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Measurement of muon partial capture rates in 16O and the induced pseudoscalar coupling constant in muon capture
Volume 29B, number 1
PHYSICS LETTERS
MEASUREMENT AND
THE
OF
INDUCED
MUON
PARTIAL
CAPTURE
PSEUDOSCALAR IN MUON
31 March 1969
COUPLING
CAPTURE
RATES
IN
160
CONSTANT
*
J . P . DEUTSCH **, L. GRENACS ***, J. LEHMANN, P. LIPNIK *** and P . C . M A C Q Centre de Physique Nucl$aire, Universit$ de Louvain, H$verl$-Louvain, Belgium Received 3 March 1969
The partial rates in the capture of muons by 160 were measured for the J~= O- and 1- excited bound states of 16N. The energy spectrum and the time dependence of the y-rays emitted by the target were observed using a Ge(Li) detector. On the basis of the Rho-Migdal theory [5], the observed k0-/~ 1- ratio led for the induced pseudoscalar coupling to a value of Cp = 10.6 ~: 1.0.
The muon p a r t i a l c a p t u r e r a t e is m o s t s e n s i t i v e to the induced p s e u d o s c a l a r coupling c o n stant in the c a s e of a c a p t u r e r e a c t i o n between z e r o - s p i n n u c l e a r s t a t e s with opposite p a r i t i e s [1, 2]. Th e c a p t u r e of muons by 160 can p r o d u c e (among o t h e r p o s s i b i l i t i e s ) the two m e m b e r s of the (lp~)p -1 (2s½)n 1 doublet in 16N: 0-(120 keV) and 1-(396 keV), with c a p t u r e r a t e s ~0- and ;~1-, r e s p e c t i v e l y . T h e s e q u a n t i t i e s have been c a l c u lated in the f r a m e w o r k of v a r i o u s n u c l e a r m o d e l s [2-5]. The f i r s t one (k0-) was computed with the p u r p o s e of p r o v i d i n g a Cp ' d e t e c t o r ' , whilst the second one i l l - ) , independent of Cp, was i n tended to s e r v e as a c r o s s - c h e c k of the t h e o r e t i cal i d eas which w e r e used. P a r a l l e l to t h e s e c a l c u l a t i o n s , e x p e r i m e n t s have been undertaken in o r d e r to d e t e r m i n e t h e s e p a r t i a l c a p t u r e r a t e s . Two r e s u l t s have been obtained [6, 7], as shown in table 1; they do not a g r e e within the stated e r r o r s . In t h e s e e x p e r i m e n t s , the d e - e x c i t a t i o n y - r a y s in 16N w e r e d e t e c t e d with NaI(T1) c r y s t a ls. The t h e o r e t i c a l [2-4] and e x p e r i m e n t a l [6, 7] r e s u l t s f o r k l - r e m a i n e d in d i s a g r e e m e n t until Rho [5], on the b a s i s of the Migdal t h e o r y , obtained v a l u e s f o r k l - c l o s e to the e x p e r i m e n t a l r e s u l t s . H o w e v e r , in spite of the s u c c e s s in p r e d i c t i n g the ;~1- r a t e , the d i s c r e p a n c y between
* Partially supported by IISN, Laboratoire des Hautes Energies, Belgium ** Present address: CERN, Geneva, Switzerland *** Chercheurs IISN. 66
the two a b o v e - m e n t i o n e d e x p e r i m e n t a l k 0 - v a l ues did not allow the v al u e of Cp to be specified. Th e advent of new y - r a y d e t e c t o r s e n c o u r a g e d us to r e - m e a s u r e the k 0 - and ~1- r a t e s . The e x p e r i m e n t s w e r e p e r f o r m e d at the CERN S y n c h r o c y c l o t r o n muon channel. The t a r g e t c o n s i s t e d of d i s t i l l e d w a t e r e n c l o s e d in a s c i n t i l l a t o r cup of 5 x 6 x 10 c m (internal dimensions). The n u m b e r of p a r t i c l e s f r o m the b e a m stopped in H 2 0 was m e a s u r e d by d e t e r m i n i n g the stop r a t e with and without H 2 0 in the cup. It was shown by a t i m e - o f - f l i g h t m e a s u r e m e n t that 99% of the stopped p a r t i c l e s w e r e muons. The o b s e r v a t i o n of the m e s i c X - r a y s and ~,-rays subsequent to a p a r t i c l e stopping in the t a r g e t was s t a r t e d by the c o r r e s p o n d i n g signal. T h i s ' s t a r t ' signal was vetoed, h o w e v e r , if the stopped p a r t i c l e was p r e c e d e d o r followed by another stopped p a r t i c l e within 6 p s e c . In o r d e r to r e d u c e the b a c k ground, the y - r a y d e t e c t o r signal was r e j e c t e d if the ' s t a r t ' signal was followed within 6 ~ s e c by an e l e c t r o n f r o m the muon decay. O t h e r w i s e , the signal d e l i v e r e d by the 35 cm 3 a c t i v e v o l u m e Ge(Li) d e t e c t o r was used as a ' s t o p ' signal f o r a t i m e - t o - p u l s e h e i g h t c o n v e r t e r . The e n e r g y s p e c t r u m and the t i m e dependence of the r e s u l t ing y - r a y s w e r e r e c o r d e d with the aid of a multichannel p u l s e - h e i g h t a n a l y s e r (4096 ch an nels o p e r a t i n g in X - Y mode). The r e l a t i v e d e t ect i o n e f f i c i e n c y of the s y s t e m in the e n e r g y r a n g e f r o m 100 keV to 400 keV was m e a s u r e d by f i l l i n g the t a r g e t h o l d e r with a w a t e r solution of 75Se. The absolute detection efficiency of the d et ect i o n s y s t e m was obtained by m e a s u r i n g the y i el d of the K - s e r i e s X - r a y s in oxygen and m a g n e s i u m . This y i el d was taken to be 100% [8].
Volume 29B, n u m b e r 1
PHYSICS
LBTTERS
N¥ 1600
31 M a r c h 1969
E(keV) 396
!
leO.P-
J~ 1-
296
1400
t 276 key30 ° ~:7.58 ps
120 O
1200
2,6N
~000
500
800
400
600
300
276key
l
%
400
0.5 ~t (psi • 60
20C 0
,
.
,
,
,
10
20
30
40
50 ~ 1
.
70
,
,
,
80
90
i00
110
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Fig. 1. G a m m a - r a y s p e c t r u m following the capture of m u o n s in H20 obtained with a 35 cm 3 Ge(Li) detector. The two p a r t s of the s p e c t n t m were i n t e g r a t e d o v e r slightly different time i n t e r v a l s a f t e r the stepping of the muon. The ins e r t shows the r e l e v a n t level s c h e m e of 16N.
N.f (t)
÷ I0C mkeV i
I
0
I
1
I
2
'r
I
3
r"
I
4
5 t(ps)
Fig. 2. The t i m e dependence~ with r e s p e c t to the muon stop signal, of the photopeak a r e a s due to the 120 keV and 276 keV T - r a y s . The heavy c u r v e s show the e x p e c t e d t i m e dependences.
Fig. 1 shows a T-ray spectrum associated with the muons stopped in H20. This spectrum i s o n e of t h e f o u r s t a t i s t i c a l l y e q u i v a l e n t s p e c t r a taken during the experiment. Fig. 2 shows the t i m e d e p e n d e n c e of t h e p h o t o p e a k a r e a s of t h e 120 k e V a n d 276 k e V T - r a y s . T h e f o r m e r i s d u e t o t h e d e c a y of t h e 0 - i s o m e r i c s t a t e a t 120 k e V i n 16N ( c r e a t e d i n m u o n c a p t u r e ) w i t h a m e a n l i f e of • = 7 . 5 8 + 0 . 0 9 / ~ s e c [9]; t h e s e c o n d r e p r e s e n t s t h e 1 - -. 0 - t r a n s i t i o n i n 16N, a n d d i s p l a y s a t i m e d e p e n d e n c e c h a r a c t e r i s t i c of t h e muon disappearance rate in 160: ~disp = = 5.12 x 105 s e c -1 [10]. U s i n g t h e r e l a t i v e e f f i c i e n c y c a l i b r a t i o n of t h e detection system, and taking into account the f a c t t h a t t h e 1 - s t a t e a t 396 k e V d e - e x c i t e s t o t h e 0 - s t a t e w i t h a 69 + 5% p r o b a b i l i t y [ 1 1 ] , t h e r a t i o of t h e c a p t u r e r a t e s t o t h e 0 - a n d 1 - s t a t e s ;~0-/~ 1- was readily obtained. The result is: ~ 0 - / X l - = 0.46 ± 0 . 0 4 . T h e e r r o r i n c l u d e s t h e statistical error, the error on the above quoted branching ratio and the error on the relative int e n s i t i e s of t h e 75Se T - r a y s [12], i . e . , t h a t of t h e relative efficiency calibration. The result has been corrected for the inhomogeneous distribut i o n of t h e p a r t i c l e s t o p s i n t h e t a r g e t . T h e k n o w l e d g e of t h e a b s o l u t e d e t e c t i o n e f f i c i e n c y a n d t h a t of t h e n u m b e r o f e f f e c t i v e ( u n v e t o e d ) m u o n s t o p s i n H 2 0 w h i c h p r o d u c e d t h e 120 k e V a n d 276 k e V T - r a y s e n a b l e d u s t o c a l c u l a t e t h e 67
Volume 29B, number 1
PHYSICS
LETTERS
31 March 1969
Table 1 The o b s e r v e d muon partial capture r a t e s in the 160 --* 16N (bound states) reaction, c o m p a r e d to other experimental r e s u l t s and to the theoretical prediction calculated by Rho [5]. The fourth column shows the value of Cp which is inf e r r e d in comparing the m e a s u r e d and the predicted h 0 - r a t e and the k 0 - / k 1- ratio. In the quoted e r r o r s of our r e sults, the upper limit contains the intrinsic e r r o r of our m e a s u r e m e n t plus the absolute calibration uncertainty. The observed quantities k 0-
k 1-
Theoretical predictions [5]
Experimental r e s u l t s ~_~+(60+85) s e e -1, p r e s e n t work ~av_60
Cp 12 "3+0.7 -(0.7+1.0)
Dependent on Cp
1 1 0 0 ± 200 sec -1 [6]
9.6 ± 2
1600 ± 200 sec -1 [7]
5.0±1.5
. . . . +(170+185) l ~ou_170 sec -1 , p r e s e n t work
2 180 see -1 b)
Independent of Cp
1880 ± 100 sec -1 [6] a) 1 4 0 0 ± 200 sec -1 [7]
k 0 - / k 1-
3-
0.46 ± 0.04, p r e s e n t work
Dependent on Cp
10.6 ± 1.0
O.59 [6]
7.8
1.14 [7]
0
--< 80 sec -1
p r e s e n t work
126 s e c -1 b)
Independent of Cp
a) C o r r e c t e d for the r e d e t e r m i n a t i o n of the 1- ~ 0- gamma branching ratio [11]. b) See for solution b) in table IV of ref. 5. ~0- and ~1- r a t e s s e p a r a t e l y . A n e s t i m a t e w a s a l s o o b t a i n e d f o r t h e r a t e of t h e t h i r d f o r b i d d e n c a p t u r e t r a n s i t i o n to t h e 3 - s t a t e i n 16N a t 296 k e Y . T h e r e s u l t s f o r k 0 - , k 1 - , a n d k 3 - a r e r e p o r t e d in t a b l e 1, t o g e t h e r w i t h t h e p r e v i o u s r e s u l t s f o r t h e s e q u a n t i t i e s . It s h o u l d b e e m p h a s i z e d at t h i s point that the absolute r a t e s we q u o t e a r e s u b j e c t to t h e a s s u m e d 100% y i e l d of the calibration K-series X-rays. This assumpt i o n w a s s h o w n t o b e c o r r e c t w i t h an u n c e r t a i n t y of 10% [ 8 ] . L e t u s now c o m p a r e t h e ~0- r a t e a n d t h e h 0 - / h 1 - r a t i o o b t a i n e d in t h i s w o r k , w i t h t h e c o r r e s p o n d i n g t h e o r e t i c a l p r e d i c t i o n s [5]. In fig. 3 a r e d i s p l a y e d b o t h k 0 - a n d t h e r a t i o ~ 0 - / k l - a s a f u n c t i o n of Cp a n d t h e c o r r e s p o n d i n g e x p e r i m e n t a l r e s u l t s (the e x p e r i m e n t a l v a l u e of ~ 0 - w a s t a k e n a s 790 ~< ~ 0 - ( s e c - 1 ) ~< 1000, i n c l u d i n g t h e m a x i m a l u n c e r t a i n t y in t h e a b s o l u t e efficiency calibration). The theoretical curves w e r e t a k e n f r o m t h e c o m p u t a t i o n of R h o [5], i n c l u d i n g t h e v e l o c i t y t e r m s up to t h e s e c o n d o r Fig. 3. The capture rate k0- and the kO-/~-l- ratio calculated by Rho [5] in Lhe f r a m e w o r k of the Migdal theory as a function of Cp, and the corresponding e x p e r i m e n tal r e s u l t s . 68
2~ inlO3 .~-~
t5
L=Xo-IX~to
X0-E'ornIbisw o r k ~
QI o
i
5
i
10
i
15
Volume 29B, n u m b e r 1
PHYSICS
der; for the nuclear parameters his most reali s t i c v a l u e s w e r e r e t a i n e d ~P0 = 0 . 3 5 , g ~ = 0 . 5 0 , f ~ = g~ = 0). F r o m t h e c o m p a r i s o n of t h e X0 r a t e s , Cp t u r n s o u t to b e n e a r l y t h e s a m e a s f r o m t h e c o m p a r i s o n of t h e X 0 - / X 1 - r a t i o s . T h e f o r m e r c o m p a r i s o n y i e l d s 10.6 --< Cp --< 13.0 a n d t h e l a t t e r , Cp = 10.6 + 1.0. T h e l a t t e r v a l u e i s t o be considered as the more reliable one from the e x p e r i m e n t a l p o i n t of v i e w ; m o r e o v e r , t h e t h e o r e t i c a l X 0 - / X 1 - r a t i o i s r a t h e r i n s e n s i t i v e to t h e c h o i c e of t h e n u c l e a r p a r a m e t e r v a l u e s q u o t e d i n ref. 5* In c o n c l u s i o n , o n e m a y n o t i c e t h a t t h e v a l u e of Cp o b t a i n e d h e r e i s i n a g r e e m e n t w i t h t h e o n e deduced from the muon capture-rate measurem e n t s i n a t o m i c [13] a n d m o l e c u l a r h y d r o g e n [14, 15]. We are indebted to J. Renuart, to the technic i a n s of t h e C e n t r e d e P h y s i q u e N u c l ~ a i r e d e L o u v a i n , a n d t o t h e C E R N MSC O p e r a t i o n G r o u p for their effective help which greatly contributed to t h e s u c c e s s of t h i s w o r k .
LETTERS
31 March 1969
References 1. I.S. Shapiro and L. D. Blokhintsev, Soviet Phys. J E T P 2 (1961) 775. 2. T. E r i c s o n , J . C . Sens and H. P. C. Rood, Nuovo Cimento 34 (1964) 51. 3. V. Gillet and D. A. Jenkins, Phys. Rev. B140 (1965) 32. 4. I. Duck, Nucl. Phys. 35 (1962) 27. 5. M. Rho, Phys. Rev. L e t t e r s 18 0967) 671; Phys. Rev. 161 (1967) 955. 6. R. C. Cohen, S. Devons and A. D. K a n a r i s , Nuel. Phys. 57 (1964) 255. 7. A . A s t b u r y et al., Nuovo Cimento 33 (1964) 1020. 8. J. L. Lathrop et al., Phys. Rev. L e t t e r s 7 (1961) 147. 9. J . A . B e c k e t , J.W. Olness and D. H. Wilkinson, Phys. Rev. 155 (1967) 1089. 10. M. Eckhause et al., Phys. Rev. 132 (1963) 422. 11. W.W. Givens et al., Nucl. Phys. 46 (1963) 504. 12. Nuclear Data, Vol. 1, No. 6 (ed. K. Way). 13. A . A l b e r i g i Q u a r a n t a et al., Phys. L e t t e r s 25B (1967) 429. 14. P.K. Kabir, Z. Phys. 191 (1966) 447. 15. J. E. Rothberg et al., Phys. Rev. 132 (1963) 2664.
* Using the k 0 - / k 1- r a t i o due to the o t h e r model calculations [2-4], and arguing that this r a t i o is r a t h e r model independent, one obtains: 7 --< Cp ~< 13.
69
PHYSICS LETTERS
MEASUREMENT AND
THE
OF
INDUCED
MUON
PARTIAL
CAPTURE
PSEUDOSCALAR IN MUON
31 March 1969
COUPLING
CAPTURE
RATES
IN
160
CONSTANT
*
J . P . DEUTSCH **, L. GRENACS ***, J. LEHMANN, P. LIPNIK *** and P . C . M A C Q Centre de Physique Nucl$aire, Universit$ de Louvain, H$verl$-Louvain, Belgium Received 3 March 1969
The partial rates in the capture of muons by 160 were measured for the J~= O- and 1- excited bound states of 16N. The energy spectrum and the time dependence of the y-rays emitted by the target were observed using a Ge(Li) detector. On the basis of the Rho-Migdal theory [5], the observed k0-/~ 1- ratio led for the induced pseudoscalar coupling to a value of Cp = 10.6 ~: 1.0.
The muon p a r t i a l c a p t u r e r a t e is m o s t s e n s i t i v e to the induced p s e u d o s c a l a r coupling c o n stant in the c a s e of a c a p t u r e r e a c t i o n between z e r o - s p i n n u c l e a r s t a t e s with opposite p a r i t i e s [1, 2]. Th e c a p t u r e of muons by 160 can p r o d u c e (among o t h e r p o s s i b i l i t i e s ) the two m e m b e r s of the (lp~)p -1 (2s½)n 1 doublet in 16N: 0-(120 keV) and 1-(396 keV), with c a p t u r e r a t e s ~0- and ;~1-, r e s p e c t i v e l y . T h e s e q u a n t i t i e s have been c a l c u lated in the f r a m e w o r k of v a r i o u s n u c l e a r m o d e l s [2-5]. The f i r s t one (k0-) was computed with the p u r p o s e of p r o v i d i n g a Cp ' d e t e c t o r ' , whilst the second one i l l - ) , independent of Cp, was i n tended to s e r v e as a c r o s s - c h e c k of the t h e o r e t i cal i d eas which w e r e used. P a r a l l e l to t h e s e c a l c u l a t i o n s , e x p e r i m e n t s have been undertaken in o r d e r to d e t e r m i n e t h e s e p a r t i a l c a p t u r e r a t e s . Two r e s u l t s have been obtained [6, 7], as shown in table 1; they do not a g r e e within the stated e r r o r s . In t h e s e e x p e r i m e n t s , the d e - e x c i t a t i o n y - r a y s in 16N w e r e d e t e c t e d with NaI(T1) c r y s t a ls. The t h e o r e t i c a l [2-4] and e x p e r i m e n t a l [6, 7] r e s u l t s f o r k l - r e m a i n e d in d i s a g r e e m e n t until Rho [5], on the b a s i s of the Migdal t h e o r y , obtained v a l u e s f o r k l - c l o s e to the e x p e r i m e n t a l r e s u l t s . H o w e v e r , in spite of the s u c c e s s in p r e d i c t i n g the ;~1- r a t e , the d i s c r e p a n c y between
* Partially supported by IISN, Laboratoire des Hautes Energies, Belgium ** Present address: CERN, Geneva, Switzerland *** Chercheurs IISN. 66
the two a b o v e - m e n t i o n e d e x p e r i m e n t a l k 0 - v a l ues did not allow the v al u e of Cp to be specified. Th e advent of new y - r a y d e t e c t o r s e n c o u r a g e d us to r e - m e a s u r e the k 0 - and ~1- r a t e s . The e x p e r i m e n t s w e r e p e r f o r m e d at the CERN S y n c h r o c y c l o t r o n muon channel. The t a r g e t c o n s i s t e d of d i s t i l l e d w a t e r e n c l o s e d in a s c i n t i l l a t o r cup of 5 x 6 x 10 c m (internal dimensions). The n u m b e r of p a r t i c l e s f r o m the b e a m stopped in H 2 0 was m e a s u r e d by d e t e r m i n i n g the stop r a t e with and without H 2 0 in the cup. It was shown by a t i m e - o f - f l i g h t m e a s u r e m e n t that 99% of the stopped p a r t i c l e s w e r e muons. The o b s e r v a t i o n of the m e s i c X - r a y s and ~,-rays subsequent to a p a r t i c l e stopping in the t a r g e t was s t a r t e d by the c o r r e s p o n d i n g signal. T h i s ' s t a r t ' signal was vetoed, h o w e v e r , if the stopped p a r t i c l e was p r e c e d e d o r followed by another stopped p a r t i c l e within 6 p s e c . In o r d e r to r e d u c e the b a c k ground, the y - r a y d e t e c t o r signal was r e j e c t e d if the ' s t a r t ' signal was followed within 6 ~ s e c by an e l e c t r o n f r o m the muon decay. O t h e r w i s e , the signal d e l i v e r e d by the 35 cm 3 a c t i v e v o l u m e Ge(Li) d e t e c t o r was used as a ' s t o p ' signal f o r a t i m e - t o - p u l s e h e i g h t c o n v e r t e r . The e n e r g y s p e c t r u m and the t i m e dependence of the r e s u l t ing y - r a y s w e r e r e c o r d e d with the aid of a multichannel p u l s e - h e i g h t a n a l y s e r (4096 ch an nels o p e r a t i n g in X - Y mode). The r e l a t i v e d e t ect i o n e f f i c i e n c y of the s y s t e m in the e n e r g y r a n g e f r o m 100 keV to 400 keV was m e a s u r e d by f i l l i n g the t a r g e t h o l d e r with a w a t e r solution of 75Se. The absolute detection efficiency of the d et ect i o n s y s t e m was obtained by m e a s u r i n g the y i el d of the K - s e r i e s X - r a y s in oxygen and m a g n e s i u m . This y i el d was taken to be 100% [8].
Volume 29B, n u m b e r 1
PHYSICS
LBTTERS
N¥ 1600
31 M a r c h 1969
E(keV) 396
!
leO.P-
J~ 1-
296
1400
t 276 key30 ° ~:7.58 ps
120 O
1200
2,6N
~000
500
800
400
600
300
276key
l
%
400
0.5 ~t (psi • 60
20C 0
,
.
,
,
,
10
20
30
40
50 ~ 1
.
70
,
,
,
80
90
i00
110
number
Fig. 1. G a m m a - r a y s p e c t r u m following the capture of m u o n s in H20 obtained with a 35 cm 3 Ge(Li) detector. The two p a r t s of the s p e c t n t m were i n t e g r a t e d o v e r slightly different time i n t e r v a l s a f t e r the stepping of the muon. The ins e r t shows the r e l e v a n t level s c h e m e of 16N.
N.f (t)
÷ I0C mkeV i
I
0
I
1
I
2
'r
I
3
r"
I
4
5 t(ps)
Fig. 2. The t i m e dependence~ with r e s p e c t to the muon stop signal, of the photopeak a r e a s due to the 120 keV and 276 keV T - r a y s . The heavy c u r v e s show the e x p e c t e d t i m e dependences.
Fig. 1 shows a T-ray spectrum associated with the muons stopped in H20. This spectrum i s o n e of t h e f o u r s t a t i s t i c a l l y e q u i v a l e n t s p e c t r a taken during the experiment. Fig. 2 shows the t i m e d e p e n d e n c e of t h e p h o t o p e a k a r e a s of t h e 120 k e V a n d 276 k e V T - r a y s . T h e f o r m e r i s d u e t o t h e d e c a y of t h e 0 - i s o m e r i c s t a t e a t 120 k e V i n 16N ( c r e a t e d i n m u o n c a p t u r e ) w i t h a m e a n l i f e of • = 7 . 5 8 + 0 . 0 9 / ~ s e c [9]; t h e s e c o n d r e p r e s e n t s t h e 1 - -. 0 - t r a n s i t i o n i n 16N, a n d d i s p l a y s a t i m e d e p e n d e n c e c h a r a c t e r i s t i c of t h e muon disappearance rate in 160: ~disp = = 5.12 x 105 s e c -1 [10]. U s i n g t h e r e l a t i v e e f f i c i e n c y c a l i b r a t i o n of t h e detection system, and taking into account the f a c t t h a t t h e 1 - s t a t e a t 396 k e V d e - e x c i t e s t o t h e 0 - s t a t e w i t h a 69 + 5% p r o b a b i l i t y [ 1 1 ] , t h e r a t i o of t h e c a p t u r e r a t e s t o t h e 0 - a n d 1 - s t a t e s ;~0-/~ 1- was readily obtained. The result is: ~ 0 - / X l - = 0.46 ± 0 . 0 4 . T h e e r r o r i n c l u d e s t h e statistical error, the error on the above quoted branching ratio and the error on the relative int e n s i t i e s of t h e 75Se T - r a y s [12], i . e . , t h a t of t h e relative efficiency calibration. The result has been corrected for the inhomogeneous distribut i o n of t h e p a r t i c l e s t o p s i n t h e t a r g e t . T h e k n o w l e d g e of t h e a b s o l u t e d e t e c t i o n e f f i c i e n c y a n d t h a t of t h e n u m b e r o f e f f e c t i v e ( u n v e t o e d ) m u o n s t o p s i n H 2 0 w h i c h p r o d u c e d t h e 120 k e V a n d 276 k e V T - r a y s e n a b l e d u s t o c a l c u l a t e t h e 67
Volume 29B, number 1
PHYSICS
LETTERS
31 March 1969
Table 1 The o b s e r v e d muon partial capture r a t e s in the 160 --* 16N (bound states) reaction, c o m p a r e d to other experimental r e s u l t s and to the theoretical prediction calculated by Rho [5]. The fourth column shows the value of Cp which is inf e r r e d in comparing the m e a s u r e d and the predicted h 0 - r a t e and the k 0 - / k 1- ratio. In the quoted e r r o r s of our r e sults, the upper limit contains the intrinsic e r r o r of our m e a s u r e m e n t plus the absolute calibration uncertainty. The observed quantities k 0-
k 1-
Theoretical predictions [5]
Experimental r e s u l t s ~_~+(60+85) s e e -1, p r e s e n t work ~av_60
Cp 12 "3+0.7 -(0.7+1.0)
Dependent on Cp
1 1 0 0 ± 200 sec -1 [6]
9.6 ± 2
1600 ± 200 sec -1 [7]
5.0±1.5
. . . . +(170+185) l ~ou_170 sec -1 , p r e s e n t work
2 180 see -1 b)
Independent of Cp
1880 ± 100 sec -1 [6] a) 1 4 0 0 ± 200 sec -1 [7]
k 0 - / k 1-
3-
0.46 ± 0.04, p r e s e n t work
Dependent on Cp
10.6 ± 1.0
O.59 [6]
7.8
1.14 [7]
0
--< 80 sec -1
p r e s e n t work
126 s e c -1 b)
Independent of Cp
a) C o r r e c t e d for the r e d e t e r m i n a t i o n of the 1- ~ 0- gamma branching ratio [11]. b) See for solution b) in table IV of ref. 5. ~0- and ~1- r a t e s s e p a r a t e l y . A n e s t i m a t e w a s a l s o o b t a i n e d f o r t h e r a t e of t h e t h i r d f o r b i d d e n c a p t u r e t r a n s i t i o n to t h e 3 - s t a t e i n 16N a t 296 k e Y . T h e r e s u l t s f o r k 0 - , k 1 - , a n d k 3 - a r e r e p o r t e d in t a b l e 1, t o g e t h e r w i t h t h e p r e v i o u s r e s u l t s f o r t h e s e q u a n t i t i e s . It s h o u l d b e e m p h a s i z e d at t h i s point that the absolute r a t e s we q u o t e a r e s u b j e c t to t h e a s s u m e d 100% y i e l d of the calibration K-series X-rays. This assumpt i o n w a s s h o w n t o b e c o r r e c t w i t h an u n c e r t a i n t y of 10% [ 8 ] . L e t u s now c o m p a r e t h e ~0- r a t e a n d t h e h 0 - / h 1 - r a t i o o b t a i n e d in t h i s w o r k , w i t h t h e c o r r e s p o n d i n g t h e o r e t i c a l p r e d i c t i o n s [5]. In fig. 3 a r e d i s p l a y e d b o t h k 0 - a n d t h e r a t i o ~ 0 - / k l - a s a f u n c t i o n of Cp a n d t h e c o r r e s p o n d i n g e x p e r i m e n t a l r e s u l t s (the e x p e r i m e n t a l v a l u e of ~ 0 - w a s t a k e n a s 790 ~< ~ 0 - ( s e c - 1 ) ~< 1000, i n c l u d i n g t h e m a x i m a l u n c e r t a i n t y in t h e a b s o l u t e efficiency calibration). The theoretical curves w e r e t a k e n f r o m t h e c o m p u t a t i o n of R h o [5], i n c l u d i n g t h e v e l o c i t y t e r m s up to t h e s e c o n d o r Fig. 3. The capture rate k0- and the kO-/~-l- ratio calculated by Rho [5] in Lhe f r a m e w o r k of the Migdal theory as a function of Cp, and the corresponding e x p e r i m e n tal r e s u l t s . 68
2~ inlO3 .~-~
t5
L=Xo-IX~to
X0-E'ornIbisw o r k ~
QI o
i
5
i
10
i
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der; for the nuclear parameters his most reali s t i c v a l u e s w e r e r e t a i n e d ~P0 = 0 . 3 5 , g ~ = 0 . 5 0 , f ~ = g~ = 0). F r o m t h e c o m p a r i s o n of t h e X0 r a t e s , Cp t u r n s o u t to b e n e a r l y t h e s a m e a s f r o m t h e c o m p a r i s o n of t h e X 0 - / X 1 - r a t i o s . T h e f o r m e r c o m p a r i s o n y i e l d s 10.6 --< Cp --< 13.0 a n d t h e l a t t e r , Cp = 10.6 + 1.0. T h e l a t t e r v a l u e i s t o be considered as the more reliable one from the e x p e r i m e n t a l p o i n t of v i e w ; m o r e o v e r , t h e t h e o r e t i c a l X 0 - / X 1 - r a t i o i s r a t h e r i n s e n s i t i v e to t h e c h o i c e of t h e n u c l e a r p a r a m e t e r v a l u e s q u o t e d i n ref. 5* In c o n c l u s i o n , o n e m a y n o t i c e t h a t t h e v a l u e of Cp o b t a i n e d h e r e i s i n a g r e e m e n t w i t h t h e o n e deduced from the muon capture-rate measurem e n t s i n a t o m i c [13] a n d m o l e c u l a r h y d r o g e n [14, 15]. We are indebted to J. Renuart, to the technic i a n s of t h e C e n t r e d e P h y s i q u e N u c l ~ a i r e d e L o u v a i n , a n d t o t h e C E R N MSC O p e r a t i o n G r o u p for their effective help which greatly contributed to t h e s u c c e s s of t h i s w o r k .
LETTERS
31 March 1969
References 1. I.S. Shapiro and L. D. Blokhintsev, Soviet Phys. J E T P 2 (1961) 775. 2. T. E r i c s o n , J . C . Sens and H. P. C. Rood, Nuovo Cimento 34 (1964) 51. 3. V. Gillet and D. A. Jenkins, Phys. Rev. B140 (1965) 32. 4. I. Duck, Nucl. Phys. 35 (1962) 27. 5. M. Rho, Phys. Rev. L e t t e r s 18 0967) 671; Phys. Rev. 161 (1967) 955. 6. R. C. Cohen, S. Devons and A. D. K a n a r i s , Nuel. Phys. 57 (1964) 255. 7. A . A s t b u r y et al., Nuovo Cimento 33 (1964) 1020. 8. J. L. Lathrop et al., Phys. Rev. L e t t e r s 7 (1961) 147. 9. J . A . B e c k e t , J.W. Olness and D. H. Wilkinson, Phys. Rev. 155 (1967) 1089. 10. M. Eckhause et al., Phys. Rev. 132 (1963) 422. 11. W.W. Givens et al., Nucl. Phys. 46 (1963) 504. 12. Nuclear Data, Vol. 1, No. 6 (ed. K. Way). 13. A . A l b e r i g i Q u a r a n t a et al., Phys. L e t t e r s 25B (1967) 429. 14. P.K. Kabir, Z. Phys. 191 (1966) 447. 15. J. E. Rothberg et al., Phys. Rev. 132 (1963) 2664.
* Using the k 0 - / k 1- r a t i o due to the o t h e r model calculations [2-4], and arguing that this r a t i o is r a t h e r model independent, one obtains: 7 --< Cp ~< 13.
69