PHYSICAL REVIEW C VOLUME 32, NUMBER 4 OCTOBER 1985

Inclusive angular distribution of ot and Li fragments producedin Fe-C and Fe-Pb collisions at 1.88 GeVlnucleon

C. O. Kim and S. N. KimDepartment of Physics, Korea University, Seoul 132, Korea

I. K. Chae and D. H. KimDepartment of Physics, Sookmyung Women's University, Seoul 140, Korea

(Received 10 April 1985)

From the measurements of laboratory system emission angles 8 of 2188 n and 298 Li fragments, pro-duced inclusively by relativistic Fe-C and Fe-Pb collisions, a target-independent differential frequency for-

mula, dlV= exp(a+ b cots) d(cot8), is obtained with the constant b =——0026 at 1.88 Gev/nucleon, which

seems also to be independent on the kinds of projectile fragments. The significance of this approximateformula is discussed in relation mainly with Kaplon's formula.

P

rI~

FeBeam

P.

Target( d mm Pb, C )

FeBeam

BackgroundMonitor Pellicle

Emulsion Stack2 x lO x0.04 (cm)

& loO Sheets

l5 crn

FIG. 1. Experimental setup at LBL Bevalac.

When nuclear interactions produced by high-energy ha-drons in nuclear emulsion ("stars") are observed in the la-boratory system (LS), heavy fragments of low velocity areeasily distinguished from relativistic shower particles.Nevertheless, the identification of these very slow frag-ments is difficult, mainly because of their high ionizationand short track lengths. Now, by virtue of the recentdevelopment of the technique of accelerating relativisticheavy ions, the "heavy fragments" in the projectile rest sys-tem (ALS; antilaboratory system) can be observed as "rela-tivistic particles" in the LS. Especially, the relativistic o. andLi fragments are easily indentified in nuclear emulsion, justby simple inspection through an optical microscope, sincethe former have about four times the grain density ofminimum-ionizing tracks, and the latter about nine times.The present paper reports the experimental result using thistechnique of identification, and compares our result withsome recent angular measurements of n fragments

The specific arrangements of the experiment to the Fe-ion beam at the Lawrence Berkeley Laboratory (LBL) Bev-alac are illustrated in Fig. 1. From the left, Fe ions were in-cident on the 3-mm thick target, either of carbon or lead.The detectors of fragments and incident Fe ions were nu-clear emulsion stacks (made of 100 Fuji ET7B pelhcles ofsheet size 2&&10X0.04 cm3), and were either placed just

behind the target plate (5 stacks) or 15 cm away from theback of the target plate (L stacks) in the downstream. Al-together, eight stacks (4 S stacks and 4 L stacks) were ex-posed primarily in order to confirm or reject theanomalous-particle-fragment (sometimes called "anoma-lon") effect. 6

The shorter edges of pellicles were exposed horizontallyto the Fe-ion beam with a track density of about 5X10'ions/cm'. Our experiment differs from previous experi-ments' mainly in several aspects: First, the target for theincident Fe ions was either pure substance of carbon orlead. Secondly, by adopting the method of "relative scatter-ing measurements" or of our reference-track method' in or-der to avoid the effect due to the distortion inherent in theprocessed nuclear emulsion, we have tried to improve theaccuracy of measuring LS emission angles 8 always in reference to nearby Fe beam tracks. Measured at —1 mmdownstream from the entrance edge of pellicles, where an-gular measurements of the fragments were usually per-formed with special care not to miss such o. and Li frag-ments as were produced with large 8, the present version ofthe reference-track method gave the angular deviations ofthe incident Fe beam tracks as 2.3+0.3 and 3.7+0.3 mil-liradians, respectively, for the detectors behind the carbonand lead targets. Semiautomatic systems of three-coordinatedigitalized Nikon OPTIPHOT 66 microscopes were em-ployed for our measurements with, at least, 1-p,m readoutaccuracy, whose precision in angular measurements exceed-ed the defining angular deviations of the incident Fe beamtracks by far.

Our results closely resemble those of Refs. 1-5, when theangular distributions (and the projection angle distributionsas well) of a fragments are plotted against 6l as shownseparately for Fe-C collisions (with vacant circles) and forFe-Pb collisions (with filled circles) in Fig. 2. The two plotseach of 5 stacks and I. stacks are indicated in the above andthe third plot underneath is that of the combined data.There seems to be a tendency of more population of o. frag-ments of 0& 10 for Fe-C collisions than for Fe-Pb col-lisions, and the same holds for those of 9& 1 . To showthis effect vividly, the data of 0'& 8& 3' and those of8 & 5' are fitted, respectively, with the Gaussian and the ex-ponential regression functions whose results are also indicat-ed as the curves and equations in Fig. 2.8

32 1454 1985 The American Physical Society

32 INCLUSIVE ANGULAR DISTRIBUTION OF n AND Li. . . 145S

(f)LLI

EXP((

005'— L

—0

~EXP((-0.7+ O.l) 8 + (1.6~0.3)8+(5.I~0.2))EXP((-0.6+O.l}8 +(1.6+0.3)8+(2.9 0.2) j

—STACKS

OJ

)0V)bJ

CL

Q

~ lOOLQ

z.'

I:EXP((-0.12

EXP [(-0.2

1 I / IL

I I I I[

I I I I1

1 0 l I1

I

S —STACKS O C TARGETIOO- Pb TARGET

EXP((—0.6+O.l) 8 + (!.4~0.4)8+(2.6+ 0.2))EXP{(-0.6 ~0.I) 8~+ (2.2+0.4)8+(2.u O.a))

~ ~

~

~

~

~ ~

~

(( 05)8+(25~0 5II

I I I I I I I I I I I I I I I I

I I m I I I I

1000—

LLI

100

O

10

CARBON TARGET

He

Li10 =

+I T+ Z

I I I I I I

IO

j-+-

20

HHMH

I I I I I I l~

100 200 300coT 9

1000— TT. T. &z. I '

loo

O

10=

I I I I I I I I I I I I I I I

I I I I

LEAD TARGET

-II— —Il-

t. . . , I

5 10 l5 20EMISSION ANGLES e OF ct IN DEGREES

IO

l t I I I

E

+a 4E ~

200

I I I I I

to 20

I I I I

FIG. 2. The differential frequency of cx fragments vs 8 in de-

grees.

We find it most reasonable and revealing to plot the dif-ferential frequency dN vs d(cot8) as shown in Fig. 3(a) forFe-C collisions and 3(b) for Fe-Pb collisions. In the figuresthe filled circles represent the angular data from 2188 afragments, and the vacant squares those from 218 Li frag-ments. Since no statistically significant differences betweenthe angular data of S stacks and those of L stacks weredetected, only the combined data are shown in the figures.For the least squares fits, we used the regression function,

dW = exp(a + b cot8) d (cot8),

with reasonable fits to most of the angular data, as seenfrom the best fitted values of a and b separately for Fe-Cand Fe Pb collisions in Table I. For the interval ofcot8=0-20, the amplified versions of dW vs d(cot8) withone-tenth the interval in the main figures are shown as theinserts, respectively. The straight lines in the figures andthe dotted lines in the inserts show the best fitted curves.Actually, sharp falloffs of dN for cot& & 4 can be seen in theinserts and some detailed but target-independent structuresseem to be common. But those portions of n and Li frag-ments, with extremely smail and large 0, which deviate ap-preciably from the general trends represented by Eq. (1)

constitute several percents.Our immediate concern about Eq. (1) is related closely

with Kaplon's formula, ~

( (82) )1l2Pgp

with (= 0.056, where 8 is in radians and up~ in GeV. Theabove equation has been a convenient tool for estimatingthe unknown primary energy of cosmic-ray primaries. '0 Byuse of our angular data of 8» 5', " the values of ((8') )'have been calculated and listed in Table I. Thus, atup~ = 1.88 GeV, the calibrated values of g are 0.057 (0.056)and 0.067 (0.062) for the a (Li) fragments, respectively, forFe-C and Fe-Pb collisions; our experiment generally con-firms Kaplon's formula, Eq. (2), with g

=—0.06.On the other hand, through integration of Eq. (1) with

the use of the variable cot8, we come to the median-angleformula

(cot8) q~2——1n2/[b [, (3)

which, with the plausible assumption of ((8 ) )'~

COT e

FIG. 3. The differential frequency vs cot8, (a) for Fe-C collisionsand (b) for Fe-Pb collisions.

1456 C. O. KIM, S. N. KIM, I. K. CHAE, AND D. H. KIM

TABLE I. Some relevant data for o. fragments (and for Li fragments inside the brackets) and the best fit-ted values to Eq. (1).

Target

Number of n fragments= number from S stacks+ number from L stacks J(e') ' x'/DI

Carbon 1103= 408+ 695

(138= 35+ 103)

0.037 + 0.002

(0.032 + 0.002)

6.3 + 0.05

(4.4 + 0.1)

—0.0248 + 0.0009

( —0.029 + 0.003)

219

(—,)

Lead 1085 = 408 + 677

(160=62+98}0.038 + 0.001

(0.035+ 0.001)

6.3+ 0.04

(4.4+ 0.1)

—0.0265 + 0.0009

( —0.030 + 0.003)

2710

(—, )

'The averages are taken only for the data of 0(5' (Ref. 11}.

=cot '[(c ot t)i/t]2gives us the values of g as 0.063 (0.074)and 0.067 (0.075), for the n (Li) fragments, respectively,for Fe-C and Fe-Pb collisions, i.e., from the use of thevalues of Ibl listed in Table I. This confirms the Kaplon'sformula again.

This kind of excellent accord cannot be accidental. Fromthe Lorentz transformation of cotH from the LS to the(double-barred) kinematic quantities of the ALS, we obtainthe relation

PL yp(PL + ppF')PT pT

MFypy (p cos8+ pp )

MFy p sin8(4)

cot8 =yppp/pr (4')

Thus, Eq. (1) suggests the following approximate differentialfrequency formula of the ALS transverse velocity,

pr = p sin0:

dW = (~/b) exp(a + ~/pr)d(1/pr),

which suggests a Lorentz-invariant constant ~, as

K = ypppb, (6)

since we believe in the limiting fragmentation shown by theexperiments of Ref. 12. [Actually, the validity of Eq. (6)

where yp [= (1 —pp~) 'i2, and uyp is the primary energyper nucleon] is the Lorentz factor of the transformation and

p[ = (y —1)'i2/y] and I) are the velocity and emission an-gle (measured with respect to the direction of the incident

primary) of a fragment of the mass Mp in the ALS. Since ycancels out and pt =pcos8= 0, " we obt—ain an importantrelation,

needs only the invariant character of the differential distri-

bution concerning the ALS transverse velocity pr, which

may come from small and constant pT and from the uncer-tainty relation only. ) Moreover, in case future experimentswith much higher values of y~ than that of the present ex-periment and those with different kinds of projectile frag-ments confirm the universality of rc, besides the limitingfragmentation, an improved method over Kaplon's formulaof energy (actually momentum) estimation of cosmic rayswill be offered through the use of Eq. (6).

Thus, through the good agreement in the general trendsand the values of b =——0.026 in Eq. (1) both for Fe-C andFe-Pb collisions, we are led to the conclusion of "limitingfragmentation" in the sense' that neither the inclusive an-gular distributions of n and Li fragments have anything todo with the kinds of the target nucleus for the majority of o.and Li fragments, as shown in Fig. 3 and in Table I, norwith the primary energy of relativistic incident heavy ions.

On the other hand, it is remarked here that the emissionof o. and Li fragments of 0» 5' seems to be the products of"sequential breakup, " which takes place far away from theCoulomb field of the target nucleus, considering the factthat the substantial increase of large-angle scattering fromthe Fe-Pb collisions over the Fe-C collisions is not detectedfrom our experiment. '

Professor M. Miyagaki of the College of Liberal Arts, andMr. C. Yokoyama and the staff of the emulsion processingteam of High Energy Physics Laboratory, Department ofPhysics, Faculty of Sciences, Kobe University, Kobe, Japanare deeply appreciated for their preparation and fine pro-cessing of the pellicles. The present research is partly sup-ported by the Korea Science and Engineering Foundation.

H. H. Heckman et al. , Phys. Rev. C 17, 1735 (1978).2J. V. Lepore and R. J. Ridell, Jr. , Lawrence Berkeley Laboratory

Report No. LBL-3086, 1974 (unpublished).K. B. Bhalla et al. , Nucl. Phys. A367, 446 (1981).

4M. M. Aggarwal et al. , Phys. Rev. C 27, 640 (1983).5G. M. Chernov et al. , Nucl. Phys. A412, 534 (1984).K. P. Hong, Ph. D. thesis, Korea University, 1984.

7C. O. Kim, Phys, Rev. D 31, 513 (1985).X of the Gaussian fits range from 90 to 300 for the degree of free-

dom (DF) of 9, but the X /DF of the exponential fits are from 1to 2.

M. F. Kaplon, B. Peters, H. L. Reynolds. and D. M. Ritson, Phys.Rev. 85, 295 (1952).

' H. Aizu et al. , Prog. Theor. Phys. 16, 54 (1961); C, O. Kim, Phys.Rev. 158, 1261 (1967); S. Y. Bahk, K. A. Choi, and C. O. Kim,New Phys. (Seoul) 18, 109 (1978).

11%hen the whole data, inclusive of those of 8) 5 are taken, ('sare 0.269 (0.306) and 0.190 (0.239) for 0. (Li) fragments, respec-tively, for Fe-C and Fe-Pb collisions. Reference 9 recommendedthe restriction of 8 & 5'.

2D. E. Greiner et al. , Phys. Rev. Lett. 35, 152 (1975). In thiswork, it has been found that (pL) = —0.03 ——0.04 GeV/c bothfor o. and Li fragments in the collisions of C-ion collisions withvarious target nuclei at 1.05 and 2.1 GeV/nucleon, anda.

~=—0.13—0.16 GeV/c, i,e., P cos0=—0.035 && P~ =—1.

PL1 M. J. Murphy et al. , Phys. Rev. Lett. 53, 1543 (1984).