DETERMINATION OF h/mn

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DETERMINATION OF h/mn

E. Krüger, W. Nistler, W. Weirauch

To cite this version:

E. Krüger, W. Nistler, W. Weirauch. DETERMINATION OF h/mn. Journal de Physique Colloques, 1984, 45 (C3), pp.C3-217-C3-222. �10.1051/jphyscol:1984336�. �jpa-00224050�

DETERMINATION OF h/mn

E. Kriiger, W. Nistler and W. Weirauch

~hysikalisch-Technische Bundesanstalt, Postfach 3345, 0-3300 Braunschweiq, F.R .G.

and Institut Laue-Langevin, 156X, F-38042 Grenoble Cedex, France

Re'sume' - La connaissance des constantes fondamentales p e u t @ t r e amgliorge en 3 F E E i i n a n t de fason pre'cise l e r a p p o r t h/mn ( h constante de Planck, mn masse

du neutron). Une mesyre p r e ' l i m i n a i r e de h/mn avec une i n c e r t i t u d e r e l a t i v e d ' e n v i r o n 10-5 e s t d e c r i t e . E l l e a e'te' effectue'e aupr\es du re'acteur de 1 ' I n s t i t u t Laue-Langevin Grenoble.

A b s t r a c t - Knowledge o f the fundamental constants can be improved by precise- l y determining t h e r a t i o h/mn ( h Planck constant, mn neutron mass). A p r e l i m - i n a r y measurement o f h/mn w i t h a r e l a t i v e u n c e r t a i n t y o f about 10-5 i s de- scribed. I t has been c a r r i e d o u t a t the r e a c t o r o f the I n s t i t u t Laue-Langevin i n Grenoble.

1. I n t r o d u c t i o n

The recommended values o f the fundamental constants are t h e r e s u l t s o f least-squares adjustments which use measured values o f these constants as w e l l as combinations o f them as i n p u t parameters. The l a s t adjustment was c a r r i e d o u t by Cohen and T a y l o r /1/ i n 1973.

A measured value o f h/mn ( h Planck constant, mn neutron mass) would be a very help- f u l new i n p u t parameter f o r t h e adjustment, provided t h a t i t s r e l a t i v e u n c e r t a i n t y i s n o t l a r g e r than about 1x10-6.

h/mn can be determined by simultaneously measuring t h e wavelength A and t h e veloc- i t y v o f monochromatic neutrons. By means o f t h e de B r o q l i e equation, i t f o l l o ~ s from these two q u a n t i t i e s t h a t

h/mn = Av. (1)

Several methods f o r such an experiment have been proposed /2-4/. The one which gives the best chance o f achieving h i g h accuracy /4/ has been used i n a p r e l i m i n a r y deter- m i n a t i o n o f h/mn.

2. The measuring method 2.1. The p r i n c i p l e

--- ---

For measuring the v e l o c i t y o f the neutrons, a beam o f p o l a r i z e d neutrons i s modu- l a t e d by p e r i o d i c a l l y changing the d i r e c t i o n o f the p o l a r i z a t i o n vector. A f t e r a p a t h o f several meters, the neutrons a r e b a c k - r e f l e c t e d by a s i 1 ic o n s i n g l e - c r y s t a l .

They thus pass the modulator f o r a second time, where the beam i s again modulated.

The modulator defines the beginning as w e l l as the end o f a f l i g h t path. The t o t a l modulation i s measured as a f u n c t i o n o f the l e n g t h o f t h e f l i g h t path. The v e l o c i t y o f the neutrons f o l l o w s from t h i s p e r i o d i c f u n c t i o n .

The wavelength o f the neutrons i s determined by b a c k - r e f l e c t i o n i n the s i l i c o n c r y s t a l . S i l i c o n i s used because almost p e r f e c t c r y s t a l s can be grown from t h i s ma- t e r i a l and i t s l a t t i c e parameter i s known w i t h the r e q u i r e d small u n c e r t a i n t y /5,6/.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984336

C3-218 JOURNAL DE PHYSIQUE

A p o l a r i z e d neutron beam i s produced by Bragg r e f l e c t i o n i n a Heusler c r y s t a l H1

.

-Fig. 1 - Arrangement f o r measuring h/mn. (HI, HZ) Heusler c r y s t a l s , ( F ) f l i p p i n g c o i l , ( C l , C2) Mezei c o i l s , (M) meander c o 3 , ( S i ) s i l i c o n c r y s t a l , (D) d e t e c t o r .

--C BO magnetic i n d u c t i o n o f the guide f i e l d , B magnetic i n d u c t i o n magnetizing a Heusler c r y s t a l , 7 p o l a r i z a t i o n v e c t o r i f t i e meander c o i l i s n o t o p e r a t i n g .

I n the f l i p p i n g c o i l F i s reversed. The neutrons then h i t a second Heusler c r y s t a l HZ which i s magnetized i n the same d i r e c t i o n as HI. Due t o the r e v e r s i o n o f 8, ^{t h e}

neutrons can t r a v e r s e i t w i t h o u t r e f l e c t i o n . I n the Mezei c o i l C 1 8 i s subsequently turned i n t o the d i r e c t i o n o f t h e x a x i s .

The neutrons t r a v e r s e t h e modulating assembly M, which should be disregarded a t t h e moment, and a second Mezei c o i l C2. They are then r e f l e c t e d by the s i l i c o n c r y s t a l mentioned above and r e t u r n t o c o i l C1.

Along t h e e n t i r e path, from l e a v i n g c o i l C1 t o reaching i t again, 7 precesses i n the guide f i e l d . But t h e precession i s c a n c e l l e d by a technique which i s s i m i l a r t o t h e spin-echo technique f i r s t used by Mezei / 7 / . F o r t h i s purpose c o i l C2 i s required.

As t h e r e s u l t 3 i s again p a r a l l e l t o t h e x a x i s when t h e neutrons e n t e r c o i l C 1 f o r the second time.

I n c o i l C l , 3 i s t u r n e d back i n t o t h e d i r e c t i o n o f t h e z a x i s . The neu rons impinge on t h e Heusler c r y s t a l H2 f o r a second time. Because 3 i s p a r a l l e l t o H, t h e neu- t r o n s are again n o t r e f l e c t e d . They cannot t h e r e f o r e reach d e t e c t o r D.

a

Assembly M used f o r modulating t h e neutron beam c o n s i s t s o f an aluminium f o i l , bent t o form a meander. I t i s t h e r e f o r e r e f e r r e d t o as a meander c o i l .

The meander c o i l forms a close sequence o f s i n g l e c o i l s , each w i t h one t u r n . I f an e l e c t r i c c u r r e n t i s passed through them, t h e magnetic i n d u c t i o n s i n neighbouring c o i l s a r e a n t i p a r a l l e l . I f a l t e r n a t i n g c u r r e n t i s used, t h e r e i s a phase d i f f e r e n c e o f .rr between the magnetic i n d u c t i o n s i n the neighbouring c o i l s . An arrangement o f t h i s type, operated w i t h d i r e c t c u r r e n t , was used by Drabkin e t a l . /8/ f o r the c o n s t r u c t i o n o f a v e l o c i t y f i 1 t e r f o r p o l a r i z e d neutrons.

To modulate t h e d i r e c t i o n o f F, t h e meander c o i l i s operated w i t h high-frequency a l t e r n a t i n g c u r r e n t . The c o i l f i e l d i s p a r a l l e l t o the guide f i e l d . The thickness s o f the s i n g l e c o i l s i s such t h a t t h e neutrons pass each o f them i n h a l f a p e r i o d o f

i n a l l o f them. I n the whole meander c o i l the precession angle adds up t o

Q ( t ) = 2 ^{COS Zsvt,} ( 2 )

( v frequency o f t h e e l e c t r i c c u r r e n t , t time, N number o f ~ i n g l e c o i l s o f which the meander c o i l consists,.p, magnetic moment o f t h e neutron, Bm amplitude o f the a l t e r - n a t i n g magnetic induction w i t h i n t h e c o i l ).

When the neutrons leave the meander c o i l f o r t h e f i r s t time, the d i r e c t i o n of $ i s modulated as given by Eq. ( 2 ) . p i s a t any time i n t h e xy plane (see F i g . 1). Re- t u r n i n g from the s i l i c o n c r y s t a l , t h e neutrons t r a v e r s e the meander c o i l f o r a second time. The d i r e c t i o n o f b i s again modulated, t h i s time by the angle

where 1 i s the distance between the meander c o i l and t h e s i l i c o n c r y s t a l . The two modulations add up t o the t o t a l modulation

A f t e r the second modulation, t h e neutrons t r a v e r s e c o i l C 1 i n which p ' i s t u r n e d from the xy plane i n t o the y z plane. ~ ~ ~ ( t , l ) i s then the angle between r a n d the z a x i s .

The neutrons again h i t t h e Heusler c r y s t a l HZ. Because the d i r e c t i o n o f ? v a r i e s , the p r o b a b i l i t y o f r e f l e c t i o n varies, too. Hence, a time-dependent neutron c u r r e n t reaches the d e t e c t o r . The d e t e c t o r measures the mean neutron c u r r e n t I which i s given by

- 1(1) = ( 1 ~ 1 2 ) - ~ ~ [ 2 9 ~ 0 ~ ( 2 n v l / v f l l . ( 6 ) Jo i s the zero-order Bessel function,-and I the neutron c u r r e n t i f $ i s a n t i - p a r a l l e l t o the z a x i s . F i g . 2 shows 1(1)/1: as c a l c u l a t e d f o r % = 0.61 a and

,.

Fig. 2 - C a l c u l a t e d r a t i o Y / I o as a f u n c t i o n o f the distance 1. Parameter: (a)

1 = 0.61 a, ( b ) 3 = 1.22 a.

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The v e l o c i t y o f t h e neutrons i s given by

v = 2Alv , ( 7

as f o l l o w s from Eq. (6): a1 i s the d i f f e r e n c e between values o f 1 belonging t o neighbouring minima o f I ( l ) / I o

.

I n o r d e r t o determine v w i t h h i g h accuyacy, a l a r g e m u l t i p l e o f a1 must be meas- ured. For t h i s purpose, two minima o f I ( l ) / I are determined, the 1 values o f which d i f f e r by several meters. To change 1, the d a n d e r c o i l i s moved.

3. P r e l i m i n a r y measurement

The measuring method was f i r s t t e s t e d a t t h e r e a c t o r o f the Physikalisch-Technische Bundesanstal t /9-11/. The experiments turned o u t very s u c c e s s f u l l y , and h/mn c o u l d be determined w i t h a r e l a t i v e u n c e r t a i n t y o f 1 x 10-3. However, d e t a i l e d t e s t s could n o t be c a r r i e d o u t because o f the small neutron c u r r e n t . The measurements were t h e r e f o r e continued a t t h e h i g h - f l u x r e a c t o r o f t h e I n s t i t u t Laue-Langevin i n Grenoble .

A p r e l i m i n a r y version o f the apparatus i s i n s t a l l e d a t t h e thermal neutron guide H21.

The neutrons are r e f l e c t e d o u t o f the guide by o r i e n t e d g r a p h i t e . They then h i t the Heusler c r y s t a l H1 ( s e e F i g . 1).

The arrangement i s as schematically shown i n F i g . 1, except f o r a small d i f f e r e n c e : the neutrons r e f l e c t e d by the c r y s t a l HZ do n o t reach d e t e c t o r D d i r e c t l y . They are f i r s t r e f l e c t e d by an a d d i t i o n a l c r y s t a l ( o r i e n t e d o r a p h i t e ) . Thus those neutrons which c r y s t a l H2 s c a t t e r s i n e l a s t i c a l l y o u t o f the incoming beam cannot reach the d e t e c t o r . I n t h i s way t h e background c o u l d considerably be reduced.

The (331) r e f l e c t i o n o f s i l i c o n i s used, corresponding t o t h e wavelength ~=0.2492 nm.

The meander c o i l i s made o f aluminium f o i l , 60 pm t h i c k and 90 mm wide. I t c o n s i s t s o f N = 99 s i n g l e c o i l s , each o f which i s s = 1.058 mm t h i c k . The modulation f r e - quency i s v = 750.3 kHz. The meander c o i l can be moved by 50 cm. I t s displacement i s measured by means o f a l a s e r i n t e r f e r o m e t e r .

Fig. 3 - Mean neutron c u r r e n t 7 measured as a f u n c t i o n of the displacement L o f t h e meander c o i 1.

minima have been o m i t t e d between the two stages o f the measurement, f o l l o w i n g from t h e p r e v i o u s l y known value o f h/m,.

A curve o f the t h e o r e t i c a l l y expected shape i s f i t t e d t o the measured values. From the p o s i t i o n s o f t h e i r minima i t f o l l o w s t h a t :

I n accordance w i t h the p r e l i m i n a r y character o f the measurement, no systematic un- c e r t a i n t i e s have been considered.

The measured value o f h/mn i s i n good agreement w i t h the more accurate one calcu- l a t e d from the recommended values o f h and mn /I/, which i s

4. The f i n a l experiment i n p r e p a r a t i o n

I n o r d e r t o reduce the u n c e r t a i n t y o f the measurement by an o r d e r o f magnitude, a new apparatus i s under c o n s t r u c t i o n . I t d i f f e r s from the p r e l i m i n a r y v e r s i o n i n the f o l l o w i n g p o i n t s :

a) The distance 1 can be v a r i e d by 10 m.

b) The neutron beam and the measuring l i g h t beam o f t h e l a s e r i n t e r f e r o m e t e r are i n - side a vacuum chamber, thus i n c r e a s i n g the neutron c u r r e n t and a v o i d i n g correc- t i o n s o f the 1 ig h t wave1 ength.

c ) The mechanical set-up i s very precise, and d e v i a t i o n s from t h e c o r r e c t adjustment are a u t o m a t i c a l l y corrected.

5. Conclusion

A p r e l i m i n a r y measurement o f h/mn w i t h a r e l a t i v e u n c e r t a i n t y o f about has been c a r r i e d o u t a t t h e r e a c t o r o f the I n s t i t u t Laue-Langevin i n Grenoble. The experiment showed t h a t i t should be possible t o reduce the u n c e r t a i n t y by a f u r t h e r o r d e r of magnitude. An apparatus s u i t e d f o r such a measurement i s under c o n s t r u c t i o n . Acknowl edgements

The authors would l i k e t o thank M.M. W. Berne, H. Schneider and J . Zorn f o r t h e i r h e l p i n c o n s t r u c t i n g and t e s t i n g t h e apparatus.

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