Temperature dependence of the positron lifetime in H2O and D2O

PHYSICS LETTERS

Volume 31A, number 3

In fig. 1 the quantity D(r) = 4 ~ Z -1 r 2 p(r) f o r k = = 0.6397 is c o m p a r e d with e x a c t v a l u e s c o m puted by I . a n g e r and Vosko [3]. F r o m eq. (5) one d e r i v e s two useful r e s u l t s : p(0) ~ Z r 3 r l _~ a r c c o t b ] 87T t~

A m o r e d e t a i l e d account of the p r e s e n t work with i n c l u s i o n of exchange and with e x t e n s i o n s to o t h e r gas d e g e n e r a c i e s and to n o n - s t a t i c p e r t u r b a t i o n s will be r e p o r t e d shortly.

(6)

References

and for large r,

Zak

1. c. Kittel, Quantum theory of solids (John Wiley and Sons, Inc., New York, 1963) Chapt. 6. 2. J. Worster and N. H. March, J. Phys. Chem. Solids 24 (1963) 1305. 3. J. S. Langer and S. H. Vosko, J. Phys. Chem. Solids 12 (1960) 196. 4. N. H. March and A. M. Murray, Proe. Roy. Soe. A261 (1961) 119; A266 (1962) 559. 5. Handbook of mathematical functions (US Department of Commerce, National Bureau of Standards, AMS 55, 1965).

Zb 2 cos (2L,r) +

p(r) ~ - 2 - ~ r e x p ( - y r ) + 4~c

9 February 1970

r-------5~

Zb4(b 2 - 3) sin (2kr) 8c 2

r4

T h e exponential t e r m and the t e r m in r -4 of eq. (7) y i e l d s i g n i f i c a n t n u m e r i c a l c o r r e c t i o n s (see fig. 1) to the r - 3 t e r m ( F r i e d e l wiggle) in the c r i t i c a l l a t t i c e r a n g e : 3 < wr < 6. *****

TEMPERATURE

DEPENDENCE IN H20

OF THE POSITRON AND D20

LIFETIME

K. PETERSEN, M. E L D R U P and G. TRUMPY Laboratory of Applied Physics H, Technical University of Denmark, Lyngby, Denmark Received 8 December 1969

It has been found that the lifetime 72 and the intensity 12 of triplet positronium in light and heavy water show a sudden transition at the respective melting points for the two substances.

S e v e r a l l i f e t i m e - m e a s u r e m e n t s on p o s i t r o n s a n n i h i l a t i n g in light w a t e r and i c e h a v e been r e p o r t e d [1-3]. Th e r e s u l t s of r e f . 3 i n d i c a t e that a sudden change in the l i f e t i m e T2 and the i n t e n s i t y / 2 of t r i p l e t p o s i t r o n i u m t a k e s p l a c e at 4 o c . A n g u l a r c o r r e l a t i o n r e s u l t s show, on the o t h e r hand, a t r a n s i t i o n at 0 o c [3-6]. In o r d e r to study t h i s a p p a r e n t d i s c r e p a n c y we h a v e c a r r i e d out l i f e t i m e - m e a s u r e m e n t s f o r p o s i t r o n s in both H 2 0 and D 2 0 , which h a v e s o m e w h a t d i f f e r e n t phase transition temperatures. T h e p o s i t r o n s o u r c e c o n s i s t e d of about 35 ~Ci 22NaC1 in each e x p e r i m e n t . T h e c y l i n d r i c a l s a m p l e of 10 m m diam. × 10 m m height w a s e n c l o s e d in a L u c i t e c o n t a i n e r . T r i p l e d i s t i l l e d w a t e r was used f o r the H 2 0 - s a m p l e and the D 2 0 - s a m p l e w a s of 9 9 . 9 9 % p u r i t y . In the c a s e of H 2 0 , an e v a p o r a t e d s o u r c e w a s s e a l e d b e t w e e n two p i e c e s of P V C - f o i l and i m m e r s e d in

the liquid. T h i s method gave a c o r r e c t i o n of 23% f o r annihilation in the P V C - f o i l . In the D 2 0 - c a s e the s o u r c e w as d i s s o l v e d in the liquid, giving a c o r r e c t i o n of 5.4% f o r annihilation in the c o n t a i n e r walls. Co n t r o l m e a s u r e m e n t s with the s o u r c e d i s s o l v e d in H 2 0 gave the s a m e r e s u l t s a s with the ' s a n d w i c h ' s o u r c e . A s d e t e c t o r s w e r e used Naton 136 1 in. × 1 in. c y l i n d e r s coupled to RCA 8575 p h o t o m u l t i p l i e r s . Th e l i f e t i m e s p e c t r o m e t e r c o n s i s t e d of the O r t e c 'leading-edge' system. Overall time resolution was T~ = 60 p s e c with -rFWHM = 460 p s e c . Th e s a m p l e t h e r m o s t a t was c o n t r o l l e d by a N T C - r e s i s t e r , and t e m p e r a t u r e was m e a s u r e d to within + 0 . 5 o c with a N i C r - N i t h e r m o c o u p l e . A t y p i c a l l i f e t i m e s p e c t r u m , as shown in fig. 1, can be r e s o l v e d into 3 co m p o n en t s. T h e i r l i f e t i m e s and i n t e n s i t i e s a r e c a l l e d -r2, r0, r 1 and I2, I0, I1 r e s p e c t i v e l y , as shown in the 109

Volume 31A, number 3

PHYSICS LETTERS

9 February 1970

~:o,1:,,~:2[nsec]

Counts [log scale] oo %+oo

Ice ~

2.0 -

0

.

~

D20 H20

~ Water ~1

0

~

1.0

.

.

~ i ]

.,,{

+- "°+ +: ++ i • o I °°I° • o

t I

• •

I

.o,°, i

°"

° t"-

.11 • "

o

2

~

I2 I2

o\'~2,1z

4

I

6 T [,sec]

I

i

I

I

1

I.

l I I

I_9_2 11

Fig. 1. Resolved lifetime spectrum for annihilation of positrons in D20, T = -21.7oc.

IL

I

5(

:o,lo

I

I

12 [°Io]

10 -~

10

"1:2

0 0

f i g u r e . T h e r e s o l u t i o n of the t i m e s p e c t r a is done under the a s s u m p t i o n that each c o m p o n e n t is an e x p o n en t i al function folded with the p r o m p t c u r v e . It is b e l i e v e d that T0, I 0 c o r r e s p o n d to a n n i h i l a t i o n of f r e e p o s i t r o n s , while T1, I 1 and r 2 , 12 c o r r e s p o n d to annihilation of s in g l e t and triplet positronium respectively. A graphical c o l l e c t i o n of the r e s u l t s i s given in fig. 2. I 1 and r l in the l i q u i d s had too l a r g e u n c e r t a i n t i e s to be determined. Fig. 2 c l e a r l y shows that the p o s i t r o n t r a n s i tion t e m p e r a t u r e s f o r v2 and 12 c o i n c i d e with the s o l i d - l i q u i d p h a s e t r a n s i t i o n t e m p e r a t u r e s both in H 2 0 and in D20. It i s a r e m a r k a b l e , and h i t h e r t o unexplained f act , that r 2 i n c r e a s e s while 12 d e c r e a s e s upon m e l t i n g . T h i s e f f e c t i s even s t r o n g e r in D 2 0 than in H20. Within e x p e r i m e n tal u n c e r t a i n t i e s the p r o d u c t 12 ~2 i s constant o v e r the p h a s e t r a n s i t i o n in H 2 0 , as a l s o found in r e f . 3. It i s about 20% s m a l l e r in h e a v y w a t e r than in h eav y i c e . No c h a n g e s w e r e found in the r e g i o n -18 to - 2 5 o c as o b s e r v e d in a n g u l a r c o r r e l a t i o n w o r k [5, 6].

110

0 ~

0 0

•

0

2

,

!°<

I , + [°?! I I t 0 -50 -30 -10 0 *3.8 +I0 Fig. 2. The lifetimes T 2, 70 and r l , the intensity 12 and the ratio 12[I 1 as a function of temperature for H20 and D20. F u r t h e r d e t a i l s and d i s c u s s i o n s of t h e s e r e s u i t s will a p p e a r in a f o r t h c o m i n g p a p e r .

References 1. w. Brandt, S. Berko and W. W. Walker, 120 (1960) 1289. 2. G. Fabri, E. Germagnoli, I. F. Quercia risi, Nuovo Cimento 30 (1963) 21. 3. P. Jauho and M. Virnes, Phys. Letters 208. 4. R. L. De Zafra and W. T. Joyner, Phys.

Phys. Rev. and E. Tur26A (1968) Rev. 112

(1958) 19. 5. P. Colombino, B. Fiseella and L. Trossi, Nuovo Cimento 38 (1965) 707. 6. L. Smedskjaer, to be published.