I1, N['()V() CI~[ENTO VOL. XXVII , N. 2 16 Gennaio 1963

Search ~or the Photoproduction of the "r~~

K. BERKELMAN~ A. ~RA~KLIN~ D. MCLEOD~ S. RICHERT and A. SILVER~IAN

Laboratory o[ Xuclear Studies (*), Cornell Ut~iversity - Ithaca, X . Y.

(ricevuto 1'8 Agosto 1962)

Summary. -- An at tempt has been made to detect the photoproduction of the -rj ~ by observation of recoil protons at fixed momentum and angle from the reaction ,~, § p ~ p @ ~r, ~ The yield as a function of bremsstrahlung peak energy should exhibit an abrupt increase as the incident peak energy becomes sufficient to produce the ~o in coincidence with the observed recoil proton. Measurements were made every 25 MeV with l~ accuracy from below the single-pion threshoh] to about 1100 MeV at a 35 ~ proton angle and at three proton momenta (420, 550 and 638 MeV/c). No steps in the excitation function were seen; in par- ticular, a statistical analysis sets upper limits of about 0.5 ~b/sr at each of the three proton momenta for the photoproduction of a mass 550 MeV particle. The over-all shapes of the curves (apart from the single-pion production) are consistent with the phase space for double-pion production.

We repor t here ,~n ~ t t e m p t to observe the p h o t o p r o d u c t i o n of t he ~0 in

the r eac t ion :

y @ p --~ p + "rf .

Tile t e chn ique used is the same as t h a t of BEJaSARDI_'~I et al. (~). Br ief ly the

m e t h o d consis ts i n m e a s u r i n g ti le y ie ld of recoil p ro tons a t fixed l a b o r a t o r y

angle a n d m o m e n t u m as the peak ene rgy of the b r e m m s t r a h l u n g r a d i a t i o n is

var ied . The onse t of the p r o d u c t i o n of ~ par t i c le of rest mass tt will be ac-

(*) Work supported by the joint program of the Office of Naval Research and the Atomic Energy Commission.

(1) C. B~m~AIr R. QUERZOLI, G. SALVINI, A. SILVERMAN and G. STOPPINI: ~-uovo Cimento, 14, 268 (1959).

32 - l l N u o v o C imen lo .

4 : 9 8 K . B E I : t K E L M A N , A . F H A N K I A N , D . M'C L E O I ) , S . R I C H E R T ~I, III| A . S I L V E I t M A N

comp~nied by an increase in this yield a t the appropr i~te energy k. The re-

lation between /~ ~nd k is ~dven by,

#2 = 2k(P~ c o s 0 , - - T ) -- P~ ~ T~o,

where: P , ---- p ro ton m o m e n t u m ,

0~---- proton labor'~tory angle,

T~ = pro ton kinetic energy,

k = energy of the photon producing the reaction.

The onset of su(:h a. (~ step ~) in the yield mus t be distinguished f rom the

smooth increase expected f rom non-resonant mult iple pion produ(,tion. I t is the presence of this smooth increase thut limits the sensit ivi ty of the method.

This technique has been used previously to look for the photoproduct ion of

neut ra l mesons of m~ss between 200 MeV ~nd 500 MeV (~); and, more re- cently, by I~VD~MAN, DIEBOLD, and I '~cK (~), a t C.I.T. to look for the ~~

200

o >-I / ~ ,.~ 100 o

E

:2

/ 0 t

400

7

/o_O_o_9-:9 ....

.9~o.o-O -a0J .o~o x l0 100

P~=420o-o"

~0~'0~0 I

. . . . . . . . o ~ 1 7 6 1 7 6 1 7 6

Pp= 5509-161 ~ 0/0 ~ 0 ~m

.flI" 0 0"0~0"0~ 0/0

/ 0 ~ " 0 0 0

. ._Q.. -~176 P p = 6 3 8 t o '~ 0 - 0 ~ 0 " o 0 I

~o.~c/ 20 / o

o ~ / P =550,638

o / n r . , / I I _ _ _ - - ~ - - - - J-- . . . . • . . . . I 0

500 600 700 800 900 1000 1100

K rn a x ---m-

60

40

Fig. 1. - The yield, Yo, of protons per equivalent quantum, per target proton, per unit solid angle, per momentum interval for 0~= 35.25 ~ and Pp= 420 MeV/c (left-hand scale), P~=550 MeV/c and Pp=638 MeV/c (right-hand scale). The arrows show the value

of k ~ at which production of a mass 550 MeV particle would occur.

(2) H. RUDERMAN, R. DIEBOLD and C. I)~CK: Report CTSL-32 (March 1962).

S E A R C I [ F O R T I l E I ) I t O T O P R O D I ; C T I O N I ) l " Til l , : :~~ 499

at itrOUlld 780 . I e ~ . No previous measu remen t s would have de tec ted t h e

p r o d u c t i o n o f z ,~ a t 550 M e V .

The p ro ton m o m e n t u m was measured in a magneti( , spec t rome te r (.on-

sisting of a single r ec t angu la r ( luadrupole. The spe( . t rometer is defo( 'using in

the hor izonta l plane so t h a t it forms a hor izonta l line focus. The range of

hor izonta l angles accep ted is A 0 = 0 . 9 5 ~ and the range of vert ical angles

A r ~ The n i o m e n t u m resolut ion is a p p r o i i n l a t e l y Gauss ian with an

IgMS half w id th <,(AP/P)->-" 3.35 ~ The m a g n e t aper ture , AY2AP/P = 1.82.10 -4 sr. P r o t o n s were de tec ted in thre.e scint i l lat ion counters and iden-

tiffed by pulse hei~llt d iscr iminat ion. All measu remen t s were inade a t

3 ( ) . a Three series of m e a su re m e n t s were m a d e in whi(.h the p ro ton p _ . . ~ , ) ~ o

m o m e n t a were 420 MeV/(., 550 ~I('~/(,, and 638 5ie,'V/e. The i)eak I)rems- s t r a h h m g energy~ k ...... , was varied in 25 MeV steps f rom below the =0 threshold

to a p p r o x i m a t e l y 1 150 5Ie'r The results are shown in FiK. 1 where the yield

per e q u i w d e n t q u a n t u m is ph)t ted ,r.s.. k.,,,. An equ iva len t q u a n t u m is de-

fined so t h a t the n u m b e r of y - rays in a given ener~.~y in terval is a p p r o x i m a t e l y

i ndependen t of k,~,~. The beam in tens i ty was measm'ed with a to ta l -absorp-

t ion q u a n t a m e t e r . The statisti(.al aeeura( 'y of m o s t of the m e a s u r e m e n t s

var ied be tween ,1, o~) and 1 o/o. The errors due to o ther sources, pr imar i ly m a g n e t

cu r ren t drift , i n t eg ra to r reset, and coun te r bias drif t is es t imated a t 0 . 5 %

per run. Each po in t consists of at h;ast nix runs separate(l in t ime. The non-

s tat is t ical errors are therefore e s t ima ted a t a b o u t 0.2 o~ for ea('h t)oint. The

150r-- -

l o o L

i

x

O,

p =55O P

~ x ~ x - l ~ - : / '/ ! / /' 2

400 500 600 k (Mw)

max

. . . . . . . P = 6-38 "

P i

i --20

1

lo

700 0

Fig. 2. - The single-pion region of Fig. I reproduced on an expanded scale. Tile solid curves are the calculated single-pion yields assuming da /d~=18 .8 , 4.96, 3.60 Fb/sr

for P r = (420, 550, 638) MeV/e.

5 0 0 K. BERKEL3IAN~ A, FRANKLIN, D. MCLEOI)~ S. RIC[{ERT and A. SILVERMAN

arrows in Fig. 1, show where the .r? <~ step ~> should occur. I t is clear t h a t

there is no obvious <~ step ~> at these energies. In fact there is no evidence for

any part icle of mass between 150 ~[eV and abou t 600 MeV.

The per formance of the spec t rometer can be checked by the (~ step ~> cor-

responding to single ~o production. Figure 2 shows a detail of the yield curves in this region. The solid curves are the calculated resolution funct ion for ~0 product ion including the effects of magne t aper ture , m o m e n t u m resolution, t a rge t size, mul t ip le scat ter ing in the target , and bremss t rah lung distr ibution.

The l~ck of a fla.t region in the 638 MeV/c d s t a is largely due to the f~ct t h a t the resolution in k is poorer and the threshold for double-= product ion (80 MeV above t ha t for single ~'s) is lower for t ha t measu remen t t han in the other two. The ~o yields ver ify t ha t the spec t rometer characterist ics are as expected.

The calculated RMS half-width of the resolution in k for the u product ion

in 18; 19; and 21 MeV for the three momenta .

The following analysis was made of the da ta in order to m a k e some quan- t i t a t ive es t imate of an upper l imit for the .~o cross-section. We make the

assumpt ion tha t , in the ~bsence of any ~o, the yield y (k,~.) is smoothly va ry ing and can be represented by y(k,~)=a§ However , if an -r? is produced the yield will have the form

Here ~ is the cross-section for ~o product ion, and y~(k~J is the yield for uni t

cross-section. We now calculate the least squares best fit to

y(km~) = y ' ( k m ~ ) - ay~,(k~,,,.) for v~rious w~lues of a .

Figure 3 shows in greater detail the 638 MeV/e da ta (expressed here in exper imenta l counting ra te ra ther than yield per equivalent quan tum) ; the

curves are the best fits corresponding to o----0; 0.29 tzb/sr; a n d 0.56 ~b/sr. F igure 4 shows the results of the stat is t ical analysis for the three different

m o m e n t a (full curves). The results p lo t ted are the logar i thm of the relat ive

p robabi l i ty of a given cross-section P(a) compared to zero cross-section. We

see t h a t the curves are nearly p~rabolic, which corresponds to the p robabi l i ty

P(a) being normal ly dis t r ibuted: i.e.,P(a)ztexp[--((;--c;o)2/2T2]. Thus, for

each curve we can quote a mos t prob~ble value, a,,, for the cross-section and a s t andard deviat ion T. These are shown in Table I. (Three top rows). These

results clearly do not const i tute significant evidence tha t the cross-section is different f rom zero. They can, however, be regarded as set t ing a l imit on

the~ cross-section for ~1~ ~ photoproduet ion . In fact , assuming a----0, the prob - abi l i ty of obtaining a worse fit to the d~ta than the one actual ly obta ined is

SEARCII FOR TItE Pt lOTOPIr OF T t tE "[j~ o 0 1

100

90

8o I

700

counting rate

~ T0.29

.G~'9 [no step ~ b / s r ~//'~ ] step

I r I I

800 900 1000 t100 E~{ PleV

Fig. 3. The yield of pro tons per sweep measured ~or P;~ 638 MeV/c. The errors shown ~re count ing statist ics. The arrow marked ~q shows the value of k ..... at which product ion of a par t ic le of mass 550 MeV would occur. The b racke t labeled 1 izb/sr shows the step size tha t would result f rom product ion of a par t ic le wi th this cross-section. The three curves are the calcula ted best fits assuming zero, 0.29 and 0.56 ,,b/sr e ross-sedion for

product ion of a 550 MeV inas~ part icle .

87 ~ , 3o~ O//o a n d 10 O//o fo r Pp = 638, 550 a n d 420 M e V / e . T h e a v e r a g e of t h e s e

is 44 %. T h u s , o u r <~ o. 'oodness of f i t )> is q u i t e c o n s i s t e n t w i t h ze ro c r o s s - s e c t i o n

fo r t h e :r~ ~

T h e ~nMys i s le~din~" t o t h e r e s u l t s of T a b l e I p r o b a b l y o v e r e s t i m a t e s t h e

TABLE I. 550 MeV mass photoprodu.ctiott cross-seetioJ~, best lit.

Proton m o m e n t u m Pho ton energy (at 35 ~ (Me\T/c) (MeV)

420 930 550 i 960 638 i 1025

Cross-section (~b/sr)

0 , 3 8 ~ 7 2 0 ,43 • 0,3 0 ,23 • 0,19

Wi th lower l imi t on multiple-r: cross-section

420 930 I - - 0 , 3 8 • 0.58 ! 102 ! o, o- 0,10

5 0 2 K. B E R K E L M A N , A. F I { A N K I , I N , I). M(' I ,E() I ) , .~. RI(?IIEIC.T a l l ( l A. ,~II~VERMAN

eros,~-section for the following reason. For any given step size, the paranlcters

of the parabolic iit are determined solely by the criterion tha t they give the

best fit to the data. This implies

+1 - - a particular form for the yield

due to multiple-pion production

,t o~

o~ o

(the portion of the yield remain-

ing after the assumed v, ~ produc-

tion is subtracted). There is, of

I 6381 1 I I

2! I I , ;

!

I

I \ \

638 \~420' k \

3 -

-o:4-o12 o o12 o. 4-o16 .. . . 1:o O" ( F b / s r )

Fig. 4. - The log of the pl'ol)ability of a cross- section I)(a) relative to zero (.lOSs-se(.tioil as deduced from the fitting procedure. The solid ('urves show the results with no supplementary condition; the (l[tshed curves are the results imposing the condition on the multiple-pion pro(luetion described iu the text. This con- (litton did not change the 550 MeV/e results.

course, no a pr ior i justification

for this choice. Any other choice

for the multiple-pion yield would

result in a worse fit to the data

for a given step size and (,onse-

quently to a smaller estimate of

the .to cross-section. Thus, the

cross-sections of Table I (first

three rows) can appropriately be

regarded as upper limits rather

than most probable values. To

illustrate this point, we have ~lso

analysed the data imposing the

following condition on the multi-

ple-pion yield. We set the rather

conservative limit tha t the multi-

ple-pion yield above the step

should be at least half the value

derived by assuming the variation

of the yield to be given by double-

pion phase-space, and normalizing

in the region below the step. lCe-

peating the least squares analysis

with this supplementary condition

imposed gives the dashed curve of Fig. 4. The corresponding cross-sections and

s tandard deviations are shown in the last two rows of Table I. This condition

does not affect the 550 MeV/c results.

The possible significance of these results cannot be evaluated without some

theory to compare them to. The only theoretical calculation we are aware

of with which they can be compared is tha t of GELL-.'~IANN and ZACI[ARIA-

S E N (: ' ) : IS modified by S A K U R A I (4) .

(:~) ,~'[. ~rEI,L-MANN and F. ZACtIARIASEN: Phys. Rev., 124, 953 (1961). (~) J . SAKtRt l p r iva te ( 'ommunica t ion to K. BERKEL.~rAX.

SEAR( ' I I F{)R TIlE PIIOT(H'IC, t)I)UCTION OF TI lE ~~ 5 0 3

Ti le bas is fo r t h e (.alc, u l a t i o n is ~ a k u r a i ' s vec . to r t h e o r y of s t r o n g i n t e r -

~tctions (5). T h i s c a l c u l a t i o n p r e s u l n e s t h e L ~ t o be p r o d u c e d b y t h e e x c h a n g e

of a xo ~lnd t h e r e f o r e r e q u i r e s a k n o w l e d g e of t h e c o u p l i n g a t t h e y.~o_xo

v e r t e x . I n v i e w of t h e u n c e r t a i n t y of t h i s c o u p l i n g i t does n o t s e e m u s e f u l

to m a k e a d e t a i l e d c o m p a r i s o n w i t h t h e t h e o r y . H o w e v e r , (~ r e a s o n a b l e )> gues -

ses fo r t h i s c o u p l i n g l e a d to c r o s s - s e c t i o n s of t h e o r d e r of 0.1 tzb/sr, w h i c h is

n o t i n c o n s i s t e n t w i t h t h e r e s u l t s of t h i s e x p e r i m e n t (~).

(~) ,l. SAKUtCAI: An~. Phys. 11, 1 (1960). (6) Since the COml)lction of t.his work, an expe r imen t performed at Frascat i was

reported by (~. SALVINI a t the 1962 In te rna t iona l Conference on t t i gh -Ene rgy Physics at C E R N in whieh ~l. neu t ra l decay m(~de of photoprodu( 'ed -~~ was detec ted . The observat ions were eonsistel~t with the -r~ ~ ->r, ~ i y, or ~o >2y. For the " r ,~ ~ . . . . the pitotol)roduction dif feremial cross-sectiml was repor ted as 5. l0 -3-0 c m 2 and for .~o_~ 2y, 3 .10 -:~" ('m ". These measurements are clearly not in cont radic t ion to the upper l imit reported here. In fact, this measurement sets a h)wer l imit for the decay mode observed at Fras( 'ati of ~.l)lir(~ximatel5 10(~o .

R I A S S I ' N T ( ) (*)

~: s ta to ten ta to di r ivelare la fo toproduzione della .:,o osservando i p ro toni di rin- culo con impulso ed angolo fisso dalla reazione ~.-~p-~ p +-5 ~ La produzione in funzione del l ' energia di picco della b remss t r ahhmg dovrebbe most ra re un accrescimento im- provviso quando I'energi~L di picco inc idente d iven ta sufficiente a produrre la .~o in eoincidenza col pi'otone di rinculo osservato. Si sono eseguite misure ad in te rva l l i di 25 MeV con la precisione d e l l ' l ~ o dal disotto della soglia di pione singolo fino ad un angolo del prr di 35 ~ e(l ~ t re impulsi i)rotonici (420, 550 e 638 MeV/c). Non si son() ~otat i g, 'adini nelIa f lmzione di ecci tazione; in 1)a.rticolare, una analisi s ta t is t ica pone [imiti suIieriori di circa 0.5 ~tb/sr per ognuno dei i re impukai protonici per la foto- pl 'oduzione di una i)art icella di massa = 550 MeV. Le forme general i delle curve (a par te la produzione di pioni isolaii) si accordaiio cl)llo spazio delle fasi per la pr(iduzione di piold dol)l)i.