- Email: [email protected]
Measurements on short-range hyperfragments
Volume 9, number 4
PHYSICS
any f e a t u r e which r e d u c e s t h e i m p o r t a n c e of t h e s e a l s o r e d u c e s t h e i m p o r t a n c e of FR. A s m a l l binding e n e r g y f o r t h e c a p t u r e d p a r t i c l e , with the consequent g r e a t e r extent of i t s w a v e function ~ n , w i l l do t h i s , a s h a s been i l l u s t r a t e d b y a c a l c u l a t i o n f o r the O18(d,p) r e a c t i o n 3). The two l = 2 g r o u p s f r o m C a ( d , H e 3 ) in fig. 2 show a m a r k e d d e p e n d e n c e , on Q - v a l u e , and h e n c e on t h e binding e n e r g y of t h e p i c k e d - u p p r o t o n . C a p t u r e into an o r b i t whose wavefunction c o n t a i n s one o r m o r e n o d e s a l r e a d y h a s b u i l t - i n s o m e c a n c e l l a t i o n of t h e i n t e r i o r c o n t r i b u t i o n s , so that F R h a s l e s s effect; t h e c o n t r a s t of the 2p with the If c a p t u r e by Ca 40 shown in fig. 1 i l l u s t r a t e s t h i s . A g a i n , if t h e r e a c t i o n i s s t u d i e d at s u f f i c i e n t l y low e n e r g y t h a t t h e Coulomb r e p u l s i o n p r e v e n t s s i g n i f i c a n t c o n t r i b u t i o n s f r o m within the n u c l e u s we would e x p e c t F R to p r o d u c e v e r y l i t t l e change; t h i s h a s been v e r i f i e d by a c a l c u l a t i o n of the W183(d,p) r e a c t i o n at a d e u t e r o n e n e r g y of 6 M e V , and w a s a l s o i n d i c a t e d by o t h e r , a ~ p r o x i m a t e , c a l c u l a t i o n s of s i m i l a r r e a c t i o n s ~J. A n o t h e r r e l e v a n t f a c t o r i s the c h o i c e of o p t i c a l p o t e n t i a l f o r c o m p l e x p a r t i c l e s ; t h e s e a r e known to be h i g h l y a m b i g u o u s . A whole s e r i e s of p o t e n t i a l s can be found which give the s a m e e l a s t i c s c a t t e r i n g , and which d i f f e r , r o u g h l y , in the n u m b e r of w a v e l e n g t h s i n c l u d e d in the n u c l e a r i n t e r i o r 5). The d e e p e r the p o t e n t i a l , the m o r e r a p i d l y d o e s the a s s o c i a t e d wave o s c i l l a t e i n s i d e the n u c l e u s , and the s m a l l e r the c o n t r i b u t i o n to the r e a c t i o n f r o m t h i s r e g i o n even in the ZR a p p r o x i m a t i o n . Then we e x p e c t , and find, the F R effect to be r e d u c e d a l s o . The two e x a m p l e s given in fig. 1 i l l u s t r a t e t h i s ; the " s h a l l o w " d e u t e r o n p o t e n t i a l i s a p p r o x i m a t e l y 70 MeV d e e p , w h i l e t h e " d e e p " one h a s a depth of about UO MeV. P o -
MEASUREMENTS
LETTERS
1 May 1964
t e n t i a l s d e e p e r than t h i s (which s t i l l r e p r o d u c e the e l a s t i c s c a t t e r i n g 6)) show a l m o s t no d i f f e r ence between ZR and F R p r e d i c t i o n s . D e s p i t e t h e s e i n i t i a l s u c c e s s e s in u n d e r s t a n d hag F R e f f e c t s , e x t e n s i v e w o r k r e m a i n s to be done i n o r d e r to d i s c o v e r t h e i r m o r e d e t a i l e d b e h a v i o u r , such a s to what e x t e n t t h e y can be r e p r o d u c e d by a n / - i n d e p e n d e n t cut-off in a ZR c a l culation. R e c e n t l y s e v e r a l p r o p o s a l s f o r a p p r o x i m a t e F R c o r r e c t i o n s have been m a d e 7), and the a c c u r a c y of t h e s e i s c u r r e n t l y being t e s t e d by c o m p a r i s o n with e x a c t c a l c u l a t i o n s . We a r e indebted to N. A u s t e r n and R. H. B a s s e l f o r m a n y d i s c u s s i o n s of t h i s p r o b l e m . References
i} N.Atmtora, in: Selected topics in nuclear thecry, ed. F. Janouch (I. A. E. A . , Vienna, 1963). 2) E.C.Halbert, R.M.Drisko, G.R.Satohler and N. Austorn, Prec. of Rutherford Jubilee Conference, Manchester, 1961 (Heywood and Co., Ltd., London, 1962); N.Atmtorn, H.M.Drisko, E.C.Halhert and G.R. Satchler, Phys. Rev. 133 (1964) B3; G.R.Satohler, to be published in Nuclear Physics. 3) G.Wickenburg, S.Hjorth, N.G.E.Johaxmson and B. Sjogren, Arkiv Fystk 25 (1963) 191. 4) A.Kermau and F.P.Gibeon, Proc. Syrup. on Nuclear Spectroscopy with Direct R e a c t t ~ , Chicago, 1964. 5) R.M.Drisko, G.R.Satohlcr and R.H. Bassel, Physics Letters 5 (1963) 350. 6) L. Lee, J.P.Schiffer, B. Zcidman, R.H.Baasel, R.M.Drisko and G.R.Satchler, to be published in Phys. Rev. 7) P. J. A. Buttle and L. B. J. Goldfarb, to be published; Gy. Beneze and J. Zlmauyt, to he published; F . P c r e y and D. Saxon, to be published. 8) J. L.Yntoma and G.R.Satohler, to be published in Phys. Hey. 9) C. L. Lin and S. Yoshtda, to be published.
ON SHORT-RANGE
HYPERFRAGMENTS
S. J. BOSGRA and W. HOOGLAND Z e e m a n L a b o r a t o r i u m , Universitett van A m s t e r d a m
Received 31 March 1964
F o r the i n v e s t i g a t i o n of s h o r t - r a n g e (<5 p~m) h y p e r f r a g m e n t s in n u c l e a r e m u l s i o n , a d i s t i n c t i o n h a s to be m a d e b e t w e e n s t a r s with one and two centres.
In o u r l a b o r a t o r y a m e t h o d h a s b e e n d e v e l o p e d to d e t e r m i n e the m u t u ~ o s i t i o u of the p r o n g s of a s t a r n e a r the c e n t r e "J. With t h i s m e t h o d double c e n t r e d s t a r s with d i s t a n c e s b e t w e e n the ..345
Volume 9, number 4
PHYSICS LETTERS
two c e n t r e s of down to 0.25 /zm can be detected. T h i s l e t t e r d e s c r i b e s the a p p l i c a t i o n of t h i s method to the study of h y p e r f r a g m e n t s p r o d u c e d by 800 M e V / c K- m e s o n s in n u c l e a r e m u l s i o n . The lower l i m i t for the p r o d u c t i o n of h y p e r f r a g merits i s found to be 11.5 ± 1.1%, which does not a g r e e with the 5.3 ± 0.3% o r lower v a l u e s given by other a u t h o r s 2,3). The method c o n s i s t s in m e a s u r i n g and r e c o r d i n g X and Y c o o r d i n a t e s of the g r a i n s of the p r o n g over a d i s t a n c e of 15 - 150 ~ m f r o m the o r i g i n . The choice of the d i s t a n c e depends on the d e n s i t y of the t r a c k . F o r t h i s p u r p o s e a K o r i s t k a MS-2 m i c r o s c o p e was supplied with: a) a m e a s u r i n g eye p i e c e with c r o s s h a i r s in X and Y d i r e c t i o n s , i n d e p e n d e n t l y a d j u s t a b l e , b) d i g i t i z e r s for both the X and Y c r o s s h a i r , c) a p u n c h e r to r e c o r d the c o o r d i n a t e s . F r o m the r e c o r d e d c o o r d i n a t e s a c o m p u t e r p r o g r a m m e c a l c u l a t e s b e s t f i t t i n g l i n e s f o r the p r o n g s and a b e s t f i t t i n g c e n t r e for the s t a r . The data given by the c o m p u t e r a r e u s e d to draw an e n l a r g e d p i c t u r e of the c e n t r e a r e a of the s t a r . M e a s u r e m e n t s w e r e p e r f o r m e d on two s a m p l e s of s t a r s o r i g i n a t i n g in 800 M e V / c K - i n t e r a c t i o n s , which w e r e found by the K - E u r o p e a n C o l l a b o r a tion* in a s t a c k of Iiford K-5 e m u l s i o n (2) by a r e a s c a n n i n g . The f i r s t s a m p l e c o n s i s t e d of 1004 u n s e l e c t e d s t a r s , which had a l r e a d y b e e n s c r u t i n i z e d by the C o l l a b o r a t i o n with the u s u a l v i s u a l method to find d o u b l e - c e n t r e d s t a r s . The second s a m p l e c o n s i s t e d of 114 s t a r s with an o u t c o m i n g hyperon. T h i s l a s t s a m p l e was u s e d to check our method. A s the p o s s i b i l i t y that t h e s e s t a r s a r e d o u b l e - c e n t r e d was a l m o s t excluded, the m e a s u r e m e n t s of t h e s e s t a r s should give u s the c r i t e r i o n , which s t a r s c a n be c l a s s i f i e d a s d o u b l e centred. Fig. 1 shows the d i s t r i b u t i o n of the p r o j e c t e d d i s t a n c e D c f r o m the b e s t f i t t i n g l i n e s to the b e s t f i t t i n g c e n t r e of the p r o d u c t i o n s t a r , for a l l 736 p r o n g s of t h e s e 114 s t a r s . Each d i s t a n c e plotted i s the a v e r a g e r e s u l t obtained f r o m two i n d e p e n dent m e a s u r e m e n t s . A s the c o m p u t e r output i n c l u d e s a p i c t u r e of the p o s i t i o n of the g r a i n s along the b e s t f i t t i n g t r a c k for a l l p r o n g s , i n f o r m a t i o n i s obtained about p o s s i b l e s m a l l s c a t t e r i n g s at the b e g i n n i n g of the t r a c k . It t u r n e d out that in n e a r l y a l l the c a s e s when the d i s t a n c e D c was m o r e than 0.15 ~zm, a s c a t t e r i n g could be detected. In s o m e c a s e s the t r a c k s would be r e c o g n i z e d as e l e c t r o n s . The d i s q u a l i f i e d t r a c k s a r e shaded in fig. 1. P r o n g s of t h i s kind will not * The authors are grateful to the emulsic~ groups of the K- European Collaboration for le-dt-~ them some plates of ]]ford K-5 emulsion and their scanning lists. 346
1 May 1964
+l . 0
.
.
.
. 0.1
.
•r
. 02
.
+
.
~ 0.3
.
.
. - O~
.
.
.
GS
Fig. 1. Distribution of Dc, the projected distance of the best fitting lines to the best fitting centre of the production star for the 736 tracks out of 114 stars with an outcoming ~.. be accepted to c l a s s i f y s t a r s a s d o u b l e - c e n t r e d in the i n v e s t i g a t i o n of the 1004 u n s e l e c t e d s t a r s . On account of the r e s u l t s of fig. 1 we decided to c a l l s t a r s d o u b l e - c e n t r e d when at l e a s t one u n disqualified p r o n g o c c u r r e d with a d i s t a n c e D c > 0.25 /~m. Following t h i s c r i t e r i o n no double s t a r s a r e found in the s a m p l e of 114 s t a r s with an outcoming ~ hyperon. In the s a m p l e of 1004 u n s e l e c t e d s t a r s , 84 d o u b l e - c e n t r e d s t a r s w e r e detected. A n u m b e r which m u s t be c o m p a r e d with the 49 double s t a r s found in this s a m p l e by the K- E u r o p e a n Collab o r a t i o n . T h r e e other s t a r s , indicated a s doublec e n t r e d by the v i s u a l m e t h o d , t u r n e d out to have only one c e n t r e . The a v e r a g e n u m b e r of p r o n g s of the p r i m a r y and s e c o n d a r y s t a r of the s h o r t r a n g e h y p e r f r a g m e n t i s 8.6, and i s , taking into account the e r r o r s , i n d e p e n d e n t of the p r o j e c t e d r a n g e RHF. M o r e o v e r the s a m p l e c o n t a i n s 6 l o n g - r a n g e (RHF > 5 ~tm) h y p e r f r a g m e n t s . We d e r i v e d a r a n g e d i s t r i b u t i o n for the s h o r t - r a n g e h y p e r f r a g m e n t s in two ways. a) In the f i r s t method we d e t e r m i n e d the p o s i t i o n of the two c e n t r e s in the e n l a r g e d d r a w i n g of the c e n t r e a r e a of the s t a r . T h i s was e a s i l y d o n e e x c e p t in the c a s e w h e r e one ~ the two c e n t r e s had only one p r o n g which did not fit
Volume 9, n u m b e r 4
PHYSICS
the o t h e r c e n t r e . In t h i s c a s e the s t a r had to be s c r u t i n i z e d with a l a r g e m a g n i f i c a t i o n u n d e r the m i c r o s c o p e to find i n d i c a t i o n s , which p e r m i t an e s t i m a t e of t h e p o s i t i o n of t h e s e c o n d v e r t e x , f o r i n s t a n c e by u s i n g the Z c o o r d i n a t e . F i g . 2 g i v e s the d i s t r i b u t i o n of the p r o j e c t e d r a n g e s R H F of t h e 81 double c e n t r e d s t a r s , f o r which we could d e t e r m i n e the p o s i t i o n of the two c e n t r e s . T h e 49 double s t a r s which w e r e a l s o found b y t h e K" E u r o p e a n C o l l a b o r a tion a r e s h a d e d . T h e h y p e r f r a g m e n t s with R H F < 1 ~tm a r e e s p e c i a l l y l o s t in t h e v i s u a l m e t h o d . It i s w o r t h n o t i c i n g that t h e n u m b e r of h y p e r f r a g m e n t s s e e m s to i n c r e a s e with d e c r e a s i n g r a n g e , a l s o f o r R H F between 1.00 and 0.25 ~ n . T h e p r o j e c t e d angle in t h e X Y p l a n e between the d i r e c t i o n of the h y p e r f r a g m e n t and the i n c o m i n g K" i s p l o t t e d in fig. 3a and 3b f o r h y p e r f r a g m e n t s with R H F < 1 /~m r e s p . > 1 ~ m . T h e a n g u l s x d i s t r i b u t i o n of t h e h y p e r f r a g m e n t s with RHF < 1 ~ m s e e m s to be more isotropic. b) In the s e c o n d m e t h o d we a v o i d e d the above m e n t i o n e d d i f f i c u l t y in t h a t w e d i d not s e a r c h f o r a s e c o n d s t a r c e n t r e . F i g . 4 g i v e s the d i s t r i b u t i o n of the p r o j e c t e d d i s t a n c e s D c of the 154 u n d i s q u a l t f t e d p r o n g s t h a t o r i g i n a t e in the d e c a y s t a r of t h e s h o r t - r a n g e h y p e r f r a g m e n t . H D c > 0.25 /~m p r o n g s w i l l b e c a l l e d d i s t i n g u i s h a b l e d e c a y s t a r p r o n g s . We a s s u m e that~ 1) the d i s t r i b u t i o n of the d i r e c t i o n s of the p r o n g s of t h e d e c a y s t a r Is i s o t r o p i c ,
0.2S
1
2
]
I EVENT
3"
~
6
Fig. 2. D i s t r i b u t i o n of the p r o j e c t e d r a n g e s RHF of 81 double c e n t r e d s t a r s . The shaded h i s t o g r a m gives the d i s t r i b u t i o n of RI; F of the 49 double s t a r s which w e r e also found b-y-the K - E u r o p e a n Collaboration.
LETTERS
1 May 1964 (a)
N
(b)
N
T
T IO
~t~=D3
10'
J ANGLE IN DEGIEES
180
ANGLE IN DE~qZES
Fig. 3. D i s t r i b u t i o n of the p r o j e c t e d angle in the X Y plane between the d i r e c t i o n of the h y p e r f r a g m e n t and the incoming K- m e s o n s . (0° is forward), (a) RHF < 1 9m, (b) R HF > 1 ~m.
2) t h e m e a n n u m b e r of p r o n g s of the d e c a y s t a r i s independent of t h e r a n g e of the s h o r t - r a n g e hyperfragment. Given t h e s e a s s u m p t i o n s one m a y d e r i v e a p r o b a b i l i t y d i s t r i b u t i o n f o r the d i s t a n c e s D c f o r e a c h p o s s i b l e v a l u e of R H F . The e s t a b l i s h e d r e lation between the d i s t a n c e s D c and R H F p e r m i t s u s i n v e r s e l y to u s e the e x p e r i m e n t a l d a t a on D c (fig. 4) to c a l c u l a t e a p r o b a b i l i t y d i s t r i b u t i o n f o r RHF. In o r d e r to c o m p a r e t h i s d i s t r i b u t i o n with the e x p e r i m e n t a l l y found d i s t r i b u t i o n of fig. 2, we h a v e , f i r s t l y , to n o r m a l i z e the p r o b a b i l i t y d i s t r i b u t i o n b y m u l t i p l y i n g i t b y the m e a n n u m b e r of p r o n g s of the s e c o n d a r y s t a r , s e c o n d l y , to t a k e into account t h a t not a l l s e c o n d a r y s t a r s have one o r m o r e d i s t i n g u i s h a b l e p r o n g s . To obtain the m e a n n u m b e r of p r o n g s of the d e c a y s t a r the o b s e r v e d d i s t r i b u t i o n of the n u m b e r of p r o n g s of t h e d e c a y s t a r h a s to be c o r rected for indistinguishable prongs. All correct i o n s due to i n d i s t i n g u i s h a b l e p r o n g s have been d e r i v e d f r o m the n o n - n o r m a l i z e d d i s t r i b u t i o n of RHF. Both t h e c o r r e c t e d and n o n - c o r r e c t e d p r o n g n u m b e r d i s t r i b u t i o n s a r e given in fig. 5. The m e a n n u m b e r of p r o n g s of t h e s e c o n d a r y s t a r w a s found to be 2.0. The n o r m a l i z e d r a n g e d i s t r i b u t i o n i s given by the dotted line in fig. 6. If we s u b t r a c t t h o s e e v e n t s which a x e l o s t b e c a u s e t h e y have only i n d i s t i n g u i s h a b l e p r o n g s , we find a d i s t r i b u t i o n which i s given by the c o n t i n u o n s line in fig. 6. The d i s t r i b u t i o n o b t a i n e d by t h e f i r s t m e t h o d (fig. 2) i s i n d i c a t e d in fig. 6 with the e r r o r s . 347
Volume 9, number 4
PHYSICS LETTERS
1 May 1964
SO ¸ ; N'
T
20
&0'
i N
T
i
3c
[ |
1 . 0
.
O2S
.
.
.
.
.
1
.
2
.
.
.
.
n . .
I
.
3
I
['-1
4
tq
30
20
I
I I
2
I l
I &
I G
I 6
N t $ 4 8 E R ~ P ~ S
Fig. 5 . Distribution of the number of prongs of the decay star. The continuous line indicates the observed distribution. The dotted line gives the distribution c o r rected for indistinguishable prongs. 348
.
.
,
2
.
.
.
!
3
.
,
]
4
6
S
Fig. 4. Experimental distribution of De, the projected distance from prongs of the decay star to the centre of the production star for the 81 double centred events.
0
.
Fig. 6. Distribution of the projected range of the hyperfragment RHF. The dotted line gives the distribution derived from fig. 4; ~ continuous line is the distribution corrected for indistinguishable prongs; the corresponding points of fig. 2 are indicated with the er r o r s. Th e a g r e e m e n t i s good. With t h i s s e c o n d p r o c e d u r e we find a t o t a l n u m b e r of 97 double s t a r s , of which 13 a r e not d e t e c t e d , b e c a u s e they have no p r o n g in the v i s i b l e a r e a . If we add: a) the 6 s t a r s with a l o n g - r a n g e h y p e r f r a g m e n t , b) an e s t i m a t e d n u m b e r of 6 s t a r s which a r e l o s t a s t h e y have a s p a t i a l r a n g e > 0.25 ~ m , but a p r o j e c t e d r a n g e < 0.25 ~ m , c) 8% to take into account the i m p u r i t y of the b e a m (2), the l o w e r l i m i t f o r the p r o d u c t i o n of h y p e r f r a g r n e n t s b e c o m e s 11.5 ± 1.1%. T h i s is a l o w er l i m i t , due to the f a c t t h a t h y p e r f r a g m e n t s with a z e r o p r o n g s t a r and h y p e r f r a g m e n t s with R H F < 0.25 ~ m a r e left out of consideration. No t r i p l e s t a r s w e r e found. C o n c e r n i n g t h e p r o n g n u m b e r d i s t r i b u t i o n of the d e c a y s t a r it i s s t i l l worth n o t i c i n g , that the n u m b e r of one p r o n g e v e n t s i s not s m a l l e r than that of two p r o n g e v e n t s , a s has b e e n found e l s e w h e r e (4). Our r e s u l t s j u s t i f y the a s s u m p t i o n that the s m a l l e r n u m b e r found, u s i n g t h e v i s u a l m e t h o d , i s due to the low d e t e c t i n g e f f i c i e n c y of t h i s m e t h o d f o r double s t a r s with only one d e c a y s t a r prong.
Volume 9, number 4
PHYSICS
T h e a u t h o r s a r e indebted to the s c a n n i n g group of o u r l a b o r a t o r y , which c a r r i e d out the m e a s u r e m e n t s . T h e y w i s h to thank P r o f e s s o r D r . J. C. K l u y v e r and D r . A. G. T e n n e r f o r t h e i r a d v i c e . T h i s w o r k i s p a r t of the r e s e a r c h p r o g r a m m e of the " S t i c h t i n g v o o r F u n d a m e n t e e l O n d e r z o e k d e r M a t e r i e F. O. M. " , f i n a n c i a l l y s u p p o r t e d by the " N e d e r l a n d s e O r g a n i s a t i e v o o r Z u i v e r W e t e n s c h a p p e l i j k O n d e r z o e k Z. W. O. ".
NEW
EXPERIMENTAL
TEST
LETTERS
1 May 1964
References 1) s . J . Boegrs and A. G. Tenner, Nuclear Instr. and Methods, to be publlBhed. 2) B.D.Jones, B.SanJeevaiah, J. Zakrzewski, M.CseJthey-Barth, J . B . Lagnaux, J. Saotcm, M.J. Beniston, E. H. S. Burhop and D. H. Davis, Phys. Rev. 127 (1962) 236. 3) I.R.Kenyon, Nuovo Cimeuto 29 (1963) 589. 4) J. Zalvrzewski, Warszawa, private communication; A.W.Key, Oxford, private communtcatica~.
OF THE DECAY 2-'_-= A_+ 43~+*
RATE
PREDICTION,
M. L. STEVENSON, J. P. BERGE, J. R. HUBBARD, G.R. K A L B F L E I S C H , J. B. S H A F E R , F . T . SOLMITZ, S. G. WOJCICKI and P. G. WHOLMUT
Lawrence Radiation Labo~'atory, University of California, Be~'keley, California Received 31 March 1964 P r e d i c t i o n s f o r a r e l a t i o n s h i p b e t w e e n the a m p l i t u d e s f o r the n o n l e p t o n i c d e c a y of ~" --~A + ~ - , A-~ P + ~ - , and D + --~ p + no have been m a d e b y L e e 1), G e l l - M a n n 2), S u g a w a r a 3) and C o l e m a n and G l a s h o w 4). L e e , u s i n g SU 3 s y m m e t r y , o c t e t d o m i n a n c e , and R i n v a r i a n c e (i. e. i n v e r s i o n t h r o u g h t h e o r i g i n Tz= 0, Y= 0) p r e d i c t s t h a t t h e nonleptonic c o v a r i a n t d e c a y a m p l i t u d e s f o r both the S wave (,4) and P wave (B) s a t i s f y the r e l a t i o n ship
6_- = A_ + 43~.~,
(1)
and hence a triangular relationship exists. Ge11M a n n finds that the relationship (1) holds for the parlty-violatlng amplitude [i.e. the S-wave (A)] u n d e r the w e a k e r a s s u m p t i o n of CP i n v a r i a n c e and SU$ s y m m e t r y with " o c t e t d o m i n a n c e " . C o l e m a n d and Glashow, l i k e L e e , p r e d i c t t h e r e l a t i o n ship to hold f o r both the S - w a v e (A) and P - w a v e (B) a m p l i t u d e s (L e . , a t r i a n g u l a r r e l a t i o n s h i p ) , but without the s t r o n g a s s u m p t i o n of R i n v a r t a n c e which i s not s a t i s f i e d f o r the s t r o n g i n t e r a c t i o n s . H o w e v e r t t h e y r e q u i r e the e x i s t e n c e of a p r e s e n t l y u n o b s e r v e d o c t e t of sc~_]~" m e s o n s . The w e a k interactions proceeding virtually through these m e s o n s v i o l a t e c o m b i n e d CP and SO 3 i n v a r i a n c e f o r the p a r R y - c o n s e r v i n g a m p l i t u d e [i. e . , the P - w a v e (B)] (M. G e l l - M a n n , p r i v a t e c o m m u n i c a tion. ) We w i s h to p r e s e n t e x p e r i m e n t a l e v i d e n c e f r o m o u r ~ - d a t a in the r e a c t i o n K - + p --* .~- ÷ K + that b e a r s on t h i s p r e d i c t i o n .
A and B a r e r e l a t e d to the d e c a y m a t r i x , and the d e c a y r a t e 5), by
•.Jr= U(b')(A - S'f5) U(b) ,
(2)
and
w = 8~--~{ IA [2 [M+m)2_ ~2] + [BI2 [M- m) 2 - ~2]), (3) The U's are the baryon spinors and M, m and /~ are the rest masses of the parent baryon (b), the decay baryon (b') and decay plon, respectively, q is the pion momentum. In Pauli spin space the decay matrix is written as
-~f= x+(b'){As+ApW ]3b,X(b) ,
(4)
w h e r e P b ' i s the unit v e c t o r in t h e d e c a y b a r y o n d i r e c t i o n , and the X'S a r e P a n l i s p i n o r s . The d e c a y p a r a m e t e r s a r e defined in t e r m s of A s and Ap r a t h e r than A and B, thus
~4pl2), 2 + lap[2),
a = meAsAD*/([Asl 2 +
= 2ImA~Ap*/(lAs[
(s)
T = ([As[ 2 - [Api2)/(IAsl 2 + I A p l 2 ) • A and B a r e r e l a t e d to A s and Ap by • This work done under the auspices of the U.S.Atomic Energy Commtssio~.
349
PHYSICS
any f e a t u r e which r e d u c e s t h e i m p o r t a n c e of t h e s e a l s o r e d u c e s t h e i m p o r t a n c e of FR. A s m a l l binding e n e r g y f o r t h e c a p t u r e d p a r t i c l e , with the consequent g r e a t e r extent of i t s w a v e function ~ n , w i l l do t h i s , a s h a s been i l l u s t r a t e d b y a c a l c u l a t i o n f o r the O18(d,p) r e a c t i o n 3). The two l = 2 g r o u p s f r o m C a ( d , H e 3 ) in fig. 2 show a m a r k e d d e p e n d e n c e , on Q - v a l u e , and h e n c e on t h e binding e n e r g y of t h e p i c k e d - u p p r o t o n . C a p t u r e into an o r b i t whose wavefunction c o n t a i n s one o r m o r e n o d e s a l r e a d y h a s b u i l t - i n s o m e c a n c e l l a t i o n of t h e i n t e r i o r c o n t r i b u t i o n s , so that F R h a s l e s s effect; t h e c o n t r a s t of the 2p with the If c a p t u r e by Ca 40 shown in fig. 1 i l l u s t r a t e s t h i s . A g a i n , if t h e r e a c t i o n i s s t u d i e d at s u f f i c i e n t l y low e n e r g y t h a t t h e Coulomb r e p u l s i o n p r e v e n t s s i g n i f i c a n t c o n t r i b u t i o n s f r o m within the n u c l e u s we would e x p e c t F R to p r o d u c e v e r y l i t t l e change; t h i s h a s been v e r i f i e d by a c a l c u l a t i o n of the W183(d,p) r e a c t i o n at a d e u t e r o n e n e r g y of 6 M e V , and w a s a l s o i n d i c a t e d by o t h e r , a ~ p r o x i m a t e , c a l c u l a t i o n s of s i m i l a r r e a c t i o n s ~J. A n o t h e r r e l e v a n t f a c t o r i s the c h o i c e of o p t i c a l p o t e n t i a l f o r c o m p l e x p a r t i c l e s ; t h e s e a r e known to be h i g h l y a m b i g u o u s . A whole s e r i e s of p o t e n t i a l s can be found which give the s a m e e l a s t i c s c a t t e r i n g , and which d i f f e r , r o u g h l y , in the n u m b e r of w a v e l e n g t h s i n c l u d e d in the n u c l e a r i n t e r i o r 5). The d e e p e r the p o t e n t i a l , the m o r e r a p i d l y d o e s the a s s o c i a t e d wave o s c i l l a t e i n s i d e the n u c l e u s , and the s m a l l e r the c o n t r i b u t i o n to the r e a c t i o n f r o m t h i s r e g i o n even in the ZR a p p r o x i m a t i o n . Then we e x p e c t , and find, the F R effect to be r e d u c e d a l s o . The two e x a m p l e s given in fig. 1 i l l u s t r a t e t h i s ; the " s h a l l o w " d e u t e r o n p o t e n t i a l i s a p p r o x i m a t e l y 70 MeV d e e p , w h i l e t h e " d e e p " one h a s a depth of about UO MeV. P o -
MEASUREMENTS
LETTERS
1 May 1964
t e n t i a l s d e e p e r than t h i s (which s t i l l r e p r o d u c e the e l a s t i c s c a t t e r i n g 6)) show a l m o s t no d i f f e r ence between ZR and F R p r e d i c t i o n s . D e s p i t e t h e s e i n i t i a l s u c c e s s e s in u n d e r s t a n d hag F R e f f e c t s , e x t e n s i v e w o r k r e m a i n s to be done i n o r d e r to d i s c o v e r t h e i r m o r e d e t a i l e d b e h a v i o u r , such a s to what e x t e n t t h e y can be r e p r o d u c e d by a n / - i n d e p e n d e n t cut-off in a ZR c a l culation. R e c e n t l y s e v e r a l p r o p o s a l s f o r a p p r o x i m a t e F R c o r r e c t i o n s have been m a d e 7), and the a c c u r a c y of t h e s e i s c u r r e n t l y being t e s t e d by c o m p a r i s o n with e x a c t c a l c u l a t i o n s . We a r e indebted to N. A u s t e r n and R. H. B a s s e l f o r m a n y d i s c u s s i o n s of t h i s p r o b l e m . References
i} N.Atmtora, in: Selected topics in nuclear thecry, ed. F. Janouch (I. A. E. A . , Vienna, 1963). 2) E.C.Halbert, R.M.Drisko, G.R.Satohler and N. Austorn, Prec. of Rutherford Jubilee Conference, Manchester, 1961 (Heywood and Co., Ltd., London, 1962); N.Atmtorn, H.M.Drisko, E.C.Halhert and G.R. Satchler, Phys. Rev. 133 (1964) B3; G.R.Satohler, to be published in Nuclear Physics. 3) G.Wickenburg, S.Hjorth, N.G.E.Johaxmson and B. Sjogren, Arkiv Fystk 25 (1963) 191. 4) A.Kermau and F.P.Gibeon, Proc. Syrup. on Nuclear Spectroscopy with Direct R e a c t t ~ , Chicago, 1964. 5) R.M.Drisko, G.R.Satohlcr and R.H. Bassel, Physics Letters 5 (1963) 350. 6) L. Lee, J.P.Schiffer, B. Zcidman, R.H.Baasel, R.M.Drisko and G.R.Satchler, to be published in Phys. Rev. 7) P. J. A. Buttle and L. B. J. Goldfarb, to be published; Gy. Beneze and J. Zlmauyt, to he published; F . P c r e y and D. Saxon, to be published. 8) J. L.Yntoma and G.R.Satohler, to be published in Phys. Hey. 9) C. L. Lin and S. Yoshtda, to be published.
ON SHORT-RANGE
HYPERFRAGMENTS
S. J. BOSGRA and W. HOOGLAND Z e e m a n L a b o r a t o r i u m , Universitett van A m s t e r d a m
Received 31 March 1964
F o r the i n v e s t i g a t i o n of s h o r t - r a n g e (<5 p~m) h y p e r f r a g m e n t s in n u c l e a r e m u l s i o n , a d i s t i n c t i o n h a s to be m a d e b e t w e e n s t a r s with one and two centres.
In o u r l a b o r a t o r y a m e t h o d h a s b e e n d e v e l o p e d to d e t e r m i n e the m u t u ~ o s i t i o u of the p r o n g s of a s t a r n e a r the c e n t r e "J. With t h i s m e t h o d double c e n t r e d s t a r s with d i s t a n c e s b e t w e e n the ..345
Volume 9, number 4
PHYSICS LETTERS
two c e n t r e s of down to 0.25 /zm can be detected. T h i s l e t t e r d e s c r i b e s the a p p l i c a t i o n of t h i s method to the study of h y p e r f r a g m e n t s p r o d u c e d by 800 M e V / c K- m e s o n s in n u c l e a r e m u l s i o n . The lower l i m i t for the p r o d u c t i o n of h y p e r f r a g merits i s found to be 11.5 ± 1.1%, which does not a g r e e with the 5.3 ± 0.3% o r lower v a l u e s given by other a u t h o r s 2,3). The method c o n s i s t s in m e a s u r i n g and r e c o r d i n g X and Y c o o r d i n a t e s of the g r a i n s of the p r o n g over a d i s t a n c e of 15 - 150 ~ m f r o m the o r i g i n . The choice of the d i s t a n c e depends on the d e n s i t y of the t r a c k . F o r t h i s p u r p o s e a K o r i s t k a MS-2 m i c r o s c o p e was supplied with: a) a m e a s u r i n g eye p i e c e with c r o s s h a i r s in X and Y d i r e c t i o n s , i n d e p e n d e n t l y a d j u s t a b l e , b) d i g i t i z e r s for both the X and Y c r o s s h a i r , c) a p u n c h e r to r e c o r d the c o o r d i n a t e s . F r o m the r e c o r d e d c o o r d i n a t e s a c o m p u t e r p r o g r a m m e c a l c u l a t e s b e s t f i t t i n g l i n e s f o r the p r o n g s and a b e s t f i t t i n g c e n t r e for the s t a r . The data given by the c o m p u t e r a r e u s e d to draw an e n l a r g e d p i c t u r e of the c e n t r e a r e a of the s t a r . M e a s u r e m e n t s w e r e p e r f o r m e d on two s a m p l e s of s t a r s o r i g i n a t i n g in 800 M e V / c K - i n t e r a c t i o n s , which w e r e found by the K - E u r o p e a n C o l l a b o r a tion* in a s t a c k of Iiford K-5 e m u l s i o n (2) by a r e a s c a n n i n g . The f i r s t s a m p l e c o n s i s t e d of 1004 u n s e l e c t e d s t a r s , which had a l r e a d y b e e n s c r u t i n i z e d by the C o l l a b o r a t i o n with the u s u a l v i s u a l method to find d o u b l e - c e n t r e d s t a r s . The second s a m p l e c o n s i s t e d of 114 s t a r s with an o u t c o m i n g hyperon. T h i s l a s t s a m p l e was u s e d to check our method. A s the p o s s i b i l i t y that t h e s e s t a r s a r e d o u b l e - c e n t r e d was a l m o s t excluded, the m e a s u r e m e n t s of t h e s e s t a r s should give u s the c r i t e r i o n , which s t a r s c a n be c l a s s i f i e d a s d o u b l e centred. Fig. 1 shows the d i s t r i b u t i o n of the p r o j e c t e d d i s t a n c e D c f r o m the b e s t f i t t i n g l i n e s to the b e s t f i t t i n g c e n t r e of the p r o d u c t i o n s t a r , for a l l 736 p r o n g s of t h e s e 114 s t a r s . Each d i s t a n c e plotted i s the a v e r a g e r e s u l t obtained f r o m two i n d e p e n dent m e a s u r e m e n t s . A s the c o m p u t e r output i n c l u d e s a p i c t u r e of the p o s i t i o n of the g r a i n s along the b e s t f i t t i n g t r a c k for a l l p r o n g s , i n f o r m a t i o n i s obtained about p o s s i b l e s m a l l s c a t t e r i n g s at the b e g i n n i n g of the t r a c k . It t u r n e d out that in n e a r l y a l l the c a s e s when the d i s t a n c e D c was m o r e than 0.15 ~zm, a s c a t t e r i n g could be detected. In s o m e c a s e s the t r a c k s would be r e c o g n i z e d as e l e c t r o n s . The d i s q u a l i f i e d t r a c k s a r e shaded in fig. 1. P r o n g s of t h i s kind will not * The authors are grateful to the emulsic~ groups of the K- European Collaboration for le-dt-~ them some plates of ]]ford K-5 emulsion and their scanning lists. 346
1 May 1964
+l . 0
.
.
.
. 0.1
.
•r
. 02
.
+
.
~ 0.3
.
.
. - O~
.
.
.
GS
Fig. 1. Distribution of Dc, the projected distance of the best fitting lines to the best fitting centre of the production star for the 736 tracks out of 114 stars with an outcoming ~.. be accepted to c l a s s i f y s t a r s a s d o u b l e - c e n t r e d in the i n v e s t i g a t i o n of the 1004 u n s e l e c t e d s t a r s . On account of the r e s u l t s of fig. 1 we decided to c a l l s t a r s d o u b l e - c e n t r e d when at l e a s t one u n disqualified p r o n g o c c u r r e d with a d i s t a n c e D c > 0.25 /~m. Following t h i s c r i t e r i o n no double s t a r s a r e found in the s a m p l e of 114 s t a r s with an outcoming ~ hyperon. In the s a m p l e of 1004 u n s e l e c t e d s t a r s , 84 d o u b l e - c e n t r e d s t a r s w e r e detected. A n u m b e r which m u s t be c o m p a r e d with the 49 double s t a r s found in this s a m p l e by the K- E u r o p e a n Collab o r a t i o n . T h r e e other s t a r s , indicated a s doublec e n t r e d by the v i s u a l m e t h o d , t u r n e d out to have only one c e n t r e . The a v e r a g e n u m b e r of p r o n g s of the p r i m a r y and s e c o n d a r y s t a r of the s h o r t r a n g e h y p e r f r a g m e n t i s 8.6, and i s , taking into account the e r r o r s , i n d e p e n d e n t of the p r o j e c t e d r a n g e RHF. M o r e o v e r the s a m p l e c o n t a i n s 6 l o n g - r a n g e (RHF > 5 ~tm) h y p e r f r a g m e n t s . We d e r i v e d a r a n g e d i s t r i b u t i o n for the s h o r t - r a n g e h y p e r f r a g m e n t s in two ways. a) In the f i r s t method we d e t e r m i n e d the p o s i t i o n of the two c e n t r e s in the e n l a r g e d d r a w i n g of the c e n t r e a r e a of the s t a r . T h i s was e a s i l y d o n e e x c e p t in the c a s e w h e r e one ~ the two c e n t r e s had only one p r o n g which did not fit
Volume 9, n u m b e r 4
PHYSICS
the o t h e r c e n t r e . In t h i s c a s e the s t a r had to be s c r u t i n i z e d with a l a r g e m a g n i f i c a t i o n u n d e r the m i c r o s c o p e to find i n d i c a t i o n s , which p e r m i t an e s t i m a t e of t h e p o s i t i o n of t h e s e c o n d v e r t e x , f o r i n s t a n c e by u s i n g the Z c o o r d i n a t e . F i g . 2 g i v e s the d i s t r i b u t i o n of the p r o j e c t e d r a n g e s R H F of t h e 81 double c e n t r e d s t a r s , f o r which we could d e t e r m i n e the p o s i t i o n of the two c e n t r e s . T h e 49 double s t a r s which w e r e a l s o found b y t h e K" E u r o p e a n C o l l a b o r a tion a r e s h a d e d . T h e h y p e r f r a g m e n t s with R H F < 1 ~tm a r e e s p e c i a l l y l o s t in t h e v i s u a l m e t h o d . It i s w o r t h n o t i c i n g that t h e n u m b e r of h y p e r f r a g m e n t s s e e m s to i n c r e a s e with d e c r e a s i n g r a n g e , a l s o f o r R H F between 1.00 and 0.25 ~ n . T h e p r o j e c t e d angle in t h e X Y p l a n e between the d i r e c t i o n of the h y p e r f r a g m e n t and the i n c o m i n g K" i s p l o t t e d in fig. 3a and 3b f o r h y p e r f r a g m e n t s with R H F < 1 /~m r e s p . > 1 ~ m . T h e a n g u l s x d i s t r i b u t i o n of t h e h y p e r f r a g m e n t s with RHF < 1 ~ m s e e m s to be more isotropic. b) In the s e c o n d m e t h o d we a v o i d e d the above m e n t i o n e d d i f f i c u l t y in t h a t w e d i d not s e a r c h f o r a s e c o n d s t a r c e n t r e . F i g . 4 g i v e s the d i s t r i b u t i o n of the p r o j e c t e d d i s t a n c e s D c of the 154 u n d i s q u a l t f t e d p r o n g s t h a t o r i g i n a t e in the d e c a y s t a r of t h e s h o r t - r a n g e h y p e r f r a g m e n t . H D c > 0.25 /~m p r o n g s w i l l b e c a l l e d d i s t i n g u i s h a b l e d e c a y s t a r p r o n g s . We a s s u m e that~ 1) the d i s t r i b u t i o n of the d i r e c t i o n s of the p r o n g s of t h e d e c a y s t a r Is i s o t r o p i c ,
0.2S
1
2
]
I EVENT
3"
~
6
Fig. 2. D i s t r i b u t i o n of the p r o j e c t e d r a n g e s RHF of 81 double c e n t r e d s t a r s . The shaded h i s t o g r a m gives the d i s t r i b u t i o n of RI; F of the 49 double s t a r s which w e r e also found b-y-the K - E u r o p e a n Collaboration.
LETTERS
1 May 1964 (a)
N
(b)
N
T
T IO
~t~=D3
10'
J ANGLE IN DEGIEES
180
ANGLE IN DE~qZES
Fig. 3. D i s t r i b u t i o n of the p r o j e c t e d angle in the X Y plane between the d i r e c t i o n of the h y p e r f r a g m e n t and the incoming K- m e s o n s . (0° is forward), (a) RHF < 1 9m, (b) R HF > 1 ~m.
2) t h e m e a n n u m b e r of p r o n g s of the d e c a y s t a r i s independent of t h e r a n g e of the s h o r t - r a n g e hyperfragment. Given t h e s e a s s u m p t i o n s one m a y d e r i v e a p r o b a b i l i t y d i s t r i b u t i o n f o r the d i s t a n c e s D c f o r e a c h p o s s i b l e v a l u e of R H F . The e s t a b l i s h e d r e lation between the d i s t a n c e s D c and R H F p e r m i t s u s i n v e r s e l y to u s e the e x p e r i m e n t a l d a t a on D c (fig. 4) to c a l c u l a t e a p r o b a b i l i t y d i s t r i b u t i o n f o r RHF. In o r d e r to c o m p a r e t h i s d i s t r i b u t i o n with the e x p e r i m e n t a l l y found d i s t r i b u t i o n of fig. 2, we h a v e , f i r s t l y , to n o r m a l i z e the p r o b a b i l i t y d i s t r i b u t i o n b y m u l t i p l y i n g i t b y the m e a n n u m b e r of p r o n g s of the s e c o n d a r y s t a r , s e c o n d l y , to t a k e into account t h a t not a l l s e c o n d a r y s t a r s have one o r m o r e d i s t i n g u i s h a b l e p r o n g s . To obtain the m e a n n u m b e r of p r o n g s of the d e c a y s t a r the o b s e r v e d d i s t r i b u t i o n of the n u m b e r of p r o n g s of t h e d e c a y s t a r h a s to be c o r rected for indistinguishable prongs. All correct i o n s due to i n d i s t i n g u i s h a b l e p r o n g s have been d e r i v e d f r o m the n o n - n o r m a l i z e d d i s t r i b u t i o n of RHF. Both t h e c o r r e c t e d and n o n - c o r r e c t e d p r o n g n u m b e r d i s t r i b u t i o n s a r e given in fig. 5. The m e a n n u m b e r of p r o n g s of t h e s e c o n d a r y s t a r w a s found to be 2.0. The n o r m a l i z e d r a n g e d i s t r i b u t i o n i s given by the dotted line in fig. 6. If we s u b t r a c t t h o s e e v e n t s which a x e l o s t b e c a u s e t h e y have only i n d i s t i n g u i s h a b l e p r o n g s , we find a d i s t r i b u t i o n which i s given by the c o n t i n u o n s line in fig. 6. The d i s t r i b u t i o n o b t a i n e d by t h e f i r s t m e t h o d (fig. 2) i s i n d i c a t e d in fig. 6 with the e r r o r s . 347
Volume 9, number 4
PHYSICS LETTERS
1 May 1964
SO ¸ ; N'
T
20
&0'
i N
T
i
3c
[ |
1 . 0
.
O2S
.
.
.
.
.
1
.
2
.
.
.
.
n . .
I
.
3
I
['-1
4
tq
30
20
I
I I
2
I l
I &
I G
I 6
N t $ 4 8 E R ~ P ~ S
Fig. 5 . Distribution of the number of prongs of the decay star. The continuous line indicates the observed distribution. The dotted line gives the distribution c o r rected for indistinguishable prongs. 348
.
.
,
2
.
.
.
!
3
.
,
]
4
6
S
Fig. 4. Experimental distribution of De, the projected distance from prongs of the decay star to the centre of the production star for the 81 double centred events.
0
.
Fig. 6. Distribution of the projected range of the hyperfragment RHF. The dotted line gives the distribution derived from fig. 4; ~ continuous line is the distribution corrected for indistinguishable prongs; the corresponding points of fig. 2 are indicated with the er r o r s. Th e a g r e e m e n t i s good. With t h i s s e c o n d p r o c e d u r e we find a t o t a l n u m b e r of 97 double s t a r s , of which 13 a r e not d e t e c t e d , b e c a u s e they have no p r o n g in the v i s i b l e a r e a . If we add: a) the 6 s t a r s with a l o n g - r a n g e h y p e r f r a g m e n t , b) an e s t i m a t e d n u m b e r of 6 s t a r s which a r e l o s t a s t h e y have a s p a t i a l r a n g e > 0.25 ~ m , but a p r o j e c t e d r a n g e < 0.25 ~ m , c) 8% to take into account the i m p u r i t y of the b e a m (2), the l o w e r l i m i t f o r the p r o d u c t i o n of h y p e r f r a g r n e n t s b e c o m e s 11.5 ± 1.1%. T h i s is a l o w er l i m i t , due to the f a c t t h a t h y p e r f r a g m e n t s with a z e r o p r o n g s t a r and h y p e r f r a g m e n t s with R H F < 0.25 ~ m a r e left out of consideration. No t r i p l e s t a r s w e r e found. C o n c e r n i n g t h e p r o n g n u m b e r d i s t r i b u t i o n of the d e c a y s t a r it i s s t i l l worth n o t i c i n g , that the n u m b e r of one p r o n g e v e n t s i s not s m a l l e r than that of two p r o n g e v e n t s , a s has b e e n found e l s e w h e r e (4). Our r e s u l t s j u s t i f y the a s s u m p t i o n that the s m a l l e r n u m b e r found, u s i n g t h e v i s u a l m e t h o d , i s due to the low d e t e c t i n g e f f i c i e n c y of t h i s m e t h o d f o r double s t a r s with only one d e c a y s t a r prong.
Volume 9, number 4
PHYSICS
T h e a u t h o r s a r e indebted to the s c a n n i n g group of o u r l a b o r a t o r y , which c a r r i e d out the m e a s u r e m e n t s . T h e y w i s h to thank P r o f e s s o r D r . J. C. K l u y v e r and D r . A. G. T e n n e r f o r t h e i r a d v i c e . T h i s w o r k i s p a r t of the r e s e a r c h p r o g r a m m e of the " S t i c h t i n g v o o r F u n d a m e n t e e l O n d e r z o e k d e r M a t e r i e F. O. M. " , f i n a n c i a l l y s u p p o r t e d by the " N e d e r l a n d s e O r g a n i s a t i e v o o r Z u i v e r W e t e n s c h a p p e l i j k O n d e r z o e k Z. W. O. ".
NEW
EXPERIMENTAL
TEST
LETTERS
1 May 1964
References 1) s . J . Boegrs and A. G. Tenner, Nuclear Instr. and Methods, to be publlBhed. 2) B.D.Jones, B.SanJeevaiah, J. Zakrzewski, M.CseJthey-Barth, J . B . Lagnaux, J. Saotcm, M.J. Beniston, E. H. S. Burhop and D. H. Davis, Phys. Rev. 127 (1962) 236. 3) I.R.Kenyon, Nuovo Cimeuto 29 (1963) 589. 4) J. Zalvrzewski, Warszawa, private communication; A.W.Key, Oxford, private communtcatica~.
OF THE DECAY 2-'_-= A_+ 43~+*
RATE
PREDICTION,
M. L. STEVENSON, J. P. BERGE, J. R. HUBBARD, G.R. K A L B F L E I S C H , J. B. S H A F E R , F . T . SOLMITZ, S. G. WOJCICKI and P. G. WHOLMUT
Lawrence Radiation Labo~'atory, University of California, Be~'keley, California Received 31 March 1964 P r e d i c t i o n s f o r a r e l a t i o n s h i p b e t w e e n the a m p l i t u d e s f o r the n o n l e p t o n i c d e c a y of ~" --~A + ~ - , A-~ P + ~ - , and D + --~ p + no have been m a d e b y L e e 1), G e l l - M a n n 2), S u g a w a r a 3) and C o l e m a n and G l a s h o w 4). L e e , u s i n g SU 3 s y m m e t r y , o c t e t d o m i n a n c e , and R i n v a r i a n c e (i. e. i n v e r s i o n t h r o u g h t h e o r i g i n Tz= 0, Y= 0) p r e d i c t s t h a t t h e nonleptonic c o v a r i a n t d e c a y a m p l i t u d e s f o r both the S wave (,4) and P wave (B) s a t i s f y the r e l a t i o n ship
6_- = A_ + 43~.~,
(1)
and hence a triangular relationship exists. Ge11M a n n finds that the relationship (1) holds for the parlty-violatlng amplitude [i.e. the S-wave (A)] u n d e r the w e a k e r a s s u m p t i o n of CP i n v a r i a n c e and SU$ s y m m e t r y with " o c t e t d o m i n a n c e " . C o l e m a n d and Glashow, l i k e L e e , p r e d i c t t h e r e l a t i o n ship to hold f o r both the S - w a v e (A) and P - w a v e (B) a m p l i t u d e s (L e . , a t r i a n g u l a r r e l a t i o n s h i p ) , but without the s t r o n g a s s u m p t i o n of R i n v a r t a n c e which i s not s a t i s f i e d f o r the s t r o n g i n t e r a c t i o n s . H o w e v e r t t h e y r e q u i r e the e x i s t e n c e of a p r e s e n t l y u n o b s e r v e d o c t e t of sc~_]~" m e s o n s . The w e a k interactions proceeding virtually through these m e s o n s v i o l a t e c o m b i n e d CP and SO 3 i n v a r i a n c e f o r the p a r R y - c o n s e r v i n g a m p l i t u d e [i. e . , the P - w a v e (B)] (M. G e l l - M a n n , p r i v a t e c o m m u n i c a tion. ) We w i s h to p r e s e n t e x p e r i m e n t a l e v i d e n c e f r o m o u r ~ - d a t a in the r e a c t i o n K - + p --* .~- ÷ K + that b e a r s on t h i s p r e d i c t i o n .
A and B a r e r e l a t e d to the d e c a y m a t r i x , and the d e c a y r a t e 5), by
•.Jr= U(b')(A - S'f5) U(b) ,
(2)
and
w = 8~--~{ IA [2 [M+m)2_ ~2] + [BI2 [M- m) 2 - ~2]), (3) The U's are the baryon spinors and M, m and /~ are the rest masses of the parent baryon (b), the decay baryon (b') and decay plon, respectively, q is the pion momentum. In Pauli spin space the decay matrix is written as
-~f= x+(b'){As+ApW ]3b,X(b) ,
(4)
w h e r e P b ' i s the unit v e c t o r in t h e d e c a y b a r y o n d i r e c t i o n , and the X'S a r e P a n l i s p i n o r s . The d e c a y p a r a m e t e r s a r e defined in t e r m s of A s and Ap r a t h e r than A and B, thus
~4pl2), 2 + lap[2),
a = meAsAD*/([Asl 2 +
= 2ImA~Ap*/(lAs[
(s)
T = ([As[ 2 - [Api2)/(IAsl 2 + I A p l 2 ) • A and B a r e r e l a t e d to A s and Ap by • This work done under the auspices of the U.S.Atomic Energy Commtssio~.
349