V O L U M E 11, N U M B E R 2 P H Y S I C A L R E V I E W L E T T E R S 15 JULY 1963

*For a l i s t of theore t ica l and exper imenta l pape r s on the one-pion exchange model , s e e , e . g . , E. F e r r a r i . and F . Se l le r i , Suppl. Nuovo Cimento 24, 453 (1962K

t h r o u g h o u t this paper , iV3/2*, Yt*t and K* s tand, r espec t ive ly , for the 3-3 r e sonance , the 1380-MeV 7T-A re sonance , and the 885-MeV K-n resonance„ The t e r m " i s o b a r " s tands for iV3/2* o r Yt*.

3 F o r vector meson exchange in p r o c e s s e s like 7r" + p-+K* + Z , see G. A. Smith e t a l . , Phys 0 Rev0

L e t t e r s J^O, 138 (1963). 4To prove th i s , jus t obse rve that k^v^-0 for ( la) and

(lb) and k^v ^ = ±(w»K2 - m^imy2- A2)/mv

2 for ( lc) and ( Id) ,

5R. H. Dalitz and D. R. Yennie, Phys . Rev„ 105, 1598 (1957).

6See, e . g 0 , W. S. McDonald, V. Z . Pe t e r son , and D. R. Corson, Phys . Rev. 1J07, 577 (1957).

7The dominance of Ml-*pz/2 i s expected on t h e o r e t ­ica l , grounds: G. F . Chew and F . E. Low, Phys . Rev. 101, 1579 (1956); G. F . Chew, M. L. Goldberger , F . E . Low, and Y0 Nambu, P h y s . Rev . _106 , 1345 (1957); S. Fubini , Y. Nambu, and V. Wataghin, P h y s . Rev . I l l , 329 (1958).

8 J . J . Sakurai , Ann. Phys . (N. Y.) 11 , 1 (1960). 9 M. Gell-Mann and F . Zachar iasen , Phys . Rev.

124, 953 (1961). 10The proport ional i ty constant in this ca se is (3/2)

x( /pA?), where / p V47r = 4y 2 / 47T-2 .0 , (?2/4TT - 1/137 . We will d i scuss a quanti tat ive t e s t of the p-photon analogy" in a s epa ra t e communica t ion .

n M . Gell-Mann, Phys . Rev. HJ, , 362 (1958). 12M. Gell-Mann, Phys . Rev. 125, 1067 (1962);

Y. Ne 'eman, Nucl. Phys . _26, 222 (1961). 1 3For the uni tary spin ass ignment of low-lying i s o b a r s ,

s ee R. E. Behrends et a l . , R e v . Mod. P h y s . 34, 1 (1962); S. H. Glashow and J . J . Sakurai , Nuovo" Cimento 255, 337 (1962); S. H. Glashow and J . J . Sakurai , Nuovo Cimento ^ 6 , 622 (1962).

In an accompanying Letter by Stodolsky and Sakurai,1 a model for isobar production by vector meson exchange is presented. In this Letter the predictions of that model are compared to the results of an experimental investigation of the process

K++p-K°+p + iT+. (1)

The model assumes that the final-state TI+ and proton are the decay products of the J = 3 / 2 , / = 3/2 nucleon isobar which was produced by the exchange of a p meson.

U L . Ber t anza et a t . , P h y s . Rev. L e t t e r s 1£, 176 (1963). 1 5 S. So Yamamoto (pr ivate communicat ion) . 1 6 B. Kehoe, following Le t t e r [Phys . Rev. Le t t e r s 11 ,

93 (1963)]. I 7R. K. Adair , Phys . Rev. 100, 1540 (1955). 18The Adair method is known to fail not only in ( lb) ,

( l c ) , and (Id) , but a lso in (la) [D . Stonehill , Ph. D. t h e s i s , Yale Univers i ty , 1962 (unpublished)] . On the o ther hand, the Adair method has been successful ly applied to N 3 / 2 * decay in 7r~+ /> —"iV3/2*"" + 7r+ [V. A l l e s -Bore l l i et a l . , Nuovo Cimento 14, 211 (1959)] ; note, however , that one-p exchange is forbidden in this reac t ion . It is worth r e m a r k i n g that at h igher energ ies ( ^ 3 . 3 BeV/c) , the reac t ion n"P~~N3/2*~ 7r+ does not occu r , whe reas the react ion ir'p — Nsft*"1*' *s observed [ Z . G. T . Gui ragoss ian , P h y s . Rev . L e t t e r s U., 85 (1963)] in ag reement with dominant p exchange.

19The re levant Clebsch-Gordan coefficients may be found in r e fe rence 13 . The re la t ion a (a) / cr(b) ~2 follows from the assumpt ion that the p is coupled universa l ly to the isospin cu r r en t ; the re la t ion cr(c) = a(d) is a consequence of any model based on K* exchange. Our re la t ions should not be confused with Eq. (5b) of S. Meshkov, C. A. Levinson, and H. J . Lipkin [ P h y s . Rev. Le t t e r s 1_0, 361 (1963)] which follows from uni tary s y m m e t r y alone.

20R. D. Tr ipp , M. B . Watson, and M. F e r r o - L u z z i , Phys . Rev. Le t t e r s 13, 175(1962) .

2 1S. B. T r e i m a n and C. N. Yang, Phys . Rev. Le t t e r s 8,, 140 (1962).

22The Tre iman-Yang dis t r ibut ion for the Ml-~/>3/2 case must be of the form 1+2 s infy . A cor re la t ion of this kind has been repor ted by S. Goldhaber et_ a l . [ Bull . Am. Phys . Soc. _8_, 20 (1963); Proceedings of the Conference on Fundamental P a r t i c l e Resonances , Ohio Univers i ty , Athens , Ohio (to be published)] in the r e a c ­tion K++p — K°+ N 3 / 2 * + + at 1.96 B e V / c .

The events were found in a scan of 40 000 pic­tures from an exposure of the Berkeley 30-in. propane bubble chamber to a separated beam of K+ mesons. The beam momentum, over the run, was distributed about 910 MeV/c with a variance of approximately 40 MeV/c. Only those events were considered which had associated with them the decay of the K° via the charged Kx° mode:

Kl°-Ti+ + 'n-. (2)

Candidates found in the scan were measured on standard digitized equipment and analyzed in the

ISOBAR PRODUCTION BY 910-MeV/c K+ MESONS*

Brandt KehoeT Universi ty of Maryland, College Pa rk , Maryland

(Received 29 May 1963)

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VOLUME 11, NUMBER 2 P H Y S I C A L R E V I E W L E T T E R S 15 JULY 1963

FOG-CLOUDY-FAIR program sequence. Each was constrained to the hypothesis that the pro­duction interaction, (1), took place on a free pro­ton. Contamination of the production events, by the same process on a proton bound in carbon, was estimated to be 4.0± 1. 5% from the observed tail in the chi-square distribution. The chi-square distribution from carbon events con­strained to the free-proton hypothesis was shown, by Monte Carlo simulation, to be flat in the region 0 < x2 < 50.

Tau decays of the beam particles,

K+-~TT+ + 7I+ + TT-, (3)

were also selected in the scan. They were meas­ured and analyzed for the determination of K+

track length and beam selection cri teria. Each event was constrained to the tau decay hypothesis, (3). The distribution of dip stretches for the K+

and the pions, taken separately, were quite asym­metric. Analysis of the reconstruction process indicated the probable cause to be an incorrectly determined optical constant. Corrections to remove the effect of this error were made on the unconstrained track data of every tau decay and production candidate. Each event was then con­strained using GUTS. The corrected data pro­duced excellent stretch and chi-square distri­butions .

The data were examined for possible systematic losses in the event selection. The only bias of any significance appeared to be against events with charged tracks which interacted very near the vertex from which they originated. The indicated loss was 2.5 + 1.0% of the production events and 2 .0+0 .7% of the tau decays. Scanning efficiency was determined to be 93.0 + 2.0% and 95.8+ 1.0% for the two event types from a rescan of 45% of the film. The indicated K+ track length was (8.19 + 0.47) x 106 cm which gave rise to 261 ± 19 production events with associated charged Kx° decays. The cross section for Reaction (1) is 2.10 + 0.20 mb assuming that the K° decays to charged pions, (2), with a branching ratio of 1/3.

A completely general form for the differential cross section for the production process (1) is

dvoc (l/lwE)(dsq'/w')6*(q' + t- q - p)

xd4td(t2-m2)dm2B9 (4)

where

B = (dBk/e)(d3p'/£')64(t-k-p')\T\2 (5)

is a Lorentz-invariant function. The quantities

94

(q,^)» ( q ' , ^ 0 , (p,£), (p ' ,£ ' ) , and (E, e) are the four-momenta of the K+, the K°, the incoming and outgoing proton, and the n+, respectively. The four-momentum of the combined n+p system, *M, is given by

t =p '+k . (6) M M M

Bergia, Bonsignori, and Stanghellini2 have dis­cussed the effects of isobar formation in inelas­tic processes, using the above formalism. They suggest that the function By evaluated in the rest frame of the rr+p system, the isobar res t frame, is given by

B=dn-(q/m)[r(m)/D2(m)]\R\2, (7)

where q is the momentum of either the 77+ or proton, m is the mass of the rr+p system,

r(m) = 0. 22 q*/M (m - M ), (8)

7T p

and

D2(m) = (w - m0)2 + q2r2(m), (9)

with m0 = 1238 MeV. IR |2 is the square of the portion of the matrix element which describes the production of the isobar.

The p-exchange model of Stodolsky and Sakurai, assuming a magnetic dipole interaction, predicts that

\R I2 = [(q xq')2/(A2 - M 2)2](1 + 3 cos20), (10)

where A2 = (w - w')2 - (q - q')2 is the square of the four-momentum transfer, cos#=£*w, and n = ( q x q ' ) / | q x q ' | . In this expression for \R\2, all vectors are to be evaluated in the isobar rest frame.

Figures 1, 2, and 3 show distributions based on all of the 218 production events which were in a predetermined fiducial volume and which satisfied selection criteria on chi-square and beam momentum and direction. The predictions of the model are shown as smooth curves. In Figs. 2 and 3, the theoretical distributions were averaged over the observed spread in barycentric energy.

Figure 1 presents the observed decay angular distribution for the isobar, relative to the pro­duction normal, n. It is compared to the (1 + 3 cos20) form predicted. The decay was also found to be aximuthally isotropic about n. The equivalent of the Trieman-Yang test suggested by Stodolosky and Sakurai involves the distribu-

VOLUME 11, NUMBER 2 P H Y S I C A L R E V I E W L E T T E R S 15 JULY 1963

-1.0 COS 9

FIG. 1. Distr ibut ion of cos 6. The angle 6 i s the decay colati tude of the i sobar with r e spec t to the normal to the production plane, n. Thus cos 9 = k*n evaluated in the i sobar r e s t f r ame .

tion of the angle cp, where

COS0 :

l (q -q ' )xk | ' (ID

As in expression (10), q, q', and k are evaluated in the isobar rest frame. For vector meson ex­change <p should be distributed as A +Bcoscp + C cos20; for the particular interaction assumed here, B/A =0 and C/A = -0.67. A least-squares fit to the data indicated

B/A =+0.10± 0.20,

C/A = -0.57 ±0.20.

The chi-square fit of the observed distribution in <p to the predicted distribution was better than 65%.

Figures 2(a), 2(b), and 2(c) display the distr i­butions of the cosines between the beam direction and the K°, the n+, and the proton, respectively, evaluated in the over-all center-of-mass system. While the peaking of the cosG^o distributions depends upon the mass of the exchanged particle, through the propagator in Eq. (5), the quality of the fit to the theory is essentially constant for masses between 550 and 850 MeV.

The Q-value (effective mass less rest mass) distributions for the (7r+,/>), the {K°,p), and the (n+,K°) pairs are shown in Figs. 3(a), 3(b), and 3(c), respectively. The distributions predicted by phase space alone [ IT12 = constant in Eq. (5)] are shown by the dashed curves. The (n+,K°) Q distribution, Fig. 3(c), is consistent with phase space, the other two are not. Note that while the 883-MeV K* is forbidden by energy

p z Li > I d

o

o z

40

20

40

20

40

20

C^l

>. . . 1

T

-

f'

^-T3U-fU-- ^ fc J B==-"

• 1 1 1

Y T

1 1 1 1 1 I

(a)

-j

N] H

I i i i Nj

coseK* 1

(b) \ \

^ ^ - r \ L\. 1

i i i i

COS 0-T+ 1

(c) J •j

i l 1 1 1

-1.0 cos ep i.o

FIG. 2 . C e n t e r - o f - m a s s angular d is t r ibut ions for the th ree f ina l -s ta te pa r t i c l e s , (a) the K°, (b) the 7r+, and (c) the proton. Displayed i s the cosine of the angle between the pa r t i c l e and the beam d i rec t ion .

FIG. 3 . Distr ibution of Q values for (a) the (7r+t p)

sys t em, (b) the (K°,/>) sy s t em, and (c) the (7r+,K°) s y s t e m .

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VOLUME 11, NUMBER 2 P H Y S I C A L R E V I E W L E T T E R S 15 JULY 1963

conservation, the recently observed TT-K reso­nance3 at 723 MeV might be expected to appear at Q = 85 MeV. The data are consistent with no formation of this resonance. The value Q0, cor­responding to m = m0, is indicated by the arrow on the (n+,p) Q distribution, Fig. 3(a). The shift of the theoretical peak from this value rep­resents the combined effects of phase space and the factor (q')2 in expression (10). For fixed barycentric energy, high isobar mass corre­sponds to low center-of-mass momentum of the

Much of the work was carried out at the Uni­versity of Wisconsin under the very stimulating guidance of Professor Ugo Camerini and Pro­fessor W. F. Fry. The author would like to thank Professor Wilson Powell for making the film available and Howard White for overseeing

most of the measurement and analysis. He would also like to acknowledge many helpful dis­cussions with Dr. James Gaidos, Professor J . J . Sakurai, Professor George Snow, Professor Jo­seph Sucher, and Professor Leo Stodolsky.

*Work supported by the U. S. Atomic Energy Com­mission and the Wisconsin Alumni Research Founda­tion.

tNational Science Foundation Cooperative Fellow, 1959-1961.

^ e o Stodolsky and J. J. Sakurai, preceding Letter [Phys. Rev. Letters 11_, 90,(1963)].

2S. Bergia, F . Bonsignori, and A. Stanghellini, Nuovo Cimentoj^, 1073(1960).

3G. Alexander, G. R. Kalbfleisch, D. H. Miller, and G. A. Smith, Phys. Rev. Letters 13, 447 (1962).

STRUCTURE OF THE WEAK INTERACTION A +N - N +N

M. M. Block* Physics Department, Northwestern University, Evanston, Illinois

and

R. H. Dalitzt The Enrico Fermi Institute for Nuclear Studies and Department of Physics,

The University of Chicago, Chicago, Illinois (Received 12 June 1963)

where T^ = T^"1 = (4.25± 0 .1)xl0 9 sec"1 denotes the free A decay rate.3 We note first that these rates are just compatible with the inequality

In this Letter, the empirical evidence available on the nonmesonic decay of A hypernuclei will be analyzed in terms of the spin and isospin depend­ence of the weak interactions

A+p ~n +p,

A +n -~n +n.

a) (2)

r ( H 4 ) nm A

2 r (He 4 ) nm A (4)

Recently, measurements on the nonmesonic decay processes of AH4 and AHe4 hypernuclei produced in K~-Re4 reactions have been reported by Block et al.1 For ^He4, they have obtained ^(^He5) = 0.52± 0.10 and C(AHe4) = 2. 2± 0. 8, where Q de­notes the ratio of nonmesonic to n" decay modes and C denotes the ratio of Reactions (1) to (2), de­termined from the energy spectrum of the final-state protons. For ^H4, they have obtained Q(^H4) = 0.26± 0.13. Using theoretical estimates2 for the 7r"-mesonic decay rates, we may deduce the non­mesonic decay rates for these hypernuclei,

T ( He4) = (0.14±0.03)r , nm A A

T ( H4) = (0.29±0.14)rA , nm A A

(3a)

(3b)

required by the A/ = ^ rule.4

We shall base our detailed analysis on a simpli­fied calculation2 for the nonmesonic decay rates, which treats the A de-excitation by different nu-cleons as incoherent. This procedure neglects final-state interactions for the two fast outgoing nucleons, and neglects the interference effects which usually arise from antisymmetrization of the final state, corrections which are not expected to be important here, because of the large energy release. In this model, these rates are expressed in terms of the elementary rates RN$ for nonmes­onic de-excitation of a AiV system with total spin S, for unit density of nucleon N at the A position. In light hypernuclei, the initial AN states are S-wave, lS0 and ^ The AN -NN transitions then possible are listed in Table I, together with the spin dependence of their corresponding matrix

96