n f o r s p i n I. F o r s m a l l v a l u e s o f t h e argument :

-

JOURNAL DE PHYSIQUE

i s , i n f i r s t o r d e r , p r o p o r t i o n a l

b ~ - f

I n an e x t e r n a l f i e l d H, t h e n u c l e a r p o l a r i z a t i o n i s o b t a i n e d b y t h e s o - c a l l e d b r u t e f o r c e method i n which t h e sample i s a t as l o w t e m p e r a t u r e as p o s s i b l e i n a f i e l d as s t r o n g as p o s s i b l e . T h i s method works w e l l f o r metals, i n most cases, c o n d u c t i o n e l e c t r o n s i n s u r i n g q u i c k t h e r m a l e q u i l i b r i u m between t h e n u c l e a r s p i n s and t h e l a t t i c e . I f t h e r e i s good t h e r m a l c o n t a c t between t h e sample and t h e coolant, T i s t h e n t h e t e m p e r a t u r e o f t h e c o o l a n t i t s e l f . T h i s method does n o t work i n i n s u l a t o r s , where s p i n l a t t i c e r e l a x a t i o n t i m e s may b e i n f a v o u r a b l e cases some hours, b u t o f t e n days, months o r l o n g e r .

T h e r e f o r e t h e f i r s t e x p e r i m e n t s were p e r f o r m e d w i t h metals.

B e f o r e d e s c r i b i n g them, we have t o e x t e n d f o r m u l a 2 ) t o t h e more g e n e r a l case where t h e atoms o f o u r c r y s t a l c a r r y a l s o an e l e c t r o n i c moment

M.

We have t h e n :

3

1 _lfl

2 - 2 2 2 2 2 2

_-

b +A ML+B I P +2bAMl.n+2bBIP.n+2ABML.

"

^{" + + - ,} P I

w i t h 3 square terms and 3 c r o s s terms. I n t h i s expression, i t i s understood

+ + +

t h a t each o f t h e b, B and M terms have t o be m u l t i p l i e d by S ( K

-

^{G), G} b e i n g a v e c t o r o f t h e r e c i p r o c a l l a t t i c e concerned : chemical l a t t i c e f o r b, n u c l e a r s p i n l a t t i c e f o r B and magnetic l a t t i c e f o r M.This expression, which g e n e r a l i z e s f o r m u l a 2 ) shows t h a t i f we want t o g e t B, i n s i g n and magnitude, a t l e a s t one of t h e two l a s t terms o f 3 ) s h o u l d come i n t o p l a y i n t h e i n t e n s i t y o f t h e Bragg r e f l e c t i o n . T h i s has two consequences :

1 ) N u c l e i have t o be p o l a r i z e d (P #o)

2) T h i s necessary c o n d i t i o n b e i n g s a t i s f i e d , 3 p o s s i b i l i t i e s remains c o n c e r n i n g t h e 2 cross-terms o f 3 ) c o n t a i n i n g B :

a) o n l y t h e f i f t h t e r m i s non zero. I t i s t h e case f o r t h e non magnetic c r y s t a l we c o n s i d e r e d b e f o r e . Neutrons have t o be p o l a r i z e d ( n # o ) b) O n l y t h e s i x t h t e r m i s non zero. Neutrons do n o t have t o be p o l a r i z e d . c ) B o t h terms a r e n o t zero. I n p r i n c i p l e , t h e s i x t h term would be s u f f i -

c i e n t t o g e t B and p o l a r i z e d n e u t r o n s a r e n o t necessary. But we s h a l l see l a t e r t h a t p o l a r i z e d n e u t r o n s are, i n most cases, r e q u i r e d . 11- E a r l y B measurements ( n e u t r o n d i f f r a c t i o n )

rsl

The f i r s t experiment was done i n 1963 b y

C.G.SHUL~

o n a s i n g l e c r y s t a l o f vanadium. T h i s experiment was o f t h e c ) t y p e . I t was an o u t s t a n d i n g achievement, f o r t h e "V n u c l e i were v e r y p o o r l y p o l a r i z e d b y b r u t e f o r c e i n a r a t h e r modest f i e l d o f 1.3 t e s l a , and t h e l o w e s t t e m p e r a t u r e o b t a i n e d was o n l y 2.8 K. Under such c o n d i t i o n s , n u c l e a r p o l a r i z a t i o n o f V was o n l y 0.04 %! A n a l y s i s o f t h e s i x terms i n 3 ) shows t h a t t h e m a i n one i s bz, i n s p i t e o f t h e f a c t t h a t

''

V has t h e l o w e s t known s p i n independent n u c l e a r s c a t t e r i n g amp1 i tude. Two o r d e r s o f magni

-

tude below, we f i n d t h e 4 t h and 5 t h terms, 2bAMn and 2BIPn, t h e r e m a i n i n g t h r e e terms b e i n g a g a i n t w o o r d e r s o f maqnitude below. The f l i p p i n g r a t i o reduces t h e n t o

(4

-

I + = 1 + 4 AM + BIP

I

-

b

a c c o r d i n g t o a T" law. N u m e r i c a l l y , one c a l c u l a t e s f o r 4 ) :

TEVP I*.) I+ = 1

-

( 0 , 5 1 L ) l O - 5 1 4 2

0 T

---

= 0.99

Z t h e s i g n i n t h e p a r e n t h e s i s b e i n g t h a t o f B.

F i g 1, which g i v e s SHULL'S r e s u l t shows

-

Nuclear P01orlz0tl.n t h a t t h e experiment i s i n accordance w i t h

C • ( 4 ' ) and t h a t t h e 6 s i q n i s u n d o u b t l y

g

^0.97 p o s i t i v e .

The second experiment, a l s o o f t h e c ) t y p e was done 6 y e a r s l a t e r , a l s o by C.G. SHULL, w i t h Y. I T O ~ " , on c o b a l t . The a p p l i e d f i e l d and t e m p e r a t u r e were t h e same as i n t h e experiment on 51 V, b u t p o l a r i z a t i o n was enhanced

(0,7 % i n s t e a d o f 0,04 %) b y t h e h y p e r f i n e f i e l d o f c o b a l t 15 t i m e s h i g h e r t h a n t h e a p p l i e d f i e l d ,

The f i r s t experiment o f a ) t y p e was performed i n 1972 a t S a c l a y o n " F, under t h e i m p u l s e o f Pr. ABRAGAM who, w i t h h i s NMR group succeeded i n g e t t i n g evidence o f n u c l e a r a n t i f e r r o m a g n e t i c o r d e r on t h e f l u o r i n e s p i n s i n a CaF, c r y s t a l L 8 '

.

I t remained t o n e u t r o n s t o c o n f i r m t h e e x i s t e n c e o f t h i s o r d e r , and t h e c o r r e c t n e s s o f t h e a n t i f e r r o m a a n e t i c c o n f i g u r a t i o n which had been proposed f r o m t h e o r e t i c a l c o n s i d e r a t i o n s . But p r i o r t o u n d e r t a k i n g t h e expe- r i m e n t , one had t o be s u r e t h a t t h e B v a l u e o f

''

F would n o t b e t o o weak,

because one expected s u p e r l a t t i c e r e f l e x i o n s w i t h an i n t e n s i t y p r o p o r t i o n a l

2 4 9

t o 6 . The s p i n i n c o h e r e n t s c a t t e r i n g c r o s s - s e c t i o n o f F gave an i n f o r - m a t i o n o f v e r y p o o r accuracy :

0 6 1B

I <

0,15 10-12cm. We c a l l e d f o r h e l p n u c l e a r t h e o r e t i c i a n s i n Saclay who gave a s t i l l more p e s s i l ~ i s t i c v a l u e : B = -0,07 We t h e n performed t h e experiment on a CaF2 c r y s t a l h i g h l y p o l a r i z e d b y microwave t e c h n i q u e s w i t h t h e f o l l o w i n g r e s u l t : a l t h o u g h t h e B s i g n p r e d i c t e d b y n u c J ~ $ r th e o r e t i c i a n s was c o r r e c t , t h e magnitude was 8 t i m e s below t h e predictionL'": Such a low v a l u e r u l e d o u t any n e u t r o n t e s t o f t h e n u c l e a r AF s t r u c t u r e i n CaF2

.

And i t i s o n l y s i x y e a r s l a t e r t h a t n e u t r o n evidence c o u l d be g i v e n o f n u c l e a r AF o r d e r , b u t on a L i H crystalK"' where t h e l a r g e p r o t o n B v a l u e was much more f a v o u r a b l e .

One y e a r l a t e r , an experiment o f t h e b ) t y p e was performed, a l m o s t a t t h e same t i m e i n U S A " ~ ' and a t ~ a c l a y ~ ' ~ ' on holmium, w i t h t h e same r e s u l t except a l i t t l e more accuracy f o r t h e US v a l u e which was o b t a i n e d on a s i n g l e c r y s t a l . The S a c l a y experiment, a v e r y s i m p l e one, was done on a powder, w i t h u n p o l a r i z e d neutrons, w i t h o u t any magnetic f i e l d , and a t temperatures easy t o get, between 4.2 and 1.4 K I n b o t h experiments, t h e t r i c k was t h e presence i n Ho a t t h e s e temperatures o f a known o r d e r e d magnetic s t r u c t u r e L 4 4 ' and o f a v e r y s t r o n g h y p e r f i n e f i e l d

(-900 t e s l a ) which, even a t t e m p e r a t u r e as h i g h as 4.2 K gave n u c l e a r p o l a r i z a - t i o n o f t h e o r d e r o f 1 0 %.

L a t e r on, B v a l u e o f Tb was measured i n a TbAg a n t i f e r r o m a g n e t , i n USSR, b y t h e [I51

same method

.

JOURNAL DE PHYSIQUE

I 1 1

-

The concept o f n u c l e a r pseudomagnetism

Ten y e a r s ago, a new way f o r measuring B has been found, which i s easy t o understand f r o m t h e concept o f n u c l e a r pseudomagneti sm i n t r o d u c e d b y A. ABRAGAM.

L e t us r e c a l l formula 1 ) and t h e f o r m a l analogy p o i n t e d o u t b e f o r e between t h e

-b +

+

^-?

two terms 2 AMs and 2 B I s . Here a g a i n we dropped t h e s u b s c r i p t l o f M, i.e. we c o n s i d e r an experiment i n which m a g n e t i z a t i o n i s p e r p e n d i c u l a r t o t h e s c a t t e r i n g

-+

v e c t o r . We f u r t h e r a s s o c i a t e to+e$ch nucle:r+spin I a f i c t i t i o u s m a g n e t i c moment

-+

M* b y e q u a t i n g t h e two terms 2AM*s and 2 BI.s, which aives, b y d e f i n i t i o n o f +

I n a forward s c a t t e r i n g experiment, A = A,=, =

-

g, r, /2r,where

on= -

1.913 i s t h e n e u t r o n g f a c t o r , r o t h e c l a s s i c a l e l e c t r o n r a d i u s and

p,

t h e e l e c t r o n i c Bohr maaneton. From (5), one has :

-+

-3

( 5 ' ) = 3.70 61

B b e i n g expressed, as u s u a l i n 10-12cm.

We n o t e t h a t t h e s e f i c t i t i o u s moments, which ABRAGAM named " n u c l e a r pseudoma- g n e t i c moments" (NPM) a r e q u i t e comparable t o t h o s e o f paramagnetic atoms. For example f r o m ( 5 ' ) and t a b l e 11, ^WE can see t h a t t h e NPM o f t h e p r o t o n i s 5.4

p B .

Moreover, ABRAGAM p o i n t e d o u t t h a t s i n c e t h e 2 terms o f o p e r a t o r & were now so s i m i l a r , t h e y o u g h t t o have t h e same e f f e c t on t h e wave f u n c t i o n s i n any experiment w i t h n e u t r o n s . I n o t h e r words, an assembly o f n u c l e a r s p i n s w i l l have on n e u t r o n s t h e same e f f e c t as t h e assembly o f t h e i r a s s o c i a t e d NPM, I n p a r t i c u - l a r , n e u t r o n s c r o s s i n g a p o l a r i z e d t a r g e t o f N n u c l e i p e r u n i t volume, w i t h pseudomagnetic moment M* and p o l a r i z a t i o n P w i l l undergo t h e same e f f e c t s as

-+

i f a magnetic i n d u c t i o n B * ( a g a i n f i c t i t i o u s ) was a p p l i e d , t h i s "pseudomagnetic i n d u c t i o n " b e i n g g i v e n by

+ (6)g* = 4 K N M* P

As a consequence, n e u t r o n s p i n s w i l l p r e c e s s around t h e n u c l e a r p o l a r i z a t i o n P at a f r e q u e n c y

yrn

b e i n g t h e n e u t r o n gyromagnetic r a t i o ( y,=2,917 Hz/pauss).

Such an e f f e c t had been p r e v i o u s l y p r e d i c t e d , f r o m n e u t r o n o p t i c s 'j6'

.

^But

t h e v e r y s i m p l e and e l e g a n t concept o f n u c l e a r pseudomaqnetism l e a d s i n a s t r a i g h - f o r w a r d way t o t h e r e s u l t .

It remained of c o u r s e t o demonstrate t h e c o r r e c t n e s s o f t h e s e p r e d i c t i o n s . T h i s was done i n an experiment proposed b y ABRAGAM i n which p o l a r i z e d n e u t r o n s c r o s s i n g a LMN t a r g e t h i g h l y p o l a r i z e d , underwent a r e s o n a n t d e p o l a r i z a t i o n f r o m t h e pseu- domagnetic i n d u c t i o n a s s o c i a t e d w i t h p r o t o n p o l a r i z a t i o n ^rq73L483

I V

-

B measurements b y n e u t r o n p r e c e s s i o n

The above experiment r e q u i r e d h i g h n u c l e a r p o l a r i z a t i o n s and was s u c c e s s f u l o n l y because o f t h e l a r g e p r o t o n NPM.

works as f o l l o w s :

P o l a r i z e d n e u t r o n s processinqJn t h e gap o f a maanet o f u n i f o r m f i e l d Ho, e n t e r w i th-their p o l a r i z a t i o n para1 l e l t o Ho ( F i g 2 ) . They f i r s t c r o s s a c o i 1

C'

i n which f l o w s a c u r r e n t a t t h e n e u t r o n Larmor frequency, o f such i n t e n s i t y as t o g i v e a 90" t u r n t o t h e n e u t r o n s p i n s . So when t h e n e u t r o n s g e t o u t f r o m C' t h e i r s p i n s precess cohe-

+ r e n t l y i n t h e p l a n e normal t o Ho. They F i a . 2 t h e n c r o s s a second c o i l C " i d e n t i c a l t o t h e f i r s t one which a a a i n r o t a t e s t h e i r s p i n s t h r o u g h 90°, and t h u s come o u t f r o m

+

C" w i t h t h e i r s p i n s a n t i p a r a l l e l t o Ho. I f now one i n s e r t s a p o l a r i z e d t a r g e t on t h e n e u t r o n p a t h between t h e two c o i l s , n e u t r o n s w i l l f e e l , i n s i d e t h e t a r g e t , t h e

-+

pseudomagnetic i s u c t i o n

I% *

6 ) a s s o c i a t e d w i t h t h e n u c l e a r p o l a r i s a t i o n , i n a d d i t i o n t o t h e Ho f i e l d , which w i l l g i v e t o t h e n e u t r o n s p i n s an e x t r a p r e c e s s i o n angle

t b e i n g t h e t r a n s i t t i m e o f t h e n e u t r o n s across t h e t a r q e t .

It i s easy t o show t h a t t h e p o l a r i z a t i o n o f t h e o u t a o i n s n e u t r o n s i s t h e n -coso(

,

i n s t e a d o f -1 w i t h o u t t h e t a r q e t . T h i s p o l a r i z a t i o n , and t h u s a

,

may be e a s i l y measured w i t h an a n a l y s e r

-

a CoFe c r y s t a l f o r example

-.

And t h i s measurement, g i v e s @ * t h r o u g h e q u a t i o n 7), whence B f r o m 6 ) and 5 ) p r o v i d e d P i s known.

We f i r s t t e s t e d t h e e f f i c i e n c y o f t h i s method i n 1973, o n n u c l e i o f known B

5 (

value, namely A~ and V"". T h e r e a f t e r , B v a l u e o f some 30 n u c l e i were measu- r e d i n t h i s way C20'-25J

.

For economical reasons, we began w i t h m e t a l s t h a t n a t u r e s u p p l i e d as p u r e i s o t o p e s . N u c l e a r p o l a r i z a t i o n was o b t a i n e d b y b r u t e f o r c e i n a f i e l d o f 2.5 t e s l a , a t temperatures down t o 40 mK w i t h a d i l u t i o n c r y o s t a t .

Fig.3 shows, as an example, t h e r e s u l t o f an experiment on ' ? ~ l showing t h e v a r i a t i o n o f o( a g a i n s t T-" i . e t h e n u c l e a r p o l a r i z a t i o n . B i s o b t a i n e d f r a n t h e s l o p e o f t h e l i n e across t h e p o i n t s .

Some B v a l u e s were o b t a i n e d i n i n s u l a t o r s p o l a r i z e d b y microwave t e c h n i q u e s (dynami c a l p o l a r i z a t i o n c 2 6 J ). T h i s p o l a r i z a t i o n t e c h - n i q u e has many advantages compared t o b r u t e f o r c e :

120

100 80 6 0

- a [deg]

-

@'

- /

- , )

L O

25,85 mm

- 4 0

[K-'1

- 6 0

,

I

10 2 0 3 0

JOURNAL DE PIIY S IQUE

It works w i t h i n s u l a t o r s

-

P o l a r i z a t i o n s o b t a i n e d a r e an o r d e r o f maqni tude h i g h e r

-

The p o l a r i z a t i o n ranqe may be doubled owing t o t h e f a c t t h a t p o l a r i - z a t i o n may be + o r

-.

^It may b e p o s s i b l e t o p o l a r i z e s e l e c t i v e l y and t h u s t o s o r t o u t t h e c o n t r i b u t i o n o f d i f f e r e n t chemical s p e c i e s and ( o r ) i s o t o p e s i n t h e sample.

The disadvantages a r e : one o f t e n needs a s i n g l e c r y s t a l , c o n v e n i e n t l y doped w i t h c o n v e n i e n t m a g n e t i c i m p u r i t i e s , and p o l a r i z a t i o n i s sometimes measured l e s s a c c u r a t e l y .

V

-

B measurements f r o m s c a t t e r i n g c r o s s - s e c t i o n s

We mentioned i n t h e b e g i n n i n g t h a t a measurement o f t h e s p i n i n c o h e r e n t c r o s s - s e c t i o n a l l o w e d t o g e t [ B l , b u t 1) t h a t t h e s i g n o f B remained unknown, and 2) t h a t a c c u r a t e measurement o f t h i s c r o s s - s e c t i o n was d i f f i c u l t .

T h i s was t r u e i n t h e e a r l y s t a t e o f t h e a r t . But d u r i n g t h e l a s t t w e n t y years, improved methods f o r a c c u r a t e measurements o f s c a t t e r i n g a m p l i t u d e s and c r o s s - s e c t i o n s have been used : m i r r o r r e f l e c t i o n , q r a v i t a t i o n , C h r i s t i a n s e n f i l t e r s , s m a l l a n g l e s c a t t e r i n g , p r i s m r e f r a c t i o n , t r a n s m i s s i o n , dynamical d i f f r a c t i o n , n e u t r o n i n t e r f e r o m e t r y C z 3 ' . From a c c u r a t e measurements o f 1) t h e n u c l e a r s c a t t e - r i n g a m p l i t u d e 2 ) t h e t o t a l c r o s s - s e c t i o n i n t h e eV ranae and 3 ) c a p t u r e c r o s s - s e c t i o n , i t i s p o s s i b l e t o e x t r a c t t h e s p i n i n c o h e r e n t s c a t t e r i n g c r o s s - s e c t i o n and t h e n t h e a b s o l u t e v a l u e o f B w i t h p r e t t y good accuracy. I t remains t o decide on t h e s i g n . Here aqain, much more i s known now c o n c e r n i n a t h e n e u t r o n resonances o f n u c l e i and t h e a s s o c i a t e d parametersc283. f r o m which i t becomes p o s s i b l e t o guess t h e s i g n of B

.

I n t h i s way, KOESTER a n d RAUCH o b t a i n e d t h e B v a l u e s o f

some 3 0 n u c l e i ^C291 V I

-

And so what ?

We must now answer t h e l a s t q u e s t i o n : o f what i n t e r e s t a r e t h e s e measurements?

The f i r s t answer i s o b v i o u s : t h e y a r e fundamental d a t a l i k e n e u t r o n s c a t t e - r i n g a m p l i tudes.

From a t h e o r e t i c a l p o i n t o f view, t h e y p l a y a m a j o r r o l e i n s h e l l model c a l c u - l a t i o n s , a t l e a s t f o r n u c l e i o f l i g h t and medium a t o m i c mass.

From t h e e x p e r i m e n t a l p o i n t o f v i e w one m i g h t say t h a t n e u t r o n d i f f r a c t i o n w i t h p o l a r i z e d t a r g e t s i s now a w e l l e s t a b l i s h e d technique. So i f we can c o n t r o l t h e p o l a r i z a t i o n o f some p a r t i c u l a r n u c l e u s o f known B value, we can v a r y i t s s c a t t e - r i n g a m p l i t u d e and g e t t h e r a t i o o f t h e s t r u c t u r e f a c t o r f o r t h a t n u c l e u s t o t h e s t r u c t u r e f a c t o r o f t h e c e l l . T h i s may o f f e r a way t o o l v e t h e phase problem i n s t r u c t u r e d e t e r m i n a t i o n : HAYTER, JENKIN and WHITEG'J have demonstrated t h a t such a t e c h n i q u e c o u l d p o s s i b l y be used.

It i s a l s o p o s s i b l e , i n p r i n c i p l e , t o g e t a p e r f e c t n e u t r o n p o l a r i z e r , f r o m a c r y s t a l i n which, f o r some v a l u e o f P and some B r a g g r e f l e c t i o n , t h e r e would be f o r one n e u t r o n s p i n s t a t e an e x a c t c a n c e l l a t i o n o f t h e s p i n dependent and s p i n independent p a r t s o f t h e s t r u c t u r e amp1 i tude.

I n t h e measurement o f B by precession, I mentioned t h a t we g e t i n f a c t t h e p r o d u c t o f B b y t h e n u c l e a r p o l a r i z a t i o n P. Whence B p r o v i d e d P i s known. But t h e converse i s t r u e : i f B i s known, one g e t s P. T h i s may b e o f i n t e r e s t i n t h e case where NMR l i n e s a r e broadened beyond d e t e c t i o n , o r f o r a d e t e r m i n a t i o n of h y p e r f i n e f i e l d s . L e t us add t h a t t h e same k i n d o f experiment a1 lows t o measure t h e s p i n - l a t t i c e r e l a x a t i o n t i m e TA o f t h e p o l a r i z e d n u c l e i , i f n o t t o o s h o r t .

guessed, Pr. ABRAGAM. P-ROUBEAU and more r e c e n t l y , J. COUSTHAM a r e r e s p o n s i b l e f o r t h e i m p o r t a n t c r y o g e n i c p a r t . H. GLATTLI, and l e s s permanently A. MALINOVSKI and J. FOURMOND a r e m a i n l y concerned w i t h t h e n o t l e s s i m p o r t a n t NMR p a r t , and G.L. BACCHELLA, M. PINOT and me w i t h t h e p o l a r i z e d neutrons.

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