Azimuthal Asymmetry of Black Particles in High-Energy Interactions — Evaporation Model Revisited

Indian J. Phvs. 71A (6), 657-667 (1997)

I J P A

— an international journal

Azimuthal asymmetry of black particles in high-energy interactions—evaporation model revisited

Dipak Ghosh, Sharmila Sarkar, Krishnadas Purkait and Asok Kumar Mallick

High Energy Physics Division, Department of Physics, Jodavpur University.

Calcutta-700 032. India

Received 2 May 1997, accepted 22 August 1997

Abstract : Azimuthal anisotropy of target fragments in C12-Em interactions at 4.5 GeV/c/n and O l6-Em interactions at 60 GeV/c/n is investigated here. The evaporation model fuils to explain the experimental data. The model of local healing is found to describe the data satisfactorily.

Keywords : Azimuthal anisotropy, target fragments, local heating model l'ACS No. : 25.75.-q

1. Introduction

In the cases of relativistic nucleus-nucleus inelastic interactions at high energies a large part of the total cross section is due to multiparticle production. It is also found that the characteristics of disintegration are functions of number of interacting nucleous of the projectile and the target nuclei and therefore, also functions of the mass of the colliding nuclei. After interaction, a spectator piece of the target is formed and if the impact parameter is sufficiently large, a spectator piece of the projectile is also formed f 1-4].

According to Additive Quark model, two incoherent 'wounded' quarks are responsible for particle production phenomena in nucleus-nucleus inelastic interactions at high energies [5], In the Dual-Parton model, exchange of colours is the first step in inelastic hadronic collisions at high energies. In the intermediate state, two chains are formed for every exchange of colours. These chains which fragment into hadrons

7 1 A(6)-6

© 19971ACS

6 5 8 Dipak Ghosh et al

are attached to different objects in the projectile and the tatget nuclei [51. According to evaporation model, black particles are emitted from a system in statistical equilibrium and the distribution of those particles are expected to be isotropic in the angular range |⁶|.

Here, we mention a few deficiencies of evaporation model. Sullivan e t a l |7], in their plastic detector experiment Kullberg and Otterlund [⁸], in their cosmic ray experiment showed deviations from evaporation model. Warwick e t a l -[9] and Gossel e t a l \1 0] also observed deviations from conventional evaporation scenario.

It is also found from the study of the energy spectrum of slow pqriiclcs that the existence of inequilihrium states exist in the system of nucleons insiVie an excited

nucleus |6- l I]. \

Powell ^{e t a l} [121 supposed local heating of the target nucleus. During collisions, some part or the whole of the target nucleus is affected. This affected part of the residual target nucleus is heated due to absorption of a part of the energy ol the projectile. This is known as local heating model (LHM). In the cases of nonccnirul collisions, the residual target nucleus is an assembly of inhomogencouslv heated nucleons which arc in statistical equilibrium. In the cases of central collisions, the degree of homogeneity in heating of the nucleons of the residual target is. significant and hence the statistical equilibrium in the excited residue is also significant. According to LHM, in the cases of noncentral collisions, those black particles which aie near the surface of locally heated region and moving towards the surface ol that icgmn may escape residual target easily, whereas those black particles which arc interior to the residual target after encountering a number of collisions, either can escape residual target or cannot escape residue due to lack of energy. In the cases of central collisions, as the affected region of the target nucleus is increased, the number of black tracks is also increased [^{1 2}].

The recent revival of interest in studying azimuthal asymmetry in detail is connected with the observation of an iniermitlency effect in nucleus-nucleus inelastic interactions at high energies 113].

This paper reports an extensive study of the azimuthal asymmetry of black particles in Cl2-Em and Ol6-Em interactions at incident beam-momenta 4.5 GcV/c/n and 60 GcV/c/n respectively, in the light of LHM (local heating model).

2. Experimental data

The required data is obtained from NIKF1BR2 nuclear research emulsion plates (25 cm x ^{1 0} cm x 600 pm) irradiated horizontally with C^{1 2} or O lft beam from JINR synchrophasotron. Primary inelastic events of Cl2-Em interactions and primary inelastic events of O l6-Em interactions are investigated here. We have classified the secondary particles in b, g, s, particles following the usual nuclear emulsion methodology.

Azimuthal asymmetry of black particles etc _{6 5 9} (i) The emission tracks having a range < 3 mm and ionisation l > 6 / 0 where / 0 is the

plateau of ionisation value of the singly charged particles in the emulsion pellicle, are known as black ( b ) tracks.

(ii) The emission tracks having a range > 3 mm and ionisation l .4^{/ 0} < / < ^{6 / 0} are known as grey (#) tracks.

(iii) The tracks having ionisation / < 1.4/ 0 and very long ranges are known as shower ( s)

tracks. The tracks with emission angle greatei than 3° are considered here to exclude the contamination of projectile associated fast fragments.

Absemetova e t a l [14) showed from the data of the energy of the evaporated slow particles and the degree of excitation of the residual target nucleus that the maximum of the energy of the slow particles in the energy spectrum shifts towards the lower energies with the increase ol the number of black-grey tracks. This phenomenon cannot be explained by cascade evaporative model (CEM).

3. Method of analysis

We have studied here the azimuthal asymmetry of black particles in non-overlapping equal width cos <9 bins and in the entire cos ⁰ range.

If the number ol black tracks and grey tracks in an event be ^{n h} and respectively, then

N, , = n h +

where N lt is the number of heavy ion tracks in the event. The events ate divided into a lew N h intervals which are ( I < N h < 5), ^{( 6} < N h < 10), ( I 1 < N h < 15), (16 < N h < 20). The non-overlapping cos ⁰ bins are ( -^{1 . 0} to -⁰.⁶ ). ( -^{0 . 6} to -⁰ .²). (-^{0 . 2} to ⁰.²). (^{0 . 2} to ⁰ .⁶), (^{0 . 6} to I ⁰ ).

For the events in a ^{N h} interval, azimuthal asymmetry of black particles of the i-th event in the j-lh cos 0 hin is defined as.

where .v(/ = number of black particles of the i-lh event in the ^j-th cos ⁰ bin whose azimuthal angles arc less than 180°.

y lf = number of black particles of the /'-th event in the /'-th cos ⁰ bin whose azimuthal angles arc greater than 180°. For the events of a given N fl interval average azimuthal asymmetry in the_/-th cos ⁰ interval is

_ X

W, = - S - V - 1 = I to AT.

' N *

where ^N* is the total number of events in the ⁷-th cos 0 bin lor a given ^{N h} interval. As the degree of excitation of the target nucleus depends on N , r we have taken N h as a parameter of the event [14],

660 DifHik Ghosh et al

The above formulae are applied for calculating average azimuthal asymmetry for the events of each N h interval in the entire cos# range.

4. Results and discussions

Figures 1(a) to ¹(d) are asymmetry (V^) v's c o s O graphs of ,²C-Em interactions at 4.5 GeV/n/c for different N h intervals. Figures ¹(e)to ¹(g) are asymmetry (W) v s co s0

♦ i.o r w

1 M ,

1 1 1

►

X j

-10 -0-5 03 . |

♦ COSO — ♦

-0 5 ♦

-10^- U)

10

w 6 <Nk<ta t o s

-1.0 -0 5* 05 ♦ '

* COS • - —

♦ -05

-l 0^- (b)

I 0 w

! 0<

1

16 C Nh € 70

♦ 1 ^

♦ -as 0 5 i

♦ COS 0 --- -

-03 -i n^„

( d )

Figure 1. (a) to (d) are plots of W vs cos 0 graphs for l2C -E m interactions al 4 5 GeV/c/n

Figure I. (e) to (g) are plots o f IV vs cos 0 graphs for ,60 -E m mteiactions at 60 GeV/c/n

graphs of l⁶0-Em interactions at 60 GeV/n/c for different ^{N h} intervals. It is seen from the graphs that with the increase of N h% average azimuthal asymmetry decreases lor both ,²C-Em and ,⁶Q-Em interactions. It is also seen from the graphs 1(a) to 1(d) that

Azim uthal asymmetry»o f black particles etc 661

average azimuthal asymmetry of black particles in the cos⁰ bins of forward emission angles (0 < 90°) are much lower than those of in the backward emission angles (6 > 90°).

Figure 2. (a) and (b) are plots of W vs N ^ graphs l2C-Em interactions and ^ - E m interactions at 4 5 GeV/c/n and 60 GeV/c/n respectively

Figures 2(a) and 2(b) are average azimuthal asymmetry v s N h graphs for the entire cos0 range for l²C-Em interactions and ,⁶0-Em interactions at 4.5 GeV/c/n and 60 GeV/c/n respectively. Graphs 2(a) and 2(b) show that average azimuthal asymmetry of black particles decreases with the increase of ^{N h} for both ^{1 2}C-Em and ^{1 6}0-Em interactions. Thus, this analysis shows that the average azimuthal asymmetry of black particles decreases with

GRf Y TRACKS

- I < IQI 0 < I

r

1

f.

^{I f} hr

0 too 200 ^{300 360}

(a)

<P

00073 0 0030 J 0075-

h i a v y t r a c k s - i < C o « e < 1

_ n

i— i— j_

J

IOC 700 —i__300 360

<P

(c)

Figure 3. (a) to (c) are plots of p{0)(for grey, black and heavy tracks respectively) vs 0graphs in the entire cos0 region for ,2C-Em interactions 4.5 GeV/c/n

662 D ip a k G h o s h et a l

(c)

Figure 4. (a) to (c) are plots of normalised p(0) (for grey, black and heavy tracks respectively) vs 0 graphs in the entire cos0 region for ,60-Em interactions at 60 GeV/c/n.

(b ) ♦

Figure 5. (a) to (c) ore plots of normalised p{0) (for grey, black and heavy tracks respectively) vs 0 in the forward emission angles (0 < 90°) region for 12C- Em interactions at 4.5 GeV/c/n

the increase of ^{N h} and the observations speak in favour of local heating model of target nucleus. From graphs 2(a) and 2(b), any significant dependence of average azimuthal asymmetry of the black particles on the incident projectile energy is not found. Our data is also consistent with the results of Absemetova e t a l [14] where similar study was made for proton-nucleus interactions at 67-400 GeV.

Here, we added a few more graphs to substantiate our results. We drew normalised azimuthal angle (⁰) distribution of tracks p(⁰) v s 0 graphs of grey, black and heavy tracks in the entire cos0 region for ,²C-Em interactions [Figures 3(a) to 3(c)] and ,60-Em interactions [Figures 4(a) to 4(c)] at 4.5 GeV/n/c and 60 GeV/n/c respectively.

/"!*>) /*(*■) /»(0I

Azim uthal asymmetry o f black particles etc 663

Figure 6. (a) to (c) ore plots of normalised p{Q) (for grey, black and heavy tracks respectively) vs 0 in the forward emission angles (0 < 90°) region for '^O-Em interactions at 60 GeV/c/n.

Figure 7. (a) to (c) are plots of normalised p ( f ) vs 0 graphs for grey, black and heavy tracks respectively in the backward emission angles (0 > 90°) region for ,2C-Em interactions at 4.5 GeV/c/n.

664 D ip a k G h o s h et a l

040A0 •

Figure 8. (u) to (c) are plots of normalised p(0)vx <p graphs for grey, black and heavy tracks respectively in the backward emission angles (0 > 90°) legion for 1 V)-Em interactions at 60 GeV/c/n

0 0150 16 O.Oioo 2 00050

G R E Y TRACKS - l < C o » 0 < 1

0 1 0 0100 200 300 360 ^(a) *

(a ) <P

(b) ^*

00250

00200

— 0 0150

*±z 00100 0-0050

0 100 200 300 360

(b) $

SL AC K t r a c k s - K C o i K l

U

A j I L ___

Figure 9._ (a) to (c) are plots of normalised N ( 0 ) v s $ (of grey, black and heavy tracks respectively of an event) in the entire cos0 range for

'^C-Em interactions at 4.5 GeV/c/n.

Figure HI. (a) to (c) are plots of normalised N ( $ ) v s 0 (of grey, black and'heavy tracks respectively of an event) in the entire cos 9 range for 160-Em interactions at 60 GeV/c/n.

Azimuthal asymmetry o f black

particles

' ± 2

0 0150 00 (0 0 0 0030

(a) 00150

El

00,00

(b)

o i c v t i a c h C « » 0 > 0

200

0

BLACK TRACKS C * » i > 0

100 200 200 500 540 0

00130-

500 140 0 0100- Z 0 0030-

(c)

HEAVY TRACKS Co iO > 0

y " v ti/k

Figure 11. (a) to (c) are plots of normalised /V(0) w 0 (of grey, black and heavy tracks respectively of an event) in the forward emission angles (0 < 90°) region for ,2C-Em interactions at 4.5 GeV/c/n

Z

oooso-

GREY TRACKS Cp i0 > 0

5

=

c—1-------*

k

fa)

(b)

z

100 200

*

0 0130'

00 1 0 0

z 0 0050 -

GREY TRACKS Co iB < 0

500 540 100 200 200 500 540

0 (a)

0 0140-f ooioo-j

Z 0 003 0-

•i a c k t r a c k s Co»4 < 0

A

$

200

0

(b)

Figure 12. (a) to (c) are plots of normalised N( 0 ) vs 0 Figure 13. (a) to (c) are plots of normalised 0 ) vs 0 (of grey, black and heavy tracks respectively of an (of grey, black and heavy tracks respectively of an event) in the forward emission angles (O c 90°) region event) in the backward emission angles (0 > 90°) region for ,60-Em interactions at 60 GeV/n/c. for t2C-Em interactions at 4.5 GeV/c/n.

71 ATM-7

666 Dipak Ghosh et al

We drew similar plot of p(0) v s 0 graphs of gre>, black and heavy tracks for

0 < 90° (forward emission angles) region [Figures 5(a) to 5(c) for ,²C-Em interactions at 4.5 GeV/n/c; Figures ⁶(a) to ⁶(c) for ,⁶0-Em interactions at 60 GeV/n/c] and for 6 > 90° (backward emission angles) region [Figures 7(a) to 7(c) for ,2C-Em interactions at 4.5 GeV/n/c; Figures 8(a) to 8(c) for l60-Em interactions at 60 GeV/n/cJ.

Then we drew normalised 0 (averaged over all tracks of the event) distribution

N( <p ) of event for grey, black and heavy tracks of the event v s 0 [Figures 9(a) to 9(c) for ,²C-Em interactions at 4.5 GcV/n/c; Figures 10(a) to 10(c) for ,⁶0-fem interactions at 60 GeV/n/c] in the entire cos#region.

1^ 0 0 1 0 0-

(a)

00200

0 0150-

— ^{00 1 0 0} z

0 0050

(b)

GREY T R A C K S C o » 0 < T O

/ V ^ - N - ^ r ^ P - n n r

0 0200 -

) 100 ? 0 0

$

3 0 0 3 6 0 — 0 0150-

z o oioo -

B L A C K T R A C K S

0 0050-

C o i 0 < 0

0

( c )

1 0 0 200

*

3 0 0 3 6 0

h e a v y t r a c e s Co i0 < 0

100 200

*

3 0 0 3 6 0

F igu re 14. (a) to (c) are plots of normalised N{ 0) v s 0 (of grey, black and heavy tracks respectively of an event) in the backward emission angles (0 > 90°) legion for *60-H m interactions at 60 GeV/n/c,

Then wc plotted N ( Q ) vs 0 graphs for grey, black and heavy tracks of event for forward emission angles ( 0 < 90°)' [Figures 1 1(a) to 11(c) for ,2C-Em interactions al 4.5 GeV/n/c; Figures 12(a) to 12(c) for ,60-Em interactions at 60 GeV/n/c| and for backward emission angles ⁶ > 90° [Figures 13(a) to 13(c) for ^{1 2}C-Em interactions at 4.5 GeV/n/c; Figures 14(a) to 14(c) for l60-Em interactions at 60 GeV/n/c] regions.

Acknowledgments

We are grateful to Prof. K D Tolstov of JINR, Dubna, Russia and Prof. P L Jain (SUNY, New York) for supplying us exposed plates for measurements. Authors are grateful to the University Grants Commission for its financial help under COSIST program. Authors acknowledge the contribution of Dr. Tapas Kumar Ballabh, Department of Physics, Jadavpur University, Calcutta in computation. S Sarkar acknowledges the receipt of a

A z im u t h a l a sym m etry o f b la c k p a rticle s etc 667

Senior Research Associateship awarded by the Council of Scientific and Industrial Research, Government of India, during the tenure of this work.

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