Volume 36B, number 6 PHYSICS LETTERS 18 October 1971

H I G H - E N E R G Y E L E C T R O N - P O S I T R O N E L A S T I C S C A T T E R I N G

B. BARTOLI, F. FELICETTI, H. OGREN and V. SILVESTRINI Laboratori Nazionali di Frascati del CNEN, Frascati , Italy

G. MARINI, A. NIGRO and N. SPINELLI Islituto di Fisica dell 'UniversitY, and Sezione di Roma dell'INFN, Rome, Italy

and

F. VANOLI Istituto di Fisica Superiore dell'Universit&, and Sezione di Napoli dell ' lNFN, Naples, Italy

Received 20 August 1971

We present the analysis of 5164 wide angle Bhabha events collected at several c.m. energies between 1.4 and 2.4GeV using the Frascati e +-e- storage ring, ADONE. The results are in agreement with the predictions of quantum electrodynamics within the experimental errors (±I0~).

Measuremen t s of wide angle high energy (1 .4- 2.4 GeV total c.m. energy) e l ec t ron -pos i - t ron e las t ic sca t te r ing have been per formed at ADONE, the F rasca t i 2x 1.5 GeV e+e - s torage ring. Some p r e l i m i n a r y resu l t s (in the c.m. ene r - gy between 1.6 and 2.0 GeV) have a l ready p re - sented e lsewhere [1 ].

The exper imenta l apparatus , shown in fig. 1, su r rounds one of the s t ra ight sect ions of ADONE,

c m P b

~, " ~ ~'~" ,~';" ,~ c, o 1o 20 ~ ' / 5 ~ ~ f

5 C ~I c m B e a m a x i s • ~ / 5C ,1

T E L E S C O P E 3 ~'~ T E L E S C O P E 4

Fig. I. Section of the experimental apparatus ortho- gonal to the beam axis. The 0 acceptance is between 60 ° and 120 ° (z-axis being along the beam direction).

and covers about 0.35 of the total solid angle, as seen from the center of the apparatus.

Each of the four telescopes T i consists of two magnetostrictive monogap wire spark chambers, SC cl and SC fl, which measure the azimuthal di- rection, ¢, of the particle (z-axis being along the beam direction) and of four scintillation counters AiBiC i and D i. There is 1.3 cm of Al between the counters A i and Bi, while two 0.7 cm Pb absorbers are placed in front of each of the counters C i and Di, forming a sandwich that is used for pulse height analysis to discriminate showering electrons from minimum ionizing par- ticles (mainly cosmic rays, C.R.). A thick ab- sorber (22 cm of Fe), covering the top tele- scopes, and the roof counters CRI, CR2, in anti- coincidence with our trigger, strongly suppress the detected cosmic ray flux. Counters CR 3 and CR 4 were added in a second set of measure- ments and will be discussed later.

A charged particle in telescope T i is defined by the coincidence T i _-= A / B / ( C i + Di) and a neu- t r a l par t ic le by N i-= (Ai+Bi)(Ci+Di) . Any coin- cidence of two (or more) charged par t ic les , Ti, each in a different telescope, defines the mas t e r t r igger , CR-= (CR I + C R 2) being i n a n t i c o i n c i - dence *

* To give a coincidence, an electron must traverse 24 g/cm 2 of absorber, corresponding to ~ 1.9 r'L- diation length, x ; to be vetoed by CRI, CR9, it must traverse 1E O :203 g/cm2; to releh Ch3, CR 4 it must traverse 25.2 x o- 282 g/cm 2

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Volume 36B, number 6 P H Y S I C S L E T T E R S 18 October 1971

100 -I = : ~ - - , ®

;.,u,e !

I

6 0 - H3,ma~

~ o , , , , @

& 8 0 - OJ

60

H3 ma,

4 0 -

H~_~ 20-

0 0

(Yl • T3,~ {p, e3 reg ton

".e~eJ r e , t o n I

: L I

• . - _

[ e ,,u ; _ r e g l o n

F

I

i i I I

L [ e~eJ reg ion

r e , / j J eegton

2 0 4 0 8 0 1 0 0 Hf mtn HI max

P u l s e h e i g h t H I . : c h a n n e l s ~

Fig. 2. Plot of pulse heights H 3 ve r sus H 1 for (T 1. T3) events. (a) in- t ime events. (b) out -of - t ime events.

o~

i,,j

Q:

t , j

t 600

40

2 0

-2 'o"- ,b ° ~" ,'¢ 2'0" 11 ~ (d~grees )

t 300 l ® 2°0

t2J i , i , i 1 ,

- 4 0 - 2 0 0 2fO 410 L (.=m.9

2 0 =

¢-%

f O =

~ O*

-fo*

-2o*

!::.:..: ... :.

i i i e ' -t~O - 2 0 2 0

-L= Lt4"L3 (ram_) 2

t 4O

4 5 5 0 5 5 6 0 5 5

l i t C c h a n n e l s ]

Fig. 3. Track analysis of a sample of [e,eJ events. (a) A~ dis t r ibut ion for in- t ime events._(b) L distr ibut ion for in- t ime events, (c) A~p ve r sus L cor re la t ion for in- t ime events. (d) A t d is t r ibut ion for events from the

source,

W h e n a m a s t e r t r i g g e r o c c u r s a P D P 8 c o m - p u t e r r e c o r d s : w h i c h c o i n c i d e n c e s T i w e r e i n - v o l v e d in the e v e n t ; the a z i m u t h a l c o o r d i n a t e s of the t r a c k s in t he s p a r k c h a m b e r s , w i th the r e - s t r i c t i o n tha t w h e n t h e r e i s m o r e t h a n one t r a c k in a c h a m b e r , on ly t ha t c l o s e s t to the m a g n e t o - s t r i c t i v e p i c k u p i s r e c o r d e d ; the p u l s e he i gh t , Hi, in c o u n t e r s (C i+ Di) fo r e a c h t e l e s c o p e ; the t i m e , ~ t, of the e v e n t w i t h r e s p e c t to the b e a m - b e a m i m p a c t *.

Date reduct ion. T h e f i r s t s t e p in the a n a l y s i s i s to d i s p l a y the e v e n t s w h i c h g ive a c o i n c i d e n c e b e t w e e n o p p o s i t e t e l e s c o p e s (T 1 • T3) , and (T 2 • T4) , a s a f unc t i on of Lx t. T h e i r d i s t r i b u t i o n s h o w s a v e r y c l e a r p e a k (~:2 n s e c h . w . h . m . ) s u p e r i m p o s e d on a s m o o t h b a c k g r o u n d of c o s m i c

In ADONE there are three bunches of e ~ and three bunches of e - , each of duration ~ 1-2 nsec (f.w.h.m.). They collide in the exper imenta l sect ions every ~100 nsec.

r a y s . T h i s a l l o w s us to d e f i n e a n i n t e r v a l of Zxl f o r e v e n t s i n - t i m e wi th the b e a m - b e a m i n t e r a c - t ion .

Fig . 2(a) s h o w s a t y p i c a l p u l s e h e i g h t p lo t of H 3 v e r s u s H 1 fo r i n - t i m e (T 1 • T 3) e v e n t s . The p lo t c o n t a i n s two h e a v i l y p o p u l a t e d r e g i o n s : a low p u l s e h e i g h t r e g i o n of m i n i m u m i o n i z i n g p a r t i c l e s (C.R.) and a l a r g e p u l s e h e i g h t r e g i o n of e v e n t s w i th b o t h p a r t i c l e s p r o d u c i n g a d e t e c t - a b l e s h o w e r , w h i c h we d e s i g n a t e a s the [e ,e] r e - g ion. O u t - o f - t i m e e v e n t s (fig. 2(b)) show only the c l u s t e r in the m i n i m u m i o n i z i n g r e g i o n , w h i l e the [e ,e] r e g i o n i s p r a c t i c a l l y e m p t y . T r a c k r e - c o n s t r u c t i o n u s i n g the w i r e s p a r k c h a m b e r s a l - lows us to c o n c l u d e t h a t a l l bu t a s m a l l f r a c t i o n of the [e ,e] e v e n t s a r e B h a b h a s c a t t e r i n g e v e n t s .

Fig. 3 s h o w s the t r a c k a n a l y s i s of a s a m p l e of i n - t i m e [e ,e] e v e n t s . In fig. 3(a) the [e ,e] e v e n t s c l e a r l y a p p e a r to be c o p l a n a r ( i .e . ~x ¢ = 0, w h e r e Lx p i s the a n g l e b e t w e e n the two p l a n e s p a r a l l e l to the b e a m a x i s c o n t a i n i n g the two

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Volume 36B, number 6 P H Y S I C S L E T T E R S 18 October 1971

t r a c k s ) . T h e +3 ° a n g u l a r s p r e a d ( h . w . h . m . ) i s due to s p a r k c h a m b e r r e s o l u t i o n a n d m u l t i p l e s c a t t e r i n g in the v a c u u m c h a m b e r w a l l s (0.15 c m of Fe ) and in t he t e l e s c o p e a b s o r b e r s . T h e [e ,e ] e v e n t s in fig. 3(b) a r e p l o t t e d a s a f u n c t i o n of the d i s t a n c e , L , b e t w e e n the t r a c k a n d the a x i s of t he b e a m . A l m o s t a l l of t he e v e n t s a p p e a r to o r i g i n a t e , w i t h i n a h . w . h . m . ± 5 r a m , of the b e a m r e g i o n . A l s o in t h i s c a s e m u l t i p l e s c a t t e r i n g and s p a r k c h a m b e r r e s o l u t i o n a c c o u n t fo r the o b s e r v - ed w i d t h ( the a c t u a l b e a m d i m e n s i o n s a r e ~ 1 x 1 r am2) . T h i s i n t e r p r e t a t i o n of the e x p e r i m e n t a l w i d t h s of the A (p a n d L d i s t r i b u t i o n s i s c o n f i r m - ed in fig. 3(c). T h e c l e a r c o r r e l a t i o n o b s e r v e d b e t w e e n A (p and t he a v e r a g e d i s t a n c e (i.) of the two p a r t i c l e s f r o m the b e a m i s w h a t one would e x p e c t if a l l of the e v e n t s o r i g i n a t e w i t h A (p = 0 in the ~ (1 × 1 ) m m 2 s o u r c e r e g i o n . F i n a l l y fig. 3(d) s h o w s how w e l l we c a n d e f i n e the r e g i o n of the [e ,e ] e v e n t s w h i c h a r e " i n - t i m e " w i t h the b e a m - b e a m i m p a c t . F u r t h e r m o r e the o u t - o f - t i m e c o n t a m i n a t i o n ( m a i n l y C.R.) a p p e a r s to be n e g l i g i b l e .

F r o m t h i s a n a l y s i s we c a n c o n c l u d e t ha t ( a p a r t f r o m s m a l l b a c k g r o u n d s u b t r a c t i o n s h e r e a f t e r d i s c u s s e d ) the [e ,e ] e v e n t s a r e two body e v e n t s w i t h c h a r g e d s h o w e r i n g p a r t i c l e s o r i g i n a t i n g in e+e - c o l l i s i o n s , i .e . t hey a r e B h a b h a e l a s t i c s c a t t e r i n g e v e n t s .

A r e l i a b l e t r a c k a n a l y s i s of the d a t a r e q u i r e s t h a t a l l t he f o u r c h a m b e r s i n v o l v e d in the e v e n t h a v e c o r r e c t l y f i r e d . S i n c e t he e f f i c i e n c y of e a c h c h a m b e r h a s b e e n m e a s u r e d to b e a b o u t 0 .85 - - 0 . 9 5 , we h a v e c o n s i d e r a b l y f e w e r "4 c h a m b e r e l e c t r o n e v e n t s " t h a n we h a v e [e ,e ] e v e n t s . How- e v e r we c o n c l u d e f r o m the a b o v e t r a c k a n a l y s i s t h a t , f o r e v a l u a t i o n of the c r o s s - s e c t i o n , we c a n u s e a l l the d e t e c t e d [e ,e ] e v e n t s , i .e . t h o s e t h a t s a t i s f y the m e n t i o n e d p u l s e h e i g h t r e q u i r e m e n t s , i r r e s p e c t i v e of s p a r k c h a m b e r i n f o r m a t i o n . In t h i s way we a v o i d any p r o b l e m s due to t he s p a r k c h a m b e r s i n e f f i c i e n c y .

D u r i n g 1341 h o u r s of r u n n i n g t i m e , w i t h an i n t e g r a t e d l u m i n o s i t y .~-~ 3 . 5 x 1035 c m -2, we h a v e c o l l e c t e d a t o t a l of 5164 [e ,e ] e v e n t s in a r a n g e of c . m . e n e r g i e s , E++ E_, b e t w e e n 1.4 and 2.4 GeV. T h e y a r e l i s t e d , a t e a c h c . m . e n e r g y , in c o l u m n (3) of t a b l e 1.

Two d i f f e r e n t t y p e s of b a c k g r o u n d a r e to be s u b t r a c t e d f r o m t h e s e n u m b e r s :

i) a C.R. b a c k g r o u n d w h i c h c a n be e a s i l y e v a l u a t e d e x p e r i m e n t a l l y f r o m the n u m b e r of ou t - o f - t i m e [e ,e ] e v e n t s . T h i s s u b t r a c t i o n i s of the order of ~ 2% (see column (4) table I);

ii) a contamination due to interactions of eith- er beam with the residual gas in the storage ring. With measurements performed with only a

Table 1. List of the experimental results and of the background corrections. The numbers marked with a * refer to runs in

which the counters CR3, CR 4 were put in ant+coincidence with the trigger.

C.m. energy Integrated Collected Normalized Normalized Corrected m E++ E_ luminosity [e,e] C . R . beam-gas e+e - Small-angle R e-e+ q2

(GeV) (cm -2) events background background Bhabha monitor = n~ (GeV/c)2 events events × 103

(1) (2) (3) (4) (5) (6) (7) (8) (9)

1.4 68xi032 212 3.9+1.2 0 . 2 + 0 . 7 7 6 1 ± 4 5 198.4x 103 3.83±0.22 0.87 1.4 113 x1032 306* 5.3 + 1.2 -0.6+0.9 1.5 52x1032 141 3.6+1.1 0 . 2 + 0 . 8 1098+45 308.9 xl03 3.56+0.15 0.95

1.5 280x 1032 738* 13.6± 1.9 -1.6+ 2.4 1.6 77x1032 176 4.5+1.2 1 . 1 + 1 . 2 222+21 64.6x i03 3.44+0.32 1,08 1.65 U4xl032 187 3.8+1.1 2 . 1 + 1 . 8 2 3 0 ± 2 0 87.6xi03 2.62+0.23 1.14

1.7 126x1032 259 3 .8±1.1 3 . 2 + 2 . 2 3 3 2 + 2 5 8 9 . 8 x 1 0 3 3.70+0.28 1.21 1.75 135x1032 192 4.2+1.2 3.7+2.3 238+22 88.3x103 2.70+0.25 1.29 1.8 135x1032 226 3.1±1.0 4 .8+2.6 283+24 81.3x103 3.48+0.29 1.36

1.85 260x1032 417 7 .7+1.6 2 .6+2.3 1470±56 377.4x103 3.68+0.14 1.44 1.85 420 x 1032 825* 7.2 + 1.5 5.6 + 10.0 1.9 134x1032 186 4.2:~ 1.2 8 .6±3.2 220+20 68.3x103 3.22±0.30 1.52

2.0 290x1032 328 7 .6+1.6 30.2+6.0 369+30 128.2x 103 2.88±0.23 1.68 2.4 148 x l032 102 3.6+1.1 4.0±2.7 1045±52 303.2 x l03 3.45±0.17 2.42 2.4 1147 x1032 869* 15.1 ±2.1 69.5 + 17.9

Totals 3499x 1032 5164 91.2+5.3 133.6+22.5 6268±117 1795.9x103

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Volume 36B, number 6

single beam or with two separated beams t we have determined that the contamination is near zero at low energy, but rises to - 8% at 2.4 GeV c.m. energy. The average contamination for the full sample is about 2% (see column (5) of table I).

After background subtractions are performed, we are left with 4939 [e,e] elastic scattering events. In order to obtain the total number of produced Bhabha events we have to apply to our data several corrections.

First, since the probability that an electron will initiate a shower before counter C and D is not 100%, we expec t that a s m a l l f r a c t i o n of e v e n t s e+e - ~ e+e - wil l not a p p e a r in the [e ,e] r eg ion . To eva lua t e the s i z e of t h i s " s h o w e r - c o r r e c t i o n " we have a n a l y z e d the e v e n t s which fal l in the [ p , e I r eg ion of fig. 2 ( i .e. the e v e n t s wi th only one p u l s e he igh t l a r g e r than H i max)" As we expec t if t h e s e [~ ,e ] e v e n t s a r e t r u e e+e - s c a t t e r i n g e v e n t s , we find tha t t h e i r L and Ago d i s t r i b u t i o n s a p p e a r to be the s a m e a s fo r the [e ,e] e v e n t s . A f t e r b a c k g r o u n d s u b t r a c t i o n s a r e p e r f o r m e d , f r o m the n u m b e r of [~ ,e ] e v e n t s we a r e ab le to d e t e r m i n e the p r o b a b i l i t y , E, fo r an e l e c t r o n to have a p u l s e he igh t l e s s than Hi, m a x . Thi s has b e e n done at e a c h e n e r g y , and the c o r - r e c t i o n f a c t o r s F s = (1 -E) -2 to be app l i ed to the [e ,e] e v e n t s a r e l i s t e d in co lumn (2) t ab le 2.

F u r t h e r m o r e , s o m e e v e n t s wi l l be los t if one of the e l e c t r o n s p a s s e s t h r o u g h the 22 cm of Fe and p r o d u c e s an a n t i c o i n c i d e n c e pu l se in coun- t e r s CR1, CR 2. F o r th i s r e a s o n i n a l a t e r p h a s e of the e x p e r i m e n t we p l a c e d o v e r the a p p a r a t u s a s e c o n d " r o o f " of 1.5 cm of Fe , 5 cm P b a n d two add i t i ona l c o u n t e r s CR3, CR 4 ( see fig. 1). T h e s e c o u n t e r s w e r e put in a n t i c o i n c i d e n c e wi th the t r i g g e r , whi le CR1, CR 2 w e r e s i m p l y r e c o r d - ed for e a c h even t . In th i s way we d i r e c t l y m e a s - u r e d the f r a c t i o n of e+e - e v e n t s that w e r e los t due to a n t i c o i n c i d e n c e in CR 1 and CR 2. The c o r - r e c t i o n f a c t o r s , FAC, e x p e r i m e n t a l l y ob t a ined a r e l i s t e d in co lum n (3) of t ab le 2. They apply only to the runs wi th CR1, CR 2 in a n t i c o i n c i d e n c e , s i n c e the n u m b e r of e v e n t s v e t o e d by CR3, CR 4 w a s d e t e r m i n e d to be neg l ig ib le . T h i s c o r r e c t i o n has a l i n e a r e n e r g y d e p e n d e n c e and v a r i e s f r o m 4% at 1.4 to 15% at 2.4 GeV ( see fig. 2(d) of ref .2) .

Co lumn (6) of t ab le 1 con t a in s the n u m b e r of e+e - - - e+e - e v e n t s c o r r e c t e d fo r al l the above

t The value of the normalization factor to be applied to the number of beam-gas events collected in the background runs has been obtained by monitoring single bremss t rahlung on the residual gas.

PHYSICS LETTERS 18 October 1971

mentioned effects i t . Analysis of the resulls. To compare our re-

sults with QED predictions, we take the ratio, R = e+e-/m, of the wide angle Bhabha scattering events (e+e -) to the "monitor" events (m), name- ly the small angle (3.5 < 0 < 60 Bhabha scattering events collected simultaneously in a separate experimental apparatus [3] in a contiguous straight section of ADONE t~t. This minimizes in the experimental data the energy dependence arising from the fact that the source (which is defined as the region of interaction of positron and electron bunches) has a finite energy depen- dent length :~ which is comparable to the linear dimensions of our counters and which reduces the effective solid angle of the apparatus to

0.18 of the total 4~ str. The experimental ra- tios are listed in table I, column (8) for each c.m. energy.

This ratio can be calculated from QED by in- tegrating the Bhabha cross section over the ex- perimental apparata in which the large angle and small angle e+e - scattering events were collect- ed. For comparison with the experimental ra- tios we have included in the calculation of Rth several energy independent systematic correc- tions. These systematic corrections are: mul- tiple scattering losses (2.5±2)%, possible geom- etrical misalignement of the apparatus with re- spect to the beam (3±3)%, and an overall un- certainty of ± 5.07o in the absolute normalization of the monitor. Radiative corrections were not ap- plied since they were calculated to be negligible (< 1%).

In fig. 4 we show as a func t ion of the c . m . t o - ta l e n e r g y the e x p e r i m e n t a l v a l u e s of R c o m -

t t Further small correct ions (like multiple scat ter ing losses and geometr ical misalignements) have not been applied to the experimental points, but, since they are calculated to be approximately constant over the whole energy range, were taken into ac- count in the evaluation of the theoretical p red ic - tions.

t~~ The symmetry of the machine and the fact that the data were collected during a long period of t ime. averaging over possible slight changes of the work- ing conditions of the machine, make it reasonable to assume that the overall resul ts are not affected by the fact that sma l l - and large-angle elast ic scat ter ing were measured in different s traight s e c - tions of ADONE. The expected distribution of the source is

N(l) = N o exp (- 12/2/2)

where l (cm) is theoretical ly expected to be 20E 3/2 (E± in GeV) and exl~erimentally has been deter--- mined as (22t-2)E+3/2 (prlv" ate communications of the ADONE machine staff).

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Volume 36B, number 6 P H Y S I C S L E T T E R S 18 October 1971

Table 2. List of the shower inefficiency correct ion factors F_ and of the ant icoincidence- losses correct ion factors ~

FAC , at each total c.m. energy E++ E_.

E+ + E_ F s FAC (GeV)

1.40 1.31 + 0.07 1.046 :L 0.018 1.50 1.18 + 0.06 1.043 :e 0.010 1.60 1.23 + 0.06 1.060 :~ 0.015 1.65 1.19 +0.05 1.066 :e 0.016 1.70 1.23 ± 0.05 1.072 ± 0.017 1.75 1.20 +0.06 1.078 • 0.017 1.80 1.20 + 0.05 1.082 • 0.020 1.85 1.14 + 0.08 1.089 + 0.020 1.90 i. 16 e 0.05 1. 094 :L 0.022 2.00 1.15 ± 0.05 1.105 • 0.024 2.40 1.10+0.08 1.153 • 0.035

p a r e d wi th the t h e o r e t i c a l va lue Rth . Due to the s y s t e m a t i c u n c e r t a i n t i e s m e n t i o n e d above , R th a p p e a r s a s a band wi th an o v e r a l l wid th of

±7.5%. F u r t h e r m o r e , due to e r r a t i c c h a n g e s of the b e a m t r a j e c t o r y wi th r e s p e c t to the m o n i - t o r a p p a r a t u s we have a d d e d a ~: 5% uncertainty:[::[: ( s m a l l r e c t a n g l e s in fig. (4)) to the s t a t i s t i c a l e r r o r of e a c h e x p e r i m e n t a l va lue of R. The s l i gh t e n e r g y d e p e n d e n c e of Rth i s due e n t i r e l y to the e n e r g y d e p e n d e n c e of the s o u r c e length . Wi th in the e x p e r i m e n t a l e r r o r s the m e a s u r e d r a t i o s a r e in a g r e e m e n t wi th the t h e o r e t i c a l p r e d i c t i o n s .

In the Bhabha s c a t t e r i n g a r o u n d 90 ° the s c a t - t e r i n g d i a g r a m d o m i n a t e s the a n n i h i l a t i o n d i a - g r a m so that our m e a s u r e m e n t s a r e m a i n l y c h a r - a c t e r i z e d by the s q u a r e of the f o u r - m o m e n t u m t r a n s f e r to the v i r t u a l s p a c e - l i k e photon , q2. The v a l u e s of q2 a v e r a g e d o v e r the a c c e p t a n c e of ou r a p p a r a t u s ( s e e fig. 4) a r e l i s t e d in t ab l e 1 c o l u m n (9) f o r e a c h c . m . e n e r g y .

We can conc lude tha t fo r a v e r a g e v a l u e s of (q2) r a n g i n g f r o m 0.82 (GeV/c ) 2 to 2.42 (GeV/c ) 2 the m e a s u r e d Bhabha c r o s s s e c t i o n a g r e e s both

,:[::~ We have evaluated this uncertainty by analyzing the relative variations of two symmet r i c te lescopes of the monitor apparatus.

?

6

5

4

3

2

?

0

CGeV/O . 9 f .O 1.1 1 .2 f .3 1.4 1.5 1.6

T I I I I I 1 I

4 ~ (q /2r , )2

\ ~ \ \ \ \ \ J k \ \ \ \ \ \ \ / / -

- Of~

I I I I I I l I I I [

1.4 1.6 1.8 2 . 0 2 . 2 2 . 4

C hi. E N E R G Y E * * E_ ( G e V . )

Fig. 4. The ratio R of wide angle Bhabha events (e~e -) to the "monitor" small angle scat ter ing events (rn) as a funetion of the total c.m. energy. The experimental points are compared with the Rth band. The q2 accep- tance of the apparatus weighted on the Bhabha e ross

section is shown in the upper right-band corner .

in s l o p e and a b s o l u t e va lue wi th the QED p r e - d i c t i o n s wi th an o v e r a l l e x p e r i m e n t a l u n c e r t a i n t y o f ~ 10%.

R e f e r e n c e s

[1] B. Bartoli , B. Coluzzi, F. Fel ieet t i , G. Goggi. G. IVlarini, F. Massa, D. Scannicchio, V. Silvestrini and F. Vanoli, Nuovo Cimento 70A (1970) 615.

[2] B. Bartoli , F. Fel icet t i , G. Marini . A. Nigro, H. Ogren, V. Silvestr ini , N. Spinelli and F. Vanoli, Phys. Let ters 36B (1971) 598.

[3] G. Barbiell ini , B. Borgia, M. Conversi and R. Santonico, Rend. Classe Sci. Mat. Fis. e Nat. dell 'Aeead. Naz. dei Lincei 44 (1968) 44: G. Barbiell ini , B. Borgia, M. Conversi , G. Iorio and R. Santonieo , Intern. Report n. 155 Istituto Fisica, Universit~ di Roma (1968).

597