LETTERE AL A'UOVO CIMENTO

VOL. 4, ~. 11

15 Luglio 1972

Measurement of the Rate ~e for the Reaction ~pq d - > ~ d ~ p Temperature. A. BERTIN, ~.

at Room

B R U N O and A. V I T A L E

I s t i t u t o d i .Fisica dell' U n i v e r s i t h - B o l o g n a I s i i t u t o 5Vazionale d i f f i s i c a _Nucleate - S e z i o n e d i B o l o g n a A . P L A C C I and E. ZAVATTINI

CERN

- Geneva

(rieevuto il 15 Maggio 1972)

The t r a n s f e r r a t e 2 e of a n e g a t i v e m u o n from a p r o t o n to a deuteron, a c c o r d i n g to the process

(1)

~ t p + d ~ ~td+p-,~ 135 eV ,

was s t u d i e d b y several groups (1.4). As m a y be seen f r o m T a b l e I, t h e e x p e r i m e n t a l results for ).~ are r a t h e r similar, and t h e i r order of m a g n i t u d e s agree w i t h t h e corresponding theoretical predictions. T h e m o r e precise e x p e r i m e n t a l v a l u e (BL]~S]~R et al. (a)) was o b t a i n e d in a t a r g e t of liquid h y d r o g e n , w h e r e a s a smaller value, w i t h a larger error, was g i v e n b y DZI-I:EL~3POV et al. (4), w h o u s e d a h y d r o g e n diffusion c h a m b e r at a p r e s s u r e of a b o u t 20 a t m and a t e m p e r a t u r e of 275 ~ Process (1) was i n v e s t i g a t e d in t h e p a s t for m a i n l y two reasons: i) it is one of t h e m o s t e l e m e n t a r y reactions in t h e field of m u - m o l e c u l a r physics, ii) as for several m u - m o l e c u l a r p h e n o m e n a , t h e k n o w l e d g e of t h e r a t e of reaction (1) is of chief i m p o r t a n c e to u n d e r s t a n d t h e results of t h e rouen c a p t u r e experim e n t s in h y d r o g e n (5) and d e u t e r i u m (s.7).

(i) S. COHEN', D. "f'. JUDD a n d R. 3. RIDDELL: P h y s . Rev.o 119, 397 (1960). (J) V. B. BELYAEV, S. S. GERSHTEIN, B. N. ZAKHAR'EV I~nd S. P. LOI~N'EV: ~ur~$. J~ksp. Tear. Fig., 37, 1652 (1959) ( E n g l i s h t r a n s l a t i o n : Soy. Phys. JIgTP, 10, 1171 (1960)). (1) E. J. BLESER, ]~. W . AN'DERSON', I4. ~[. LEDERMAN., S. L. M E Y E R , J. L. ROSEN, ~. E. R O T H B E R G a n d I. T. WANG: Dhys. Rev., 132, 2679 (1963); O. CON.FORTO, C. RUBBIA, ]~. ZAVATTIN.I a n d S. FOCARDI: Nuovo Cimento, 33, 1001 (1964). (4) V. P. DZHELEPOV, P. F. ~.RMOLOV, E. A. KUSHNIRE.N'KO, V. I. MOSK.~LEY a n d S. S. GF,RSHT~I~r: Zurn. Eksp. Teor. Fiz., 42, 439 (1962) ( E n g l i s h t r a n s l a t i o n : Soy. Phys. J E T P , 1S, 306 (1962)). (6) R. HILDEBRAND: Phys. Rev. Left., 8, 34 (1962); E. J. BLESER, L. IVI. LEDER,~VL4.N',J. L. ROSEN', J. E. ROTHBERO adl(1 E. ZAVATTIN'I: Phys. Rev. Lett., 8, 288 (1962); E. BERTOLINI, A. CITRON, G. GI~LI~&NELLA, S. FOCXRDI, A. MUK~N, C. RUBBIA a n d F. SAPORETTX: Proceedings o/ the International Gonyerence on

449

450

A. BERTIN~ .~. B R U N O , A. VITAL]'], A. PLACCI

and E. ZAVATTINI

TABLE I. -- S u m m a r y o] theoretical and experimental results on 2~ (*). Authors

COHEN et al. (o)(**)

BELYAEV et al. (b)(*o)

BLESER et al. (c)

DZHELEPOV et al. (~)

Present experiment

~t~. 10 -1~ (s -I)

1.4

1.43

1.43 =t= 0.13

^u.g,~_o.21 .~.+o.84

0.84 -{- 0.13

H~ density (molecules cm -8)

--

--

2.11 91022

5.102~

1.5.1020

T e m p e r a t u r e (~ exp, condition)

--

--

20.4

275

293

(*) T h e v a l u e s f o r ~e r e p o r t e d i n t h f s T a b l e r e f e r to t h e r a t e a t w h i c h process (1) t a k e s p l a c e w h e n t h e d e n s i t y of d e u t e r i u m m o l e c u l e s is e q u a l t o 2 . 1 1 . 1 0 ~ m o l e c u l e s cm-*. (**) T h e o r e t i c a l v a l u e s . (a) See r e f . (~). (b) See r e f . (*). (c) See r e f . ('). (d) See r e f . (').

F o r a correct i n t e r p r e t a t i o n of the latest m u o n c a p t u r e e x p e r i m e n t in gaseous deut e r i u m (v), in particular, it was felt t h a t a more direct d e t e r m i n a t i o n of 2. was requested, to be p e r f o r m e d in the same conditions in which t h e e x p e r i m e n t itself had been done. W e h a v e p e r f o r m e d this m e a s u r e m e n t at t h e m u o n channel of t h e 600 MeV C E R N s y n c h r o c y c l o t r o n , b y slowing-down n e g a t i v e muons in a gaseous t a r g e t of u l t r a p u r e h y d r o g e n , c o n t a m i n e d b y small a m o u n t s of d e u t e r i u m and xenon. T h e e x p e r i m e n t was carried out using an a l r e a d y existing a p p a r a t u s (s.9) to m e a s u r e t h e t i m e distrib u t i o n of t h e d e c a y electrons c o m i n g from m u o n s stopped in t h e gaseous target. In t h e m e n t i o n e d e x p e r i m e n t a l conditions, t h e initially f o r m e d ~p muonic a t o m s diffuse t h r o u g h o u t t h e gas, u n d e r g o i n g the following c o m p e t i n g processes (see Fig. 1): i) R e a c t i o n (1), at a r a t e ~eD2., where ~ is t h e ratio b e t w e e n the density of h y d r o g e n at t h e chosen pressure and the density of liquid hydrogen, and c n is the ratio b e t w e e n t h e d e u t e r i u m partial pressure and the t o t a l pressure P0 of t h e gaseous m i x t u r e . ii) Muon transfer from t h e ~p s y s t e m to a xenon atom, at a rate qCx~ 2x~, ~ where Cx~ is n o w t h e ratio between t h e xenon partial pressure and P0, and ~xp is the rate for t h e process (s) (2)

~zp+Xe~ ~zXe+p. iii) F o r m a t i o n of a p~p molecular ion, according to the process

(3)

~p + p -~ p~p

w h i c h occurs at a r a t e ~.pp. High.Energy Physics ( G e n e v a , 1962); J . E. :ROTItBERO, E. W . A.~DERSO~', E. J . BLESER, L. M. LEDERMAI~', S. I,. MEYER, J . L . ROSEN" a n d I. T. WA~'O: Phys. Rev., 132, 2664 (1963); A. ALBERIGI QUARANTA, A. BERTI~, O..~r F. I~AL~OI~ARI, G. TORELLI, l~. DALPIAZ, A. I)LACCI a n d E. ZAVATTINI: Phys. Rev., 177, p a r t I, 2118 (1969). (') and (~) (a) (')

E. I. A. A. A.

J . I~LESER, •. W . A~'DERSON', L. ~[. LEDERMA~', S. T. WANG: Phys. Rev., 132, 2679 (1963). t>LACCI, E. ZAVATTINI, A. BERTIN a n d A . VITALE: PLACCI, E. ZAVATTINI, A . BERTIN tbIld A. VITALE: PLACCI, E. ZAVATTINI, A . ]:IERTI~" v,Ild A. VITALE:

L. MEYER, J . L. l~0SEl~-, J . ~. ]~OT/IBERG

Phys. Rev. Lelt., 25, 475 (1970). NUOVO Cime~to, S 2 A , 1274 (1967). NUOVO Cimento, 6 4 A , 1053 (1969).

MEASUREMENT

OF ' H I E R A T E

/'e F O R "rH~: R E A C T I O N

Fp ' - - d - . , ~ d + p

XTC.

451

z~"

I t should be n o t e d t h a t t h e values for ~ , 2x~,~" and to be considered here are t h e rates at ~ h i c h process (1), (2), and (3) occur when t h e density of d e u t e r i u m , xenon, and h y d r o g e n molecules arc r e s p e c t i v e l y equal to t h e d e n s i t y of molecules a s s u m e d

I~p / ~cl)~(' (N1)

~'~

~c$ (N2)

\

IP-P

PCxe Xe

p.cl ~'Xe

p. Xe

J'Xec Io

't~

I

Ic

10

'8-+ Ve ~ l,'p.

~2g. 1. - ~ - a t o m i c a n d ~z-molecular p r o c e s s e s i n t h e g a s e o u s t a r g e t .

for liquid hydrogen, i.e. 2.11.1022 molecules em -3. In this c o n d i t i o n we h a v e /.x~.~"----4.41.1011 s -1 (~). F o r ].pp" two different values are available (see ref. (~)). T h e final results r e p o r t e d below are i n d e p e n d e n t on t h e choice b e t w e e n t h e s e two values. T h e ~d m u o n i c a t o m s formed as a c o n s e q u e n c e of process (1), on t h e o t h e r h a n d , go t h r o u g h the following reactions: ^lLd iv) Muon t r a n s f e r from t h e ~d s y s t e m to a x e n o n a t o m , at a r a t e ~Cx.Zx., where ~x~ is the rate for the process (s)

(4)

~td+Xe-+ ~Xe+d

.

v) F o r m a t i o n of a p~d m o l e c u l a r ion, t h r o u g h t h e r e a c t i o n

(5)

~d+p-~ p~d,

w h i c h takes place at a r a t e r - t/.d Also the rates /.xe and ~pd to be t a k e n into a c c o u n t here refer to processes (4) and (5) w h e n t h e density of xenon and h y d r o g c n moleculcs arc r e s p e c t i v e l y e q u a l to the dcnsity

A. BERTIN. M. BRUNO: A. VITALE, A. PLACCI and E. ZAVATTIN1

452

of molecules of liquid hydrogen. ( W e assumed here 2x~ = 2.36-1011s-1(~) and 2~d = 1.8.10 ~ S-X (lo)). T h e ~Xo atoms, f o r m e d as a result of processes (2) and (4), can disappear due to t h e nuclear c a p t u r e of m u o n b y the X e nucleus, at a r a t e 2x~ (11). On the o t h e r hand, muon decay ~-~c-+~+v~

(6)

,

w h i c h t a k e s place at a r a t e ;to = 4.54.105 s -~, c o m p e t e s w i t h all processes at each t i m e of the m u o n life. B y solving t h e s y s t e m of e q u a t i o n s a~sociated to t h e scheme of Fig. 1, t h e differential t i m e d i s t r i b u t i o n of t h e m u o n decay electrons (dno/dt) can be expressed as

dn./dt = A;to ~ .N,(t) = A;to ~ B, exp [-- 2,t] ,

(7)

where ~V~(t) g i v e t h e p o p u l a t i o n of t h e different m u o n i c systems at a t i m e t (see Fig. l), A is a constant, a n d t h e 2~'s are g i v e n by t h e following expressions: [s

21= 20+ q~cv;to+ ~ e x o ; t x , + ~o;tp~, 22 = ;to + 9ex~

(8)

gd

+ ~2pd,

;t3 = ;to + 2 x " , ;t4 - - ;t5 -~ 2.0 9

T h e nuclear c a p t u r e r a t e of m u o n s b y h y d r o g e n and d e u t e r i u m nuclei, as well as t h e f o m a t i o n r a t e of d~d molecular ions, were neglected in the a b o v e formulae. T h e B,-coefficients in eq. (7) are o b t a i n e d by i n t e g r a t i n g t h e corresponding system of diff e r e n t i a l e q u a t i o n s w i t h t h e initial conditions NI(0 ) = 1, and N2(0) = 13(0) = ,~4(0) ---= N ~ ( O ) = O. T h e value of 2, can t h e n be d e t e r m i n e d b y fitting the e x p e r i m e n t a l t i m e distribution of t h e m u o n d e c a y electrons to t h e theoretical yield. Tnis is g i v e n b y adding to dne/dt of eq. (7) one t e r m which keeps into account t h e b a c k g r o u n d counts (a.9). T h e dne/dt d i s t r i b u t i o n s were m e a s u r e d in t h e different e x p e r i m e n t a l conditions listed in T a b l e I I . R u n 1 was carried out to d e t e r m i n e the lifetime of t h e background counts, t h e v a l u e of 2~xp. being sufficiently well k n o w n ('). R u n s 2 and 3 were p e r f o r m e d to get two i n d e p e n d e n t d e t e r m i n a t i o n s of 2.~ for different d e u t e r i u m concentrations. TABLE I I . - Experimental conditions ]or the measurements reported in the present work. R u n No.

H y d r o g e n pressure (atm)

Xenon concentration (Cxo)

D e u t e r i u m concentration (eD)

1

6

(1.65 + 0.08)" 10 -4

--

2

6

(1.65 --' 0.08)" 10 -~

(6.95 -4- 0.48)" 10 -3

3

6

(1.65 + 0.08) 910 -~

(1.44 • 0.10) 910 -2

(to) V. P. DZHELEPOV, p. F. E R M O L O V , Y. I. M O S K A L E V

and V. V. FIL'CHEI~KOV: ~urn. Eksp. Teor. Fiz.,

50, 1235 (1966) ( E n g l i s h tramslatlon: Soy. Phys. J E T P , 23, 820 (1966)). ( " ) J . C. SENS: Phys. Rev., 113,[679 (1959).

OF T I t E R A T E )'e FOR T I I E R]']ACTION ~ P t d - ~ ~ d - ~ p ETC.

MEASUREMENT

453

F i g u r e 2 s h o w s t h e dnJdt d i s t r i b u t i o n s o b t a i n e d d u r i n g R u n s 2 a n d 3 t o g e t h e r w i t h t h e t h e o r e t i c a l fits. T h e d a t a w e r e c o l l e c t e d w i t b a l o w e r t i m e c u t of 0.7 m i c r o s e c o n d s , w h i c h c o r r e s p o n d s to t h e origin of t h e abscissae in Fig. 2.

1o3

{0

2

~

a) 101

b) I

I

I

I

I

I

3

I

I

6

I

I

I

9 0 t(ps)

I

I

3

Fig. 2. - D i f f e r e n t i a l t i m e d i s t r i b u t i o n s dne/dt o b t a i n e d i n t h e p r e s e n t w o r k : Background counts are not subtracted in the Figures.

T h e o b t a i n e d r e s u l t s are s u m m a r i z e d i n T a b l e I I I . r e s p o n d i n g to R u n s 2 a n d 3, one g e t s t h e n

I

6 a) R u n

2;

b) R u n 3.

F r o m t h e m e a s u r e m e n t s cor-

I~ = (0.84 • 0.13).101~ s -1 . TABLE I I I . -

Results.

R u n No.

),~xP,(910 -11 s -1)

2e(. 10 -1~ s -l)

1

4.5 ~ 0.3

--

2

--

3

--

Z2

N u m b e r of p o i n t s

92

93

0.85 • 0.19

104

93

0.83 -': 0.18

74

93

As a final r e m a r k , w e w o u l d like to m e n t i o n h e r e t h a t t h e r e s u l t s s h o w n in T a b l e I s e e m to p o i n t at a d e p e n d e n c e of t h e m e a s u r e d v a l u e for I e on t h e t e m p e r a t u r e a n d d e n s i t y of t h e t a r g e t in w h i c h t h e ~p a t o m s are f o r m e d .

T h e a u t h o r s a r e i n d e b t e d to P r o f s . A. ALBERIGI QUARANTA a n d P . BASSI for t h e i r encouragement and support.