6
VOLUME 15, NUMBER 9 PHYSICAL REVIEW LETTERS 30 AUGUST 1965 excite t h e 2~~ bands and show the enhanced B(E3) values (as has been done for the K = 0~ bands). 13 It is not likely that a K - 0~~ band lies below the K = 2~ band in Cm 246 , and thus the lowest octu- pole band has probably changed between pluton- ium and curium from K = 0~ to K = 2~. It is interesting that in just this same region the lowest quadrupole vibration changes from K = 0 + (beta) toK = 2* (gamma). This must have to do with the general type of orbitals filling in these regions, and the calculations of Soloviev and Siklos bear out both of these crossovers in a general way, although they have probably underestimated the collective nature of the K ~2~ bands. This work would not have been possible with- out the help of the staff of the Lawrence Radia- tion Laboratory at Livermore, who produced the Pu 246 . We are particularly grateful to Dr. Richard W. Hoff. The initial chemical process- ing on one of the Pu samples was done at Ar- gonne National Laboratory. We appreciate the help of their chemistry staff, especially that of Dr. Herbert Diamond. The initial chemical processing for the other Pu 246 sample was done by the Berkeley Heavy Element Production Staff. Special thanks are due to Mr. Thomas C. Par- sons . 1 D. Engelkemeir, P 0 R. Fields, S. Fried, G. L. Pyle, C M . Stevens, L» B. Asprey, C. I. Brown, H. Louise Smith, and R. W. Spence, J. Inorg. Nucl. Chem. 1., 345 (1955). 2 D. C. Hoffman and C. I. Brown, J. Inorg. Nucl. Chem. _2, 209 (1956). 3 H. L. Smith, C. I. Brown, D. C. Hoffman, J. P. Mize, and M. E. Bunker, J. Inorg. Nucl. Chem. 3^, 93 (1956). 4 J. M 0 Hollander and J. Haverfield, unpublished data, 1965. 5 S. G. Nilsson, Kgl. Danske Videnskab. Selskab, Mat.-Fys 0 Medd. 29, No. 16 (1955). 6 B. R. Mottelson and S. G. Nilsson, Kgl. Danske Videnskab. Selskab, Mat.-Fis. Skrifter JL, No. 8 (1959); F. S. Stephens, F. Asaro, and I. Perlman, Phys. Rev. 113, 212 (1959). 7 V. G. Soloviev and T. Siklos, Nucl. Phys. 5£, 145 (1964). 8 C. J. Gallagher and V. G. Soloviev, Kgl. Danske Videnskab. Selskab, Mat.-Fis. Skrifter 2, No. 2 (1962). 9 A. Bohr and B. R. Mottelson, to be published. 0. Nathan and S. G. Nilsson, Alpha-, Beta-, and Gam- ma-Ray Spectroscopy, edited by K. Siegbahn (North- Holland Publishing Company, Amsterdam, 1965), Chap. X 0 10 Nathan and Nilsson, reference 9. U F. Asaro, A. Chetam-Strode, F. S. Stephens, and 1. Perlman, unpublished data. 12 F. Asaro, B. G. Harvey, and I. Perlman, unpub- lished data. i3 R 0 3VL Diamond, B. Elbek, G. Igo, and F. S. Ste- phens , in Proceedings of the International Conference on Nuclear Structure, Kingston, 1960 edited by D. A. Bromley and E. W. Vogt (University of Toronto Press, Toronto, Canada, 1960), p. 563. U(12) PREDICTIONS FOR NN ANNIHILATION AT REST INTO FOUR MESONS* Y. C. Leung and M. A. Rashid International Atomic Energy Agency, International Centre for Theoretical Physics, Trieste, Italy (Received 5 May 1965) In an earlier note 1 ' 2 we have, together with Delbourgo and Strathdee, reported some pre- dictions based on the U(12) symmetry scheme 3 for pp annihilation at rest into three mesons (annihilation at rest into two mesons is forbid- den). Most of these predictions are in reason- able agreement with experiments, and they are interesting because none of these results can be reached using SU(6) alone. In this note we apply the same procedure to the study of the problem of NN annihilation at rest into four mesons. The aim of the present analysis is to obtain predictions for annihila- tion modes where the final products consist entirely of pseudoscalar mesons, since experi- mental information on these is most easily ac- cessible. In particular, final products contain- ing two K mesons a r e of special interest as these modes are forbidden in the previously considered case. Toward this aim we have reached conclusions which are very specific. In the present as well as the previous anal- yses, we consider the annihilation amplitudes to consist only of the "regular" couplings, which are U(l2)-invariant quantities before an actual identification of the external lines with physi- cal particles is made. In this manner, one obtains the interesting results that (a) NN an- 424

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Page 1: Annihilation at Rest Into Four Mesons

VOLUME 15, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 30 AUGUST 1965

excite the 2~~ bands and show the enhanced B(E3) values (as has been done for the K = 0~ bands).1 3

It is not likely that a K - 0~~ band l ies below the K = 2~ band in Cm246 , and thus the lowest octu-pole band has probably changed between pluton-ium and cur ium from K = 0~ to K = 2~. It is in te res t ing that in just this s a m e region the lowest quadrupole vibrat ion changes from K = 0+

(beta) toK = 2* (gamma). This mus t have to do with the genera l type of orb i ta l s filling in these reg ions , and the calculat ions of Soloviev and Siklos bear out both of these c r o s s o v e r s in a genera l way, although they have probably underes t imated the collective na ture of the K ~2~ bands.

This work would not have been poss ib le with­out the help of the staff of the Lawrence Radia­tion Laboratory at L i v e r m o r e , who produced the Pu246. We a r e pa r t i cu la r ly grateful to Dr. Richard W. Hoff. The initial chemical p r o c e s s ­ing on one of the Pu samples was done at A r -gonne National Laboratory . We apprec ia te the help of their chemis t ry staff, especial ly that of Dr . Herbe r t Diamond. The initial chemical p rocess ing for the other Pu246 sample was done by the Berkeley Heavy Element Product ion Staff. Special thanks a r e due to Mr. Thomas C. P a r ­sons .

1D. Engelkemeir, P0 R. Fields, S. Fried, G. L. Pyle,

C M . Stevens, L» B. Asprey, C. I. Brown, H. Louise Smith, and R. W. Spence, J. Inorg. Nucl. Chem. 1., 345 (1955).

2D. C. Hoffman and C. I. Brown, J. Inorg. Nucl. Chem. _2, 209 (1956).

3H. L. Smith, C. I. Brown, D. C. Hoffman, J. P . Mize, and M. E. Bunker, J. Inorg. Nucl. Chem. 3̂ , 93 (1956).

4J. M0 Hollander and J. Haverfield, unpublished data, 1965.

5S. G. Nilsson, Kgl. Danske Videnskab. Selskab, Mat.-Fys0 Medd. 29, No. 16 (1955).

6B. R. Mottelson and S. G. Nilsson, Kgl. Danske Videnskab. Selskab, Mat.-Fis. Skrifter JL, No. 8 (1959); F. S. Stephens, F. Asaro, and I. Perlman, Phys. Rev. 113, 212 (1959).

7V. G. Soloviev and T. Siklos, Nucl. Phys. 5£, 145 (1964).

8C. J. Gallagher and V. G. Soloviev, Kgl. Danske Videnskab. Selskab, Mat.-Fis. Skrifter 2, No. 2 (1962).

9A. Bohr and B. R. Mottelson, to be published. 0 . Nathan and S. G. Nilsson, Alpha-, Beta-, and Gam­ma-Ray Spectroscopy, edited by K. Siegbahn (North-Holland Publishing Company, Amsterdam, 1965), Chap. X0

10Nathan and Nilsson, reference 9. U F . Asaro, A. Chetam-Strode, F. S. Stephens, and

1. Perlman, unpublished data. 12F. Asaro, B. G. Harvey, and I. Perlman, unpub­

lished data. i3R0 3VL Diamond, B. Elbek, G. Igo, and F. S. Ste­

phens , in Proceedings of the International Conference on Nuclear Structure, Kingston, 1960 edited by D. A. Bromley and E. W. Vogt (University of Toronto Press , Toronto, Canada, 1960), p. 563.

U(12) PREDICTIONS FOR NN ANNIHILATION AT REST INTO FOUR MESONS*

Y. C. Leung and M. A. Rashid

International Atomic Energy Agency, International Centre for Theoretical Physics, Trieste, Italy (Received 5 May 1965)

In an e a r l i e r note1 '2 we have, together with Delbourgo and Strathdee, r epor ted some p r e ­dict ions based on the U(12) s y m m e t r y scheme 3

for pp annihilation at r e s t into th ree mesons (annihilation at r e s t into two mesons is forbid­den). Most of these predic t ions a r e in r e a s o n ­able ag reemen t with exper imen t s , and they a r e in teres t ing because none of these r e s u l t s can be reached using SU(6) alone.

In th is note we apply the s a m e p rocedure to the study of the problem of NN annihilation at r e s t into four mesons . The a im of the p re sen t analys is i s to obtain predic t ions for annihi la­tion modes where the final products cons is t

ent i re ly of pseudosca la r mesons , s ince e x p e r i ­mental information on these is most easi ly a c ­ces s ib l e . In pa r t i cu la r , final products contain­ing two K mesons a r e of specia l in t e res t a s these modes a r e forbidden in the previously considered c a s e . Toward this a im we have reached conclusions which a r e ve ry specif ic .

In the p resen t a s well as the previous ana l ­y s e s , we cons ider the annihilation ampli tudes to consis t only of the " r e g u l a r " couplings, which a r e U( l2)- invar iant quantit ies before an actual identification of the external l ines with phys i ­ca l pa r t i c l e s i s made . In th is manner , one obtains the in teres t ing r e s u l t s that (a) NN an-

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VOLUME 15, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 30 AUGUST 1965

nihilation at r e s t into two mesons is forbidden, and (b) the couplings for annihilat ions into t h r e e mesons is unique. However, s ince the U(12) s y m m e t r y is in t r ins ica l ly broken for a phys i ­ca l S -mat r ix e lement , t he re i s no r e a s o n a p r i o r i to exclude couplings which contain s y m ­me t ry -b reak ing k ine t i c -energy p a r t s , r e f e r r e d to as " i r r e g u l a r " couplings. This point has been emphasized by seve ra l au thors recent ly . 4

These i r r e g u l a r coupling t e r m s a r e indeed needed in o r d e r to avoid ce r t a in difficulties encountered in the theory such as the p rob lem of z e r o polar izat ion. 5 The inclusion of these t e r m s would invalidate all the conclusions reached in r e f e r ences 1 and 2. However, s ince the r a t e of pp annihilation into two mesons i s , in fact, smal l for no other r e a s o n s , and the predic t ions for the t h r e e - m e s o n modes a r e in reasonab le agreement with expe r imen t s , we a r e led to believe that t e r m s involving k i ­ne t i c -energy p a r t s a r e for some r ea son sma l l in these c a s e s , and it i s meaningful to a t t r ibute all p r o c e s s e s to proceed via the coupling given h e r e . It i s on th is bas i s that the r e s u l t s of the p r e sen t ana lys i s a r e to be unders tood.

In this context, the ampli tude A for NN an ­nihilation at r e s t into four mesons may be w r i t ­ten as

A = £ NABC{-P)NAfnfrf{P) ' - ' pe rm A'B'C

XMAA'{K1)MBB'{K2)MCD{K1

x M D

(KjFiK^K^K^Kj (1)

where P = (0 ,m) is the momentum vec tor of the nucleon iV", F(KX;K2;KS,K4) i s an invar iant function of the momenta of the mesons , and " p e r m " denotes permuta t ions over the indices 1, 2, 3, and 4 appear ing in M(Kj) and in F. By making use of the s y m m e t r y of the nucleon indices , t he re will be 12 dis t inct t e r m s in the summat ion of pe rmuted quant i t ies . The r e a ­son that al l invar iant functions F have the s a m e form is a consequence of Bose s t a t i s t i c s . One obvious s y m m e t r y of F is that F(Kf9Kj;K^,Ki) = F(Kj;Kj;Ki,Km), which follows from the s y m ­

m e t r y of the nucleon ind ices . The nucleon wave function N may be expanded

as follows:

ABC &p,l3q,yy

-u a{P)uhp)u C(P)N A . , (2) a 13 y ap,bq,cy

where ua a r e the usual Di rac sp ino r s , and p,q,y a r e the SU(3) ind ices . The meson field M wri t ten out explicitly is

MAB(K)=M $>q{K)

A a,p

+ [{yK+ij.)y ] &cp (K)hq, (3)

v a v p

where <p5 and <p „ r e f e r to pseudosca la r and vec tor mesons , r e spec t ive ly . Let us define, a s before,1

u(-P)M(K )u(P)

= X t M D + * « (D+7r.(l)T. + a p . ( D T . ] X , (4) a a i i a at t

where 77(1), ^ ( 1 ) , w a ( l ) , p m - ( l ) denote objects which t r a n s f o r m like the 77,7^, u)a, paj compo­nents of the SU(3) mul t ip le t s . They a r e a lso propor t ional to momentum-dependent functions, and by an explicit evaluation of the ma t r ix e l e ­ment , they a r e

and

< * " - * > 8 a 0 +

KlaKW 10 K, 10

/ w l | 3 \

(5a)

(5b)

The only thing to notice h e r e is that al l the m a ­t r ix e lements with pseudosca la r mesons a r e given by the s a m e momentum-dependent func­tion while those with vec tor mesons a r e given by another .

In a s i m i l a r way, we can decompose

u(-P)M(KJM(K )u(P) = x t[J?(l, 2) +<r S> (1, 2) +H (1 , 2 )T +a p (1, 2)r ] X , L CJ Ot OL Z Z OL Oil i

(6)

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VOLUME 15, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 30 AUGUST 1965

where

(o> (1,2) , 77(1, 2)) a

K%+«liVKl+K2--KlOK2°K, 0)

+ Kw2p + w 1 ^ 2 + f f l i p 2 » + P l # f f » + V X 2 i 3 " * + ^ - + * ^ " ^ O i ? - 0 * - , f - 0 * ^ C ' + 1/3

1(3 2y Ifil 2yt 1/3 2y 1/3 2y j3y(a, 0)

(j5 a°(l ,2),Jf°(l ,2))

= [V2° + VVVV-VV+VV+V^Vo)

1 2/3 1/3 2 J j8(a,0)

•^VVvv^Vvwv^M) + \(JL>A K^2y°+^13H+Pl/V-pw"V+XW+*V*+iCWOV*1V(a,0)'

(p ±(1,2) , ^ ( 1 , 2 ) )

+ V2/+"10*2*+*i\e+pifi\+7ri V +V^i V'VV^VV*

(We use h e r e the vector notation in displaying the contents of 77, o>, 77, and p , i .e . , B ^ goes with ooa and B 0 goes with 77, etc.) BQ,, C a , DQ,, C0 , and D0 a r e functions of the momenta , and

Explicit ly,

Ba{1>2)-kla{k20-^-k2a{k10-^ ( 8 )

C0,Ca,D09Da a r e given by r a t h e r lengthy ex­p r e s s i o n s which we shal l not r e c o r d h e r e . We a r e express ing h e r e the fact that u) and 77 a s well a s 7T and p have the s a m e SU(3) content, but they a r e proport ional to different momen­tum-dependent functions. The t i lda objects a r e a lso decomposed into P 5 - P 5 , P 5 - V , and V-V p a r t s , each of which involves a different

momentum-dependent function a s given. In t e r m s of these decomposi t ions , the anni­

hilation ampli tudes , AJJ, where J and / denote, respec t ive ly , the spin and isospin of the nucleon-antinucleon sys tem, can be wri t ten down. Since the ampli tudes a r e r a t h e r lengthy, we give h e r e instead the ampli tudes for N +N *3M and s p e c ­ify the p resc r ip t ion one needs to obtain the ampli tudes for N +N - AM. We do so in o r d e r to give the co r r ec t ed express ions for the N +N — 3M ampli tudes which, a s given in re fe rence 1, have omitted some t e r m s . Most of the conclu­sions reached in re fe rence 1, however, a r e not affected by these correct ions, , The only conclusion that i s modified gives an improved compar i son between predict ion and exper iment . 8

^00aSperm^3Wl)i^2)-a,a(l)«a(2)-, f(l) f f f(2)+paf(l)pa£(2)W3)

A01 =S p e r m ^{3Wl) , (2) - | % ( l ) % (2) - . ( l ) , . (2 ) +Pa,(DPa,(2)>.(3)

-3S*^otf(1V2^3) + W ^ 426

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VOLUME 15, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 30 AUGUST 1965

A10^r»^3W1)^2)-V1S(2)-|,r<(1)V2)+V1V2)lw«(3)

+ 2[-,.(l)%(2),(3)+%(l)^(2)^(3) + , . ( l ) p ^ ( 2 ) ^ ( 3 ) - p ^ ( l ) ^ . ( 2 ) p ^ ( 3 ) ]

(9)

One of the amplitudes for N +N~4M can be obtained from these by replacing the object designated by the index 3 by the corresponding tilda object with momentum dependence given by Ks and K4. The invariant function FiK^K^Kj is replaced by F{K{;K2;KS,K^ in this procedure. The remaining 11 amplitudes can now be obtained from this one by the use of permutations on the indices 1,2,3,4, as mentioned in Eq. (1). For example, taking a term from the N +N~3M amplitude, such as

= [7T.(l)u> (2)p .(3)+w (Dp .(2)?r.(3)+p .(1)IT.(2)W (3)+terms(l ~2)]F(K,,KK), (10) t a at a at i at t a. 1 Z 6

the corresponding terms in the N +N - AM amplitude take the form

[TT.(DCO (2)p . (3,4)+O> (l)p .(2)7f.(3,4)+p .(l)7r.(2)£> (3,4) + terms(l ~ 2 ) ] ^ \K*9K 9K ) i a at a at t at % a 1 z d 4

+ [TT.(DW (3)p .(2,4)+CO (Dp .(3)if.(2,4) + . . - ] F ( ^ 1 ; ^ ; / i C 9 , ^ J + ---- (11) e a r n a at t 1 3 z 4

There is obviously a great deal of information contained in these expressions for the amplitudes. We shall point out only those predictions which are easily accessible to experiments.

Let us write out explicitly the expression for the process of pp annihilation into four pseudoscalar mesons:

K jr AT, = S ff[-57r.(l)7r.(2)5> (3 4 ) a -5ir (1)TT (2)j5 (3,4)a T p+p -* 4P^ perm z z a? a k k at at

+ 27T.UW (2)p .(3,4)a r . + (terms involving rj)]NF(K. ;K-KQ,K). (12) i k an at 1 z o 4

Since B0 = 0, this tells us that rj and n never contain a pair of pseudoscalar mesons. Hence, for these processes there are only contributions from terms involving p and u>. Thus, N+N -* 4P5 processes cannot proceed via the 'S state of the NN system, and proceed entirely via the 3S state.

The processes which are of special interest to us and are particularly simple to deal with are those involving two K mesons. In such cases there is only one amplitude that contrib­utes. This is evident when one considers the decomposition of the 143-U(12) multiplet with respect to the subgroup U(8). We shall state this argument in terms of the SU(4) subgroup of SU(6). Nucleon-antinucleon at rest in U(12) corresponds to the 300-dimensional represen­tation of SU(4), while the npw and K belong to the 15- and 4-dimensional representations of this group. In the product 15®15®4® 4, the

representation 300 occurs just once, which leads to the unique amplitude mentioned above.

With a single coupling, all the K processes can then be correlated. The magnitude of the amplitudes is given in Table I for comparison.

There are several observations we can make of the p +p~»K+K + 77 + 77 processes: (1) All allowed modes proceed via the 3S state of the pp system, and the two K mesons emerge with a relative £ wave; (2) the K0K°ii+'n'" mode is forbidden, a conclusion already reached by Harari, Lipkin, and Meshkov7 on the basis of the r 0 selection rule; (3) the singly charged and neutral K modes are definitely suppressed relative to the doubly charged K modes. Un­fortunately, the present published data are in­sufficient to either confirm or reject this p re ­diction. It is , however, probably not difficult to extract the necessary information from the

427

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V O L U M E 15, N U M B E R 9 P H Y S I C A L REVIEW LETTERS 30 A U G U S T 1965

Table I. U(12) predic t ions for NN annihilation at r e s t .

Amplitudes Relat ive

magnitudes Amplitudes Relat ive

magnitudes

p +p — K+ +K~ + 7T+ + 7T~ — K++K- + ir° + n0

—K++ JK° + 7r"- + 7r° - K ° + ^ 0 + 7r0+7r° -*K°+K° + TT+ + TT-

1 0

8 2V2

2 0

n+p-*K-+K° + Tr° + n°

-»K++K° + ir- + i{-

—K u +K u + 7r- + 7rl irO

5V2 3V2 2>/2

2

available data to test this point. A few more relations among the processes

can be obtained if we make, in addition, the assumption that F is a totally symmetric func­tion with respect to the permutations of the meson momenta. The experimental implica­tion of this assumption is that in the case of p+p-~4P§, all but a single pair of the P$ me­sons are in relatively even angular-momentum states. With this assumption we deduce, in the same unit as that used in Table I, the mag­nitudes of the following amplitudes: (a) p +p - 2ll + + 277" ~ 4 0 ; (b) p +p + 7T+ + 77 ~ + 77° + 77° - 6 .

The conclusions that can be deduced on the branching ratio of p + 377 and oo + 37T processes are less specific, since both the J - 0 and J = l states of the initial nucleon-antinucleon pair contribute to these processes. In the J=0 state, the co + 377 amplitude is favored, and in the J=l state, the p + 377 amplitude is favored. If we consider only the J= 1 amplitude (as is suggest­ed in reference 1, the J = 1 state is very like­ly enhanced over the J=0 state due to some symmetry-breaking effects), a totally symmet­ric F, and drop one particular term from Alx, namely, ^^aPy^ijk^z^^Pyky which due to its skew symmetry would have small contributions to the cross section,8 we deduce the following branching ratio:

a(p+p-*p + 3ir) ^25 <j(p+p-~u+3n)~ 3 : (13)

which may very well explain the large differ­ences between the decay rates into these two modes.9

Finally, we want to summarize some of the distinctive features of the U(12) predictions calculated on the basis of the regular couplings alone. The predictions make the following com­parisons with the experiments:

(1) KK and KKir modes,10 which are forbidden, are in fact very small (-0.4%), whereas the

KKMT with n ^ 2 which are allowed occupy as much as 20% of the total decay rate.

(2) The 277 mode (forbidden) is again of the order of 0.4% and the 3T7 mode (allowed) is, however, not large and is only of the order of 2.5%.

(3) The major discrepancy between predic­tion and experimental results occurs in the 77p mode which is forbidden, and yet the measured ratio is as large as 3.5%, while the 7777p mode (allowed) does not show up with a much larger decay rate (-5.5%).

In the two- and three-meson annihilation modes, the kinematics of the processes may be referred to as colinear and coplanar, respectively. It has been argued that these cases do not con­stitute a real test of U(12) because only a sub­group of U(12) is actually involved. Therefore, the present analysis of N +N -+4M would pro­vide a test of the experimental implications of U(12).

The authors are grateful to Professor Abdus Salam and the IAEA for the hospitality extended to them at the International Centre for Theo­retical Physics, Trieste, and Dr. R. Delbourgo and Dr. J . Strathdee for helpful discussions.

1R. Delbourgo, Y. C. Leung, M. A. Rashid, and J . Stra thdee, Phys . Rev. L e t t e r s 14, 609 (1965).

2A s imi la r ana lys is i s c a r r i e d out independently by Ngee-Pong Chang and J . M. Shpiz, Phys . Rev. Le t ­t e r s 14> 617 (1965).

3R. Delbourgo, A. Salam, and J . Stra thdee, P r o c . Roy. Soc. (London) A284, 146 (1965); R. Delbourgo, M. A. Rashid, A. Salam, and J . St ra thdee, P r o c . Roy. Soc. (London) A285, 312 (1965); M. A. B . Beg and A. P a i s , Phys . Rev. L e t t e r s 14, 267 (1965); B . Sakita and K. Wali, Phys . Rev. L e t t e r s 14, 404 (1965).

4W. Ruhl, Nuovo Cimento 37, 319 (1965); Phys . Le t ­t e r s 15., • 340 (1965). J . M. Charap and P . T. Matthews, Phys . L e t t e r s 16., 95 (1965); R. Oehme, Phys . Rev. Le t t e r s 14, 664, 866 (1965).

5R. Blankenbecler , M. L. Goldberger , K. Johnson,

428

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VOLUME 15, NUMBER 9 P H Y S I C A L R E V I E W L E T T E R S 30 AUGUST 1965

and S. B. Trieman, Phys. Rev. Letters 14, 518 (1965); J. M. Cornwall, P. G. O. Freund, and K. T. Mahan-thappa, Phys. Rev. Letters 14, 515 (1965).

6In reference 1 it states that the three-meson decays involving 37r, 77 + 27r, p + 27r, and a> + 27r are comparable. Actually, it is found that the p + 27r and 00 + 2TT modes are favored over the 37r and 77 + 2TT modes, although it probably is still insufficient to account for the vast differences in decay rates between these two types of processes without introducing symmetry-breaking ef­fects. The p + 27r and a) + 2TT modes are found to be com­parable. For a detailed list of branching ratios, see reference 2.

7H. Harari, H. J. Lipkin, and S. Meshkov, Phys.

The flux of high-energy neutrinos from the decay of K, 7r, and M mesons produced in the earth's atmosphere by the interaction of pri­mary cosmic rays has been calculated by many authors.1 In addition, there has been some con­jecture1 as to the much ra re r primary flux of high-energy neutrinos originating outside the earth's atmosphere. We present here evidence2

for the interactions of "natural" high-energy neutrinos obtained with a large area liquid scin­tillation detector (110 m2) located at a depth of 3200 m (8800 meters of water equivalent, average Z2/A~ 5.0) in a South African gold mine.

The essential idea of the present experiment3

is to detect the energetic muons produced in neutrino interactions in a mass of rock by means of a large area detector array imbedded in it. Backgrounds are reduced by the large overbur­den and by utilizing the fact that the angular distribution of the residual muons from the earth's atmosphere is strongly peaked in the vertical direction at this depth. The angular distribution of the muons produced by neutrino interactions should show a slight peaking in the horizontal direction.1

The detector array, shown schematically in Fig. 1, consists of two parallel vertical walls made up of 36 detector elements. The array is grouped into 6 "bays" of 6 elements

Rev. Letters 14, 845 (1965h 8The absence of this term implies that the magni­

tudes of the p+7r_(27r), p_7r+(27r), and p07r0(27r) ampli­tudes are the same, and that the introduction of this term displaces the magnitude of the p+7r_(27r) ampli­tude one way, and that of the p_7r+(27r) amplitude the other way with equal amounts. Therefore, the statis­tical average of the p + Sir processes should not be greatly perturbed.

9See reference 1 for a summary of the experimental data.

10R. Armenteros et al., Phys. Letters JL7, 170 (1465); N. Barash et. al. , "Antiproton Annihilation in Hydro­gen at Rest I, Reactionp+p-+K+K + ir" (to be published).

each. Each detector element, Fig. 2, is a rectangular box of Lucite of wall area 3.07 m2

containing 380 liters of a mineral-oil based liquid scintillator,4 and is viewed at each end by two 5-in. photomultiplier tubes. The array constitutes a hodoscope which gives a rough measurement of the zenith angle of a charged particle passing through it. In addition, the event is located along the detector axis by the ratio of the photomultiplier responses at the two ends. The sum of the responses then pro-

FIG. 1. Schematic of detector array.

EVIDENCE FOR HIGH-ENERGY COSMIC-RAY NEUTRINO INTERACTIONS*

F. Reines, M. F. Crouch, T. L. Jenkins, W. R. Kropp, H. S. Gurr, and G. R. Smith

Case Institute of Technology, Cleveland, Ohio

and

J. P . F . Sellschop and B. Meyer

University of the Witwatersrand, Johannesburg, Republic of South Africa (Received 26 July 1965)

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