Study of forward-backward multiplicity correlations in collisions
of 4.1A GeVOc
22Ne and 4.5A GeVOc
28Si with emulsion
A. EL-NAGHY(1), N. M. SADEK(1) and M. MOHERY(2)
(1) Physics Department, Faculty of Science, Cairo University - Giza, Egypt
(2) Physics Department, Faculty of Science, South Valley University - Sohag, Egypt (ricevuto l’8 Luglio 1996; revisionato il 14 Novembre 1996; approvato il 27 Gennaio 1997)
Summary. — The correlations between the multiplicities of secondary charged
particles emitted in collisions of 4.1A GeVOc22Ne and 4.5A GeVOc28Si with emulsion
have been studied. The correlation coefficients are calculated. The dependence of the correlation strength on the mass number of the projectile has been analyzed. Moreover, the dependence of the average multiplicities of shower particles emitted in the forward and backward hemispheres on the number of target fragments has been investigated.
PACS 29.40.Rg – Nuclear emulsions.
PACS 25.70 – Low and intermediate energy heavy-ion reactions.
1. – Introduction
The target nucleus, being an extended object, gives a unique opportunity for studying the space-time development of the multiparticle production process. It is useful to analyze the features of the correlations between multiplicities of the shower particles emitted in the forward and backward hemispheres. During the last decades, the production of particles, emitted in the backward direction, in (e1-e2) and hadron-hadron (h-h) collisions over a wide range of centre of mass (c.m.s.) energy has been studied [1-3]. The experimental data have been analyzed within the frame of cluster model [4] and a reasonable agreement has been obtained if the final-state particles are assumed to be created by the decay of clusters with a mean cluster size which is energy dependent. The forward-backward multiplicity correlations in (p2-p, K1-p) and p-p collisions at 250 GeVOc have been studied [5] and the correlation parameter was found to be positive for h-h collisions at c.m.s. energy C5 GeV, while this happens for e1e2starting from c.m.s. energy 30 GeV. The study of the emission of produced particles in the backward hemisphere in case of hadron-nucleus (h-A) and nucleus-nucleus (A-A) interactions became the subject of considerable interest. This interest may be attributed to the fact that the backward emission of particles in high-energy hadron-nucleon (h-N) collisions is kinematically restricted. The backward 125
emission of protons and pions has been investigated in: 1 GeV p-nucleus [6], 4.5 GeVOc p-nucleus [7] 15–65 GeVOc p-nucleus [8], 4-300 GeV p-nucleus [9], 400 GeV p-nucleus [10], 5 GeVOc p2-C [11], 40 GeVOc p2-C [12], 250 GeVOc p1 and K1-nucleus [13], 4.2A GeVOc 2H and 12
C-Ta [14], 4.5A GeVOc 12
C-emulsion(Em) [7, 15, 16], 4.5 GeVOc 28Si-Em [17], 4.1A GeV22
Ne-Em and 4.5A GeVOc 28Si-Em [18, 19], 14.6 and 200A GeV 16O-Em [20], 200A GeV 32
S-Em [20] and 11.7A GeVOc Au-Au [21] interactions. The backward proton production was attributed to the absorption of secondary pions by a nucleon pair in the target nucleus. The dependence of secondary pions absorption on the target mass number, AT, was fitted by a power law (constant ATa) with the exponent a 40.2760.05.
The pions emitted in the backward hemisphere were shown to be consistent with the cumulative effect [22]. Although a correlation between the multiplicities in the forward and backward hemispheres has been obtained in the experiments of h-h and h-A, there is still a lack of experimental investigations in A-A collision. The present paper deals with the correlations between the multiplicities of the backward emitted particles (u D907) and those emitted in the forward hemisphere (uG907) in the laboratory system, for the interactions of 4.1 and 4.5A GeVOc 22Ne and 28Si with emulsion, respectively. The correlation coefficients are calculated. The dependence of the correlation strength on the mass number of the projectile, Ap, has been analyzed. Moreover, the dependence of the average multiplicities of shower particles emitted in the forward and backward hemispheres on the number of target fragments has been investigated.
2. – Experimental techniques
Nuclear emulsions of the type Br-2 were exposed to 4.1A GeVOc 22Ne and 4.5A GeVOc28Si beams at the Dubna Synchrophasotron. The pellicles of emulsion have the dimensions of 20 cm 310 cm3600 mm (undeveloped emulsion). The intensity of the beam was B104
particlesOcm2 and the beam diameter was approximately 1 cm. Along the track, a double scanning has been carried out fast in the forward direction and slow in the backward one.
The scanned beam tracks have been further examined by measuring the delta-electron density [23] on each of them to exclude any track having a charge less than the beam particle charge. The scanning has been perfomed using Leitz-Laborlux-S microscope. The numbers of the picked up inelastic interactions of 22Ne-Em and28Si-Em are 2000 and 1322, respectively.
In the measured interactions all the charged secondary particles have been classified according to the range L in the emulsion and the relative ionization I * 4IOI0, where I is the particle track ionization and I0 is the ionization of a relativistic shower track in the narrow forward cone of an opening angle u G37, into the following groups [24]:
1) Shower tracks producing “s-particles” having a relative ionization I * G1.4. Such tracks, having an emission angle u G37, have been further subjected to multiple scattering measurements for momentum determination [25] in order to separate the produced pions from the singly charged projectile fragments.
2) Grey tracks producing “g-particles” having a relative ionization I * D1.4 and
TABLEI. – Classification of particles according to their kinetic energies in MeV.
Particle Shower track
particle Grey track particle Black track particle p K 1H F 60 F 212 F 400 12 EKEE60 20 EKEE212 26 EKEE400 G 12 G 20 G 26
3) Black tracks producing “b-particles” having L E3 mm. The classification of these particles according to their kinetic energies (KE) is given in table I.
4) The “b” and “g” tracks are both called heavily ionizing tracks producing “h-particles”.
5) The determination of the momentum of the s-particles emitted within u G37 enables the separation of the produced pions from the non-interacting singly-charged projectile fragments (protons, deuterons and tritons) [26]. The g-particles emitted within u G37 and having LD2 cm are considered as projectile fragments having Z42. The b-particles having u G37 and LD1 cm are due to heavy-projectile fragments
Z F3. The number of delta-electrons has been measured for each of these particles in
order to determine the corresponding charge Z 43, R , Zb, where Zbis the charge of the beam nucleus.
Thus, all the particles have been adequately divided into: projectile fragments with
Z varying from 1 to Zb, target fragments, i.e. h-particles, and the generated shower particles. The polar angle u of each track, i.e. the space angle between the direction of the beam and that of the given track, has been measured. The azimuthal angle f of each track, i.e. the angle between the projection of the given track in the plane normal to the beam (the azimuthal plane) and the direction perpendicular to the beam in this plane (in anticlockwise direction), has been measured.
3. – Results and discussions
The picked-up 2000 and 1322 inelastic interactions of 22Ne-Em and 28Si-Em, respectively, have been analyzed. Table II presents the overall average multiplicities of shower particles emitted in the forward, ansFb, and the backward, ansBb, hemispheres for 4.1A GeVOc 22
Ne-Em and 4.5A GeVOc 28Si-Em interactions compared with the corresponding values in ref. [18]. This comparison shows agreement between the two results. Table II shows that ansFb increases with the projectile mass number, Ap, while ansBb is approximately constant. All errors, from here on, are statistical ones. In order to study the correlation between nsFand nsB, the correlation coefficient R between them has been determined from
R 4 a(ns F 2 ansFb)(nsB2 ansBb)b [a(nsF2 ansFb)2ba(nsB2 ansBb)2b]1 O2 . (1)
The dependences of ansFb on nsBand ansBb on nsFare fitted by the relations ansF(nsB)b 4aF1 bFnsB,
TABLE II. – The values of ansFb and ansBb for 4.1A GeVOc 22Ne-Em and 4.5A GeVOc 28Si-Em interactions. Interaction anF s b ansBb Ref. 22Ne-Em 9.71 6 0.23 9.85 6 0.04 0.40 6 0.02 0.45 6 0.01 present data [18] 28Si-Em 11.43 6 0.35 11.36 6 0.09 0.35 6 0.02 0.44 6 0.02 present data [18] ansB(nsF)b 4aB1 bBnsF, (3)
where ansF(nsB)b and ansB(nsF)b are the average multiplicities of shower particles emitted in the forward and backward hemispheres at certain values of nsB and nsF, respectively. The slopes bF and bB give measures of the correlation strengths. The correlation strengths can be also defined as
rF4 a(nsF2 ansFb)(nsB2 ansBb)b a(nsB2 ansBb)2b , (4) rB4 a(nsF2 ansFb)(nsB2 ansBb)b a(nsF2 ansFb)2b . (5)
From eqs. (1), (4) and (5) we get
R24 rFQ rB. (6)
If the projectile and target nuclei are the same, then
rF4 rB, (7)
when the dependences of ansF(nsB)b on nsBand ansB(nsF)b on nsFagree well with straight line relations, we may get
rF4 bF and rB4 bB. (8)
Figure 1 presents the relations between ansF(nsB)b and nsB for both 22Ne-Em and 28
Si-Em interactions at 4.1 and 4.5A GeVOc, respectively. The fitting of the experimental data with eq. (2) gives the values of the slopes, bF4 6.426 6 0.181 for 22Ne-Em and b
F4 8.138 6 0.408 for 28Si-Em. Our value of bF for 28Si agrees with the corresponding value in ref. [17] (bF4 7.681 6 0.701). Figure 2 shows the ansB(nsF)b as a function of nsF for 4.1A GeVOc 22Ne-Em and 4.5A GeVOc 28Si-Em interactions. The points with error bars are fitted by eq. (3) and consequently the values of the slope are found to be bB4 0.029 6 0.002 for 22Ne-Em, bB4 0.017 6 0.002 for 28Si-Em and the corresponding value for28Si-Em in ref. [17] is b
B4 0.041 6 0.003. The value of bBfor28Si does not agree with that in ref. [17] which may be due to different experimental conditions. Since the value of ansFb is proportional to the number of interacting projectile nucleons, one can see from fig. 2b) of ref. [18] that the value of bB for 4.1A GeVOc 22
Fig. 1. – The value of ansF(nsB)b as a function of nsB for 4.1A GeVOc22Ne-Em and 4.5A GeVOc 28Si-Em interactions.
interaction. The present data and those of ref. [18] show that the slope parameter bB slightly increases with the decrease of the mass number of the projectile.
Comparing the data of22Ne-Em with that of 28Si-Em, it is observed that the slope parameter bFfor the former is less than that for the latter. The values of R , rF, rB, bF and bB for 4.1A GeVOc 22Ne-Em and 4.5A GeVOc 28Si-Em interactions are listed in table III. From the analysis of figs. 1, 2, tables II and III, it may be noticed that ansFb increases with the projectile mass number, Ap, while ansBb remains nearly constant, within the experimental errors. This is due to the fact that the average number of all shower particles depends on the number of the interacting nucleons from the projectile. Since the shower particles are very fast (of large Lorentz factor), they are emitted mainly in the forward direction in the laboratory system. The value of the correlation coefficient R for22Ne approximately equals the corresponding value for28Si. This result contradicts the conclusion, drawn in ref. [20], which implies that the value of
Fig. 2. – The value of ansB(nsF)b as a function of nsF for 4.1A GeVOc22Ne-Em and 4.5A GeVOc 28Si-Em interactions.
R increases with Ap. From the analysis of our data, the correlation parameters bF and
rF significantly increase with Ap, whereas bB and rB slightly decrease with the projectile mass number (see table III).
The dependences of ansFb and ansBb on the number of target fragments, nh, for 22Ne-Em and 28Si-Em interactions are shown in figs. 3 and 4, respectively. It is seen
TABLEIII. – The values of the correlation parameters for 4.1A GeVOc22Ne-Em and 4.5A GeVOc
28Si-Em interactions. Interaction R rF rB bF bB 22Ne-Em 28Si-Em 0.987 0.988 24.332 32.573 0.041 0.031 6.426 6 0.181 8.138 6 0.408 0.029 6 0.002 0.017 6 0.002
Fig. 3. – The dependence of ansFb on nh for 4.1A GeVOc 22Ne-Em and 4.5A GeVOc 28Si-Em
interactions.
that the values of ansFb and ansBb increase linearly with nh up to nhC 30 and become approximately constant, within experimental errors, for nhD 30. The comparison of our data with those of refs. [17, 18], shows that the observed constancy of ansFb and ansBb was not seen there. This may be due to the fact that in ref. [17] the data points at
nhF 30 were averaged over a wide range of nh, whereas in ref. [18] the data points above nh4 35 were not considered. If the present data were treated in such ways, the relations of ansFb and ansFb with nh would be straight lines and the effect would be smeared out. However, to reveal this contradiction, the statistics should be increased to enable one to get more significant results.
4. – Conclusions
Studying the 4.1A GeVOc22Ne-Em and 4.5A GeVOc28Si-Em interactions and comparing with the corresponding data in refs. [17, 18] the following conclusions can be drawn:
Fig. 4. – The dependence of ansBb on nh for 4.1A GeVOc 22Ne-Em and 4.5A GeVOc 28Si-Em
interactions.
1) The overall average multiplicity of shower particles emitted in the backward hemisphere remains nearly constant, within the experimental errors, for projectiles of mass numbers larger than or equal to 12.
2) The correlation parameters for the shower particles emitted in the forward hemisphere increase with the projectile mass number, whereas for the backward emission they decrease slightly as the projectile mass number increases.
3) The average values of shower particles emitted in the forward and backward hemispheres increase linearly with the number of the target fragments up to a certain limit at which they seem to attain a nearly constant value.
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