t/ Jtl - CERN · 2 CERY/TC /PIWSICS 65-25 'I'his report olnstic scnttoring nt 3.0 GcV/c and ropresonts the first pnrt Ll study of K+p interactions at 3.0, 3.5 and 5.0 Gc_)V/c. Proli11inc~ry

TO BE SUBMITTED TO NU"VO CIMENTO

CERN/TC/PHYSICS 65-25 18.11.1965

K+p ELASTIC SCATTERING AT 3.0 GEV/C

J. Debaisieux, F. Grard, J. Heughebaert, L. Pape and R. Windmolders, Laboratoire des Hautes Energies, Bruxelles

R. George, Y. Goldschmidt-Clermont, V,P. Henri, D.W.G. Leith, G.R. Lyncl:i1~ F. Muller and J .-M. Porreau,

CERN, Geneva

G. Otter~ and P. Stlllstr~m, Institute of Physics, Stockholm.

~tract

In the course of a systematic study of K+p interactions at 3.0 GeV/c, the

elastic scattering reaction ho.s been investigated. A total of 1720 events were

identified as elastic scatters, giving a cross-section of (4.8 ± .4) mb. The

angular distribution shows characteristic diffraction peaking and was fitted

using dcr ( dcr ) d /t/ = d Jtl 0

at + ~t2 e

in the momentum transfer region (0.05 - 1.14) (G0 V/c) 2 •

a= 4.55 ± 0.39 (GeV/c)-2 and ~ = 0.64 ± 0.42 (GeV/c)-4.

The best fit gave

The extrapolated

experimental cross-section at o0, (dcr/dt) 0 , is found to 2

be (19.5 ± 2.3) mb/(GeV/c),

o.nd exceeds the optical theorem prediction by (3.8 ± 2.3) mb/(GeV/c) 2,

implying that there is a contribution from the real part of the K+p scattering

amplitude at 3.0 GeV/c.

Introc1uct:!,9n

The elastic scattering of K+ mesons on protons has been studied up to

2.0 GeV/c using emulsion, bubble chamber and counter techniques. From the data

of Cook et al .. (l), and later Chinowsky et al. ( 2 ) ,it appears that at 1.97 GeV/c

the distribution of the centre of mass scattering angle of the K+ is strongly

peaked in the forwo.rd direction. The same effect w2s found by J!'oley et al. (3)

in the region 7 - 15 GeV/c. No results have been published between 2 - 7 GeV/c.

31: Now at Institut ftl.r Theoretische Physik, Vienna, Austria + Now at Lawrence Rc.-:diation Laboratory, Berkeley~ Ce,lifornia

PS/5133/mhg

2 CERY/TC /PIWSICS 65-25

'I'his report olnstic scnttoring

nt 3.0 GcV/c and ropresonts the first pnrt Ll study of K+p interactions at 3.0,

3.5 and 5.0 Gc_)V/c. Proli11inc~ry rosuhs h:we boon pres(.;nted c,t tho Dubnn

Conference, 1964 ( 4 ).

Tho Sc1,clrw 80 cm hydrogen bubble ch:cmbor WD,s exposed to ::i, separated beam of

K+ ( 5 ) mosorn:; .':\t the CERJ'T proton-~>yrichrotron. Tho momontum of tho bu:om wns deter­

mined by me0,Gm"cnont of -f-dece,ys ;md wc:s founcl to be 2.97 GoV/c cct tho centre of

tho chnmber, uith n DOicienturn s;:iro,,d of ± 0.015 GeV/c. '.L'ho pion contamine,tion wns, 0'

nvernge, not more than 5 / o.

A tot::cl of· :;,bout 40, 00() :pictures wore scccnnod for 0,J_J_ two-prong events

occurring within ~' reduced fiducL:i,l volumo chosen in order to minimise moe,suremont

errors. At sconning~ events which ·vrnre obviously ino 10,stic, ~:w recognized from

the moment:, of outgoing trncl1:cs, wero rejoctod. Tho solocted events were moo.sured

nnd processed through the CERN programs THRESH, GRIND ~md Bl-i . .KD. An event vms

c.ccepted ns elastic if tho .X,2 vms loss thccn 20 for cm olccstic hypothesis compatible

with the observed bubble densities. After remee,surernents, .'.1 totcl of 1720 elastic

t . ' t . n • ' mh . . . d. t . b t . ' 1'~1~ di" s+ri· but J·_on oven s were icwn n iecl. T. o ir mis sing mc::.ss is ri u ion ana 't.. v -

e,re shown in Figs. 1 :md 2, respoctivoly.

Those events fit ting cmd id.ent ifiocl -tho rocwtion + + 0

K p -~ K pn have

been shown in Fig. 1 ::cs tho d,:::,rkonod nro.-:;,. A good sopar0,tion of tho elastic

events is obtri.in.ed on tho bnsis of missinc: mc,ss o,lone (tho contamint:.tion under

the "olcwtic peoJc 11 boing rr:O 3°/o). However, when ono rcpplios all the nve,ilccblo

kinomc:::tic constraints, no evont is found to fit simultMeously this reccction nnd

the efostic hy1!othesis.

Ths scc.u"1.ning cffj_cioncy hD,s bco:on ostime,tod from a second scan performed on

c:,bout half of the 2nD,lyzod pictures C'cnd was found to bo 96° / o for events with

cos g (where G is tho centre of mc~ss sc.':\ttoring nngle) less than O. 98, corTcs-

pondinG to '-' recoil proton rctngo of 1.7 cm. It rn:n.'orcrod th,:,t the scrn1ning

efficiency dotc:riorc,ted rnpidly for vn1 ucs of ·cos G z-md it wo,s therefore

decided to lrnop for fu.rthor ,n,n2lysis only those events uith cos Gloss thm1 0.98.

'rho de1xrndonco of tho scm1nin[,· efficiency versus tho dip ,~glo, '"A, hns boon studiod

for cos ~ ~ 0.98. The dip '"A, is doi'incd o,s the ::,nglo between the plane of

PS/5133/mhg

3 CERN/TC/PHYSICS 65-25

the chamber window ond the scattering plane (for small scattering angles it is

essentially the angle between the recoil proton and the window). The distribution

of "A is shown in Fig. 3 for o.11 ident:.:.fied events with cos Q ~ 0.98. It appears

to be compatible with isotropy in the region o0 -- 60°. We made a general cut-off

in "A at 80° because the configuration of the track for events with "A ~80° makes

the geometrico.l reconstruction more difficult and less o.ccurate. The fall-off

in the region 60°~/I. ~ 80° is found to result from events emitted ~t small

scattering angle, and thus for 0. 95 ~ cos Q ~ O. 98, a cut-off was set at the

value A = 60°.

Results and Discussion

(a) Cross-sectio~

+ The K p total elastic cross-section, 0el' has been determined from the number

of elastic events, corrected for scanning efficiency and for the A and cos Q

cut-off's, and from the number of -C-decays occurri:ne:,· in the fiducial volume

considered in this experiment. Using the following values

(l.229 ± 0.008) x 10-8 sec. for the K+ lifetime( 6),

(0.055 ± 0.001) for the branching ratio for K+ decay into three charged

pions( 6),

0.062 g/cm3 for the density of liquid hydrogen in the bubble chamber

the elastic cross-section has been found to be

ael = (4.8 ± 0.4) mb.

A summary of the dependence of the elastic cross-section(l),( 2),(3),(7) versiIB

the incident K+ momentum is shown in J:Pig. 4, together with the K+p total cross-

t . ( 2) ' ( 7) ' ( 8)' ( 11) sec ion • It may bo expected from the rapid increase of the in-

elastic cross-section at about 2 GeV/c (i.e. shown by the difforence between total

and elastic cross-sections in Fit;. 4), thnt the elastic differential cross-section

should begin to show diffraction type behaviour above this onorgy. The present

results do in fact demonstr::cte this tron.d.

(b) Differential Cross~sectio~

The experimental angular distribution corrected for the imposed angular cut­

offs, is represented as a function of cos Q or -t (momentum transfer squared) on

Fig. 5. The values are given in Table I.

PS/5133/mhg

The expe;~imental

function

4 GERE/TC/PHYSICS 65-25

cU.stri but ion hccs l:ieon fitted to the following

( dcr 1 d 1tj 10

! ' o:t

e ( 1)

where a repres;:mts the slope of the distribution c:nd (a_l~t )0 is the value of

the cross-section at t=O. 1fii.o fit has been made using tho maximum likelihood

method. The probnbili-Cy element is

P(t) dt

J> -co

(2) ext

G dt

where t cind t 0 ,. - 1 ccre, respectively, the lower :md upper limits betueen which

the m1gu le.r dis tri but ion i.s considered. The lilrn lihood function is then n

L(cx) = lT jj( t 1 )_J i=l

(3)

where the product runs ovor thE) total number of selected events (n). Tho best

value of a is obtgined whon Log I,( a) renches its ma..'CirnuG value nnd the error

6cx is given by ; -1/2

I:og I,(a)_} . , (4)

for a gauss:Lonly distributed L(a). Tho maxir;mrn likelihood fit ;,;0,s performed ( 0 \

using the llIALIK progn::m :;; ) .

The results of the fit ::1re in T~,ble II, for tuo different "t 11 inter-

vals, together uith the corresponding forward differential cross-section.

It may bo seon from Table II that tho slope a is found to be steeper • +' l.t. CL

smnll rz:rngo of cos Q is used. In f.J.ct, results obtained from fits made by trucing

cos G intervals of internedie,to ra:1ge between solutions I and II showed that tho

coefficient a vctries linec;rly, betwocm the two vccluos c1uoted in Table II, within

tho limits of tho estirnntod errors, Tho f~wt th2,t the value of a seems to vn.ry

monotonically throughout the region of the angular distribution investigated,

suggests that tho experioontnl data would bo bc:d;ter represented by an exponential

with a quadratic term in t

dcr

d /t/ 2

at + ~t e (5).

A maximum likelihood fit to the do.to. ho.s been made for two 11 t" intervals,

and the results are presented in To.ble III PS/5133/mhg

(10)

5 CERN/TC/PHYSICS 65-25

At 2.0 GoV/c, Cook et c::,1. 8.nd Chi.nowsky et al. found thnt their differential

cross-section could bu ccdequately describod an exponent ie,l of the type

d l~( = (a_ l~/ )0 oo:t (i.e. ~ = 0); however, the dat,'.l of Foley et 21. in the

region (7 - 15) GGV/c reouirod n torm in ~t2 , as described above for this experi-2

mont. These expor iments lw:vo been crn.nlysed in the 11 i:; 11 rcmge up to 0,bout 1 (Ge V / c).

The; p2crcc111eters shown in TablErn II and III lie between ·che result of Chinowsky et

al. L1t 1.97 GoV/c (viz. o: = 2.9 ±. ), and Foley et al. Elt 7.0 GeV/c (viz.

o: = 6.2 + 0.9). This verifies the rnpid shrinking in the K+p diffrnction peak

between 2 and 7 G0 V/c, ~rhich m.._cty b::; interpreted ::w refloct~Lng the rapid ch31lge of

the ine lr:.stic cru;s-section at these' energies ( 4).

The re0ul ts of tho diff'erenti1.cl crosD-soction in tho forward direction given

in Tnbles II ~rn.d III mo.y bo cotapL'.red to tho prediction of tho optical theorem.

To.ldng the v2luo of tho toted cross-section nt 3.0 G8 V/c :

found by

a tot

BcJccr et

= (17.51

a1.(ll),

± 0.27) mb

po cross-section if5

The forwnrd scnttering cross-0ection, ns determined by this experiment, is

larger than would be predicted if the scdttering nrn.J)li tudG were purely imaginary.

In fact, choosing tho two-po.rameter fit (i.e. the best parmneteriso.tion), the

following results are obtninod :

I:-;:\ = 0.49 ± 0.31 for

0.52 ± 0.25 for

ltj·~ 1.1 (GcJV/c) 2 (i.e. Sol.II~ T.nblo III)

(i.o. Sol, I, T b 1 rr) ,ci, __ e __ L •

The de.ta indicate tkit, at the 90°/o confidenco lovol, there is some real

part to the K+p scnttoring t 3.0 GoV/c. '11ht.J relntive mc:\gnitude of tho real cmd

irn.0,ginary partc is poorly cloturmined in this experiment but it i:::: clo~"Crly com­

patible with tho results o:f }l'oloy ot :0,J_,( 3), where ::,t higher momenta (7 - 15

I ) 200/ n '1 1 G0 V c , " contribution of as r;1uch E~s o rrom -cno roa of the Dlllplitude,

could not be ozclucled.

PS/5133/mhg

6 CERN/TC/PHYSICS 65-25

( d) Conm_arison w~ th 0.Qticn], Model Theories

Recently, Simmons(l2 ) ho.s attempted to fit the n±p elastic scattering do.ta

at 2. 0 Ge V / c, assuming a model in which cell pnrti2l waves with nngular momentum,

i,, less than o. cut-off, L, are equally nbsorbod cmd trot all other waves do not

interact. This dtempt was justified in view of tho appearance of n secondary ±

diffraction reek in the n p sco,ttering d;:J,ta. Here no such secondary peoli: is

present (Fig. 4) but it is still of interest to ·interpret our resul is in terms of

this model due to its success in explaining n±p (l3),(l4 ) and ICp (l4 ) scattering

in our energy region.

1 This modol corresponds to the scattering by a grey disc of ro.dius R - -

k where k ropresonts the wc:.ve number of the incident K+. The totnl end elastic

cross-sections are given by :

(1 + 1)2

(1 + 1) 2 (6)

and tho cmgular distribution is described by

dO' (dO'~ lL (cos 9) + PL+i (cos Q) J 2

(7) = (1 + 1)2 dQ dQ

2 (· \4 ( do), __ n 1..1+1..L_, where

dQ 0 4k:2 Legendre Polynominls, ond

are the Associated

is the absorption coefficient. Such a fitting to

our do/ca, for L = 3 (the valuo derived fror.1 the measured O'tot' O'el and tho

solution of equations (6)) is shown in Fig. 6. This choice of 1 corresponds

to the sco.ttering fror,1 a disc of ro.clius ( 14 ), R ~ 0. 55 f. The absorption coeffi-

cient, a, in this case would be ?d 0. 6. I'or values of cos G greater them 0. 7

(i.e. for -t~ 0,7 (GeV/c) 2 , tho fit is fair, but as on overall fitting to the

angular distribution this clGscription is hardly ndequnte.

We also compared our dett0, wi-ch tho depondence suggested by Mino.mi (l6 ) for

+ K p scattering

whore f(G) is the elnstic sc2ttoring omplitude, and A and A are taken to be 0 1

independent of energy.

PS/5133/mhg

7 CElliif/TC/PJrISICS 65-25

The dt:cta at 3.0 GeV/c o..re not in good overall o.greement with such a para ...

meterisation in which A and 1\ are taken from Min<J.mi 1s

energy data ( 3), nnd C i~ optimised for our experiment.

for momentum tro.nsfers smaller than 1 (GeV/c) 2 (soe Fir:;.

the A's wore determined.

Conclusion

L:.nalysis of the high

However, the fit is good

6), the region in which

It has been shown above that tho differontir,l cross-section for the renction

+ + I K p ~ K p at 3.0 G0 V c is dominated by n sharp forward sco..ttering peak. The

fall-off with

nontinl of the

(tv 15° /o of

momentum tro..nsfer of this peak nmy be well represented by an expo­a:t + ~t2 form Ae , uhero ~ is found to bo o. rn.ther smnll correction

a nround -t==l (G0 V/c) 2 ). Tho elnstic sco.ttering cross-section

is found to be in good <'.l.greement with d<J.tn from neighbouring memento., and confirms

the rnpid decro:::.se in the cross-section implied by tho previous dntr,. The vnlues

of the paro..meters a o.nd ~ are found to lie between the vo.lues found o.t 2.0

nnd 7 GoV/c, o.nd demonstrnto the rapid change of tho nngular distribution in this

region. This effect may bo interproted 2s reflocting tho rapicl cho.nge in the in­

elastic cross-section over this snme momentum interval. Although the o.ngulo.r

distribution hc .. s a shape which is typicnl of o. diffraction scattering distri­

bution, tho detailed shape cannot be so.tisfnctorily explained by a simple two­

parnmoter optical E1odel theory. No ovidenco for the existence of secondary

diffraction peaks in K+p sco.ttering at this energy is observed. Finally, it is

nlso shown that the data indicate the presenco of some real part in the scattering

amplitude, but do not nllow a good determination of the ratio I ~:.ti; the results

obtained show l·i:~l ;-v 0.5 ± 0.3, the result being fairly independent of the Htn

rango used in the fit.

Acknowledgments

The Belgio..n group is grateful to Dr. J. Reignier for helpful discussion,

nnd the Institut Royal Metoorologique de Belgique, especinlly to Hr. J. Vnn

Isncker, for his help :Ln the use of tho IBH 7040 computer. They would like to

thank Professor L. Rosenfeld for his support nnd interest.

PS/5133/mbg

8 CF'RN/mc jpuv---. Ir',., ul _J l. Hl.0 v1:::i 65-25

Tho StockhoL1 group ncknowleclgos support fron tho Swodj_sh ,tomic Reseccrch

Council. Thu robc::irch reported in this pnpor h~s boon sponsored in part the

United ,str~tos il.ir Force uncLer Gr,;,nt Hos. 63-11 ::ind 64-57, Europoon Office of

Aorospnce Rosonrch.

Cur thnnks .'~re duo to the crmr of the; 8lcn S:;:,clc:,y hydrogeri bubble charaber,

to the stc,ff of tho CERN 1;roton-synchrotron, to the coepu dj_vision, and to

our sc::tnning c,ncl measuring st~d'f, '\Io ccre grc,toful to Professor R. Arnentoros

for helpful discussion, and to Professor Ch. Pcyrou for his support.

PS/5133/mbg

9 CERN/rrc/PHYSICS 65-25

Reforence,s -----· ~~ --~~-""'--"" (1) V. Coot, D. Keefe;, I,.T, Korth, P.G. Eurphy, W.A. 'Jonzol, T.F. Zipf,

Phys.Rov. 129., · 2743 (1963).

(2) U. , G. Golclhnbor, [i. Golclho.bfJr, 'I'. O!tfallorcm cmcl B. Schwcmgschild, U. C.R. I,, 116(.9 ( un1mbl:LE;hod).

(3)

(4)

K. J. lo lo y, ~) • J • Lindenbo.1E 1 , .A. .Rov.Lotters Jl,

Love, 503 (

S, O:c-;c:Jci., J.J. Russell c:md 963).

, R. \!indi;oldors, IL l:'o:;.~ro , Ic. Geor{:,o, Y. Golcloc:1nidt-Clerr;iont, V.P. Ecmri, B. Jonge-jo.ns, D •• G. Lo:Lth, G.R. Lynch, F. Eullor, J.-Iif. 1\-;rro:::J.I, G. Otter 2.nd P. SiUJotrdn, Dubmc Conferonco on DlonFmtnry Fr~rticlos, 1964.

(5) J. Goldberg 1>,nd J,l'1I. Perrnau, C2RJT 63-12 (1963).

(6) A.H. Eosonfeld, .~. Bnrbnro·~Gnltiori, 'T, , J3c,rkns, P,L, Bc;Dtien, J. King cmd IL Roos, U.C.~~.L. 8030 (revised 1965)

(7) T. Stubbs, II. Bradnor, D. Stork nnd N. Ticho,

lT. Chinowsky, G. Goldhnber, S. Golclh::-,bor, W. Slo.ter, Phys .Hov. LettGI'S ,I, 188 ( 1961)'

S. Goldhnber, U. Chinowsky, G. Golclh::JJer, TJ. Leo, T. 0 1Hnllornn, T. Stubbs, G.M. Pjorrou, D. Stork rmd H. 'richo, Phys.Hev.Lettors ~2' 135 (1962).

(8) V. Cook, D. Koofo, I,,T. Korth, P.G. Murphy, U.L .• Wenzel ·'.:md 'I'. Zipf, Phys.Hov.Lettor~J :l, 182 (19{il),

( 9)

PS/5133/mhg

W.F. R'::.ker, R.L. Cool, D.W. Junkins, T.F. Kyc:L:, R.H. PhiJJJ.ps c,nd A.L. Rend, Phys.Rev. 129, 2285 (1 ),

W. Gclbrrdth, E.W. Jenkins, T.F. KycL, B • L0 ontic, R.H. PhiJlips r:.nd li.L. f<.GC1.d, Pl1yc. Ro~v. -~]§._, B913 ( 1965).

F. Nucluc~r Instrur1ento 2nd J'!lethocls .2.:l, 24'.2 (1965).

Tho mnxii;1um lH::elihood u,'ls performed on n distribution divided into srnc;,11 intorv::cls of corJ Q c,nd not on .'ln ovcnt ovon t bo.siG. Howevor, tho

st1cl1 tb.r:t tl1G ros;_~lts \'.Jore prncticD..lly

At cn incident ntum ~f 3 GeV / c ,'.',nd for con tre of l0ss thc:.n 90°, K lJ c~nd 1c-r-p elo.stic sc~.., ovcmts r;ro undis fro:1.:l t:t1e poirit of v·io1v of lcinc:E10,-Cics nnd ionis:=~tio11. S:ho so.111ple of selected K+p evonts thoro:i\we m2y contnin c~ cont~".minntion of n +p elnstic evcmts. In orcier to ov::J,ucc te the; in.fl uence of this cont ~::minntion on the sr1c,pe of the oxporinontal :-cngular distribution, thu pnrnmotors o: nnd ~

s

1 'b 1 I , • rO/ I • t. n I 1 b d . 11nvo oon re-ovc, uc»cen ~-,,ssunung cc :::> o conn1Dinn ion or -c11e or.:ra, nn using the n+p d'.'.t:1 of Porl et eel. nt 2.92 GeV/c (loc.cit.). This investigdion

( 11)

( 12)

( 13)

( 14)

( 15)

(16)

10 CE:RH/TC/PErlSICS 65-25

shoued tic tendency for the .Pc.,r:iraeters to decro:cse but never exceedinc; the ::cssignod errors, Tvo:iicr:cllv, tho TJ3I'tcr:Jetors for Solution I 4 in TeJJlG IIJ bocz,ne a == 4. ± o:26 (GeV/c)-2 ;nd ~ = O. ± 0.21 (GeV/cf. Since 5°/o is .. n up:;Jer limit for tho contamin,-.,tion, vrn reL:;nrd the effect of tho pion h.ckground on tho e.nc;-ulo.r distribution 2s negligible.

TI. ll1. B2lGJ r, ·;iJ .. . · .•

nnd H. Rudernri.n, Jenkins, T.l'. Kycic·., E, Phillips, L .• L. Rend, K.F. Riley

Sienncc Conference on E:lemontc:.ry Po.rticles, p.634, 1963.

L.M. Sinnons, Phys.n.ev,Letters J~.' 229 (1964).

E.L. Perl, I,,,J. Jonos r:.ncl C.C. Ting, Phys,H.ev. l.2.?., J-252 (1963).

This r!1dius is }19 .. t tho r<cdius ord:Lnc.rily quoted for diffraction on o. disc: r--

R = v2a~0.7 forrni, t2 formuL: which is strictly voJ.id only o.t very high energy.

D.I~. D2moutll, L.W. Jonos nnd Il,L. PorJ., Phys.Hov.Lotters JI, 287 (1963),

R. Crittondun, H.J. IvL:~rtin, • Kor112n, ;L. LoipunoJ~~ .'..,C. Iii, F'. Ayor, 1. Tt~.rsl1~tll :~11d TI.1. Stc:nronson., Pl13rs .li.ev. Lotters l? ... , 9 (1964).

.H.ov. J3=2., 1263 (1964).

PS/5133/mhg

.

11 CERN/TC/PHYSICS 65-25

TABLE_)_

Exporiraonto.l o.ngul:::cr distribution of K+p olnstic sco.ttoring D.t

2.97 GeV/c.

In column 2, -t represents tho vnluo of tho momentum tr[msfor

squc,red o:t tho middle of tho cos Q intervo.l. Tho nunbers of events

o.re given for aip nne::les r.-:mging· from 0 to so0 • Tho nunbers corres-

ponc1il1f,' to tl10 first cos G interval have been obtained after o.

correction wo.s no.do for loss of events with lgre;e dip vnluos (s'ee text).

No mention 11'.::Cs been Lmde of cos G intervnls in which no event was

recorded.

"'_,,___...,__-= ~~.-.~----- --- -=--·--- - . --~--

G (Momentum \f b f Number of di~! (mb/(GoV/c) 2 )

cos _._ f )2 rum or o · Gvents . vrans or intervccl (GeV/c)2 events corrected

-t --~--~ .. -.,.-~-""-"~' ·-

0.98 - • 95 o.oso 383 718 14.65 ± 1.51 0. 95 - • 90 0.171 391 440 8.98 ± 0.91

• 90 - .85 0.287 261 294 6.00 ± o.65 .85 - .80 0.401 155 174 3.55 ± 0.43 .BO - .75 0.516 101 114 2.32 ± 0.31 .75 - .70 o.630 63 71 1.45 ± 0.23 .70 - .65 0.745 56 63 1.29 ± 0.21 • 65 - .60 0.860 27 30.4 0.62 ± 0.13 .60 - .55 o. 974 21 23.G 0.48 ± 0.12 .55 - .50 l.OBS 8 9.0 } .50 - .45 1.203 9 10.1 0.19 ± 0.04 .45 - .40 1.318 7 7.9 .40 - .35 1.433 6 6.8

} .35 - .30 1.547 4 4.5 .30 - .25 1.657 l 1.1 0.04 ± 0.01 .25 - .20 1. 772 2 2.3 .20 - .15 1.886 1 1.1 .15 - .10 2.000 1 1.1

o.o - -0.05 2.343 1 1.1 1-.

-0.05 - -0.10 2.457 2 2.3 -0.10 - -0.15 2.572 2 2.3 -0.20 - -0.25 2.800 3 3.4 0.01 ± 0.01 -0.30 - -0.35 3.029 1 1.1 >-

-0.50 - -0.55 3.486 l 1.1 -0.75 - -o.so 4.058 l 1.1 -0 • 90 - -0 • 95 4.401 1 1.1

~

-0. 9'.'i - -1.00 4.515 I

PS/5133/mbg

Sc1,II

p '.l' t: cct

e

----"'·" .. ,, __ ,. ......... ~ ~-"' - ,._ ... ~ ~ ----· .. "-·=. - ~ •·f< ~-"' ,._ ....... __ _.. --~ ..,_ __ ..__ ........ -~-·"k--~--..___.._ _ _,.__...._._ __ .,_~-----"'-·"'----'-_.._·"'--"'i""-~ ... -. ...._ ..... _ ............. ,._.....____ i · J>r.~,ib. I~~::J,~= "" ·1u, fl ix( v/c)-~ v/ (fr,2:·;\·.,

1,...~lJ..;__),.... .l. ~- _, J .X ; ~ ........ ....._ ;>." ..... &- ~ ~ ..... R ,._ .W.- .... ~ >- ~ .... $ '>< ,,._ ~ .... __,.-"'. "< -""-""- .. ~ .,._, ,.....__...__,.,__,,.__......_.__,.. .... ~ ,,.,__.,._,.,__,_ ...... _,,...,_""-'•"- "··---"---~ .. ~-

( '_,,Q, 1 (' ':'7 ·:1 + (' -; -ir~'"'"" ± 1 i-" L. • ..._1. :,_ ..... _1_. .J _,) • ,_; - -'- ( • ) _._. { \.j •

i 1 -'~ .. '~.,~S + C.17 ..

·-··· -·-··· -·~· .-~-· •.•.. -· .•••..••..•••.•..•• · .•• L

cos g

SoJ.. I G.98 - 0.20

Sol. II (). c:~: - 0.50 _;~.,.

PS/5133/rnhg

13

-t

O.U46-1.L:29 4.64 +

CJ.04G-1.143 /~. 55 +

0.25

0.3S

(i':C"[Y':/r'"1C'/1P}fVSI"CS u ..... JJ_lJ_·; l -......1.. 65-25

? at + ~t~

e

2

(c)

4

F'~L.. 5

6

~ -. ..., ,-r-1

.L ---• ~=>

I ,, .

c-~_-,r~:'· ;Ct°'~-;d

::.c

')

«11 ,X'- (~:~~D 'Cl'~~--bt1_

c:. j_ ·_-, c

,_,,, C\)8~.:no

( - - \ -'-.L; '

( '7, '1 ( '·,· \ .-/ j 'j \

.J_ -

GU c.

l ··:c

s 65-25

'. ·cJl<:::

GJ.'.:-~stic

tn 1 distribu~ion h-

t ~-~_-._-.; s c: ~ ) , fer

tic cross-section

' ,:_:_.i1cl -:cLij_[:J ·w or1c) , :Lr:5 , for

PS/5133/mhg

15 CERN/TC/PIWSICS 65-25

and ui th 1 = 3 • Tho curve (b) is tho ; ' 088-C fit using the I!lin2Jni

f OTL1-Uln ti on,

e

A +'1 t "~o 1i.l

Tho cooff~l.cients

+ 2C

anc1

while C was vnriod to

l/2(A +:~1 )t 0 -'-

e +

') ,_. bE:ost fit. C wc;s found to be 0 .4.

p ne trals

o.

25

2

12

100 I 80

c 60 (a) > .. co

40 ... c

0) 20 CD ti...

0 CD

"O 0 a

1 0

! ..... 60 Cl)

Q.

en 40 I .... c CD > 20 (b) CD

~

0

~ 0 ·~ ( ' CD

~~ .c E I :J I z 40 -i

I

20 ( c)

0 0 30 60 90

Dip Angle,)~ (degrees)

+ '

I 6

+I , ;+

l

l + • ! ~

t

l t ' i '

! ~ ' I j

ii!; ~

)

ti

00

(J) (/)