Characteristics of compound multiplicity in ⁸⁴Kr₃₆ with various light and heavy targets at 1 GeV per nucleon

Abstract

Interactions of ⁸⁴Kr₃₆ having kinetic energy around 1 GeV per nucleon with NIKFI BR-2 nuclear emulsion detector’s target reveal some of the important features of compound multiplicity. Present article shows that width of compound multiplicity distributions and value of mean compound multiplicity have linear relationship with mass number of the projectile colliding system.

1 Introduction

The investigation of final state particles produced through nucleon–nucleus or nucleus–nucleus interactions at high energy is lately becoming an active research area. The nuclear emulsion detector (NED) is one of the oldest detector technology and has been in use from the birth of experimental nuclear and astroparticle physics. The interaction of nucleus (such as ⁸⁴Kr₃₆) with NED’s target at relativistic energy reveals the picture of nucleus–nucleus collisions. Recoil target nucleons are emitted shortly after the passage of leading hadrons. Therefore, it is worth studying the compound multiplicity of recoil target nucleon and freshly produced particles (mainly pions) during interactions as it contains important information about the interaction. The number of target’s recoil nucleon and produced charged particles have been taken together and termed as compound multiplicity. Most of the experiments on high energy collisions have been carried out to investigate characteristics of newly created particles which are mostly pion meson and Kaons (shower; N _s ). The study of characteristic of grey particles (grey; N _g ) produced in such collision has also increased due to the fact that their emission takes place on the time scale of same order (~10⁻²² s) as that of shower particles. Hence, they are expected to keep some memory of the reaction history [1]. Furthermore, grey particle may also be taken as a good measure of the number of encounters made by impinging hadrons inside the struck nucleus [2, 3]. In order to refine the models for multiparticle production in hadron-nucleus and nucleus–nucleus collisions, a new variable termed as compound multiplicity (N _c  = N _g  + N _s ), has been introduced by Jurak and Linscheid [3]. The interesting characteristics of grey and shower particles, taken together per interaction, have been investigated by several workers [2–8]. Relativistic high energy interactions of various heavy ions (projectile) with emulsion have been studied [9–12]. Therefore, it is interesting to study the use of compound multiplicity of grey and shower particles. Present work is mainly devoted to discussion of experimental data of compound multiplicity distribution and their characteristic with respect to other emitting particles in inelastic collision of ⁸⁴Kr₃₆ with the nuclei of NED at ~1 GeV per nucleon.

2 Experimental details

NEDs are composed of silver halide crystals immersed in a gelatin matrix [2, 13–18] consisting mostly of hydrogen, carbon, nitrogen, oxygen, silver and bromine. A small percentage of sulfur and iodine are also present. In present experiment, we have employed a stack of high sensitive NIKFI BR-2 NEDs of dimensions 9.8 × 9.8 × 0.06 cm³, exposed horizontally to ⁸⁴Kr₃₆ ion at kinetic energy of ~1 GeV per nucleon. The exposure has been performed at Gesellschaft für Schwerionenforschung (GSI) Darmstadt, Germany. Interactions have been found by along-the-track scanning technique by using an oil immersion objective of 100× magnification. The beam tracks have been picked up at a distance of 5 mm from the edge of the plate and carefully followed until they either interacted with NED nuclei or escaped from any surface of the emulsion. A total of 700 inelastic events produced in ⁸⁴Kr–emulsion interactions have been located. All charged secondary particles emitted or produced in an interaction are classified in accordance with their ionization, range and velocity, as shown below [13–18].

2.1 Shower tracks (N _s )

These are freshly created charged particles with normalized grain density or ionization g* < 1.4 (g* is the normalized grain density). These particles have relative velocity (β) > 0.7. In case of a proton, kinetic energy (E _p ) should be more than 400 MeV. They are mostly fast pions with a small admixture of Kaons and released protons from the projectile which have undergone an interaction.

2.2 Grey tracks (N _g )

Particles having ionization in the interval 1.4 < g* < 6.0 and range L > 3 mm are defined as grey. This particle has relative velocity (β) in between 0.3 < β < 0.7. They are generally knocked out protons (NED can not detect neutral particle) of targets having kinetic energy in between 30 < E _p  < 400 MeV. They are also admixture of deuterons, tritons and some slow mesons.

2.3 Black tracks (N _b )

Particles having range L < 3 mm from interaction vertex (from which they originated) and g* > 6.0 are termed as Black tracks (N _b ). This corresponds to a relative velocity (β) < 0.3 and a proton with kinetic energy (E _p ) < 30 MeV. Most of these are produced due to evaporation of residual target nucleus.

In present analysis, out of 700, 570 events have fulfilled the above required criteria (N _s , N _g and N _b ) for further investigation. The number of heavily ionizing charged particles (N _h  = N _b  + N _g ) depends upon target breakup. The peaks in N _h distribution have strong correlation with the classes of emulsion target. Three very distinct regions can be seen from N _h distribution and each region belongs to a known target as shown earlier [16]. Therefore, we have used such distribution to fix criteria for target separation.

2.4 Ag/Br target events

N _h  ≥ 8 and at least one track with R < 10 μm is present in an event. This class of target is known to have cleanest interaction and high statistics are known as Ag/Br target events.

2.5 CNO target events

1 < N _h  < 8 and no tracks with R < 10 μm are present in an event. This class always contains very clean interaction of CNO target.

2.6 H target events

N _h  ≤ 1 and no tracks with R < 10 μm are present in an event. This class includes all ⁸⁴Kr₃₆ + H interactions & also some of the peripheral interactions with CNO and also very peripheral interactions with Ag/Br targets.

In previous work [16], we have shown the percentage variation of target interactions with respect to projectile mass number for fixed target emulsion experiments. We obtained 13.4, 39.0 and 47.6 % of interactions with H, CNO and Ag/Br targets, respectively.

3 Results and discussion

Figure 1 represents compound multiplicity distributions for ⁸⁴Kr₃₆ interactions with different target groups of NED such as H, CNO and Ag/Br, selected on the basis of heavily ionizing charged particle (N _h ). Figure 1 reveals that multiplicity distributions become wider with increasing target size. The average value of compound multiplicity $\left\langle {{{N}}_{{c}} } \right\rangle$, its dispersion D (N _c ) = $\sqrt {\left\langle {{{N}}_{{c}}^{2} } \right\rangle - \left\langle {{{N}}_{{c}}} \right\rangle ^{2} }$ and the ratio $\left\langle {{{N}}_{{c}} } \right\rangle$/D (N _c ) are represented in Table 1, while Table 2 summarizes compound multiplicity of different projectiles [7, 19–25]. Figure 2 shows the dependence of average compound multiplicity $\left\langle {{{N}}_{{c}} } \right\rangle$ on mass number of beam nucleus (A _p ). It may be observed from Fig. 2 that $\left\langle {{{N}}_{{c}} } \right\rangle$ increases rapidly with increasing mass of the incident beam. The points represent experimental data while continuous line is result of fitting by the relation $\left\langle {{{N}}_{{c}} } \right\rangle$ = KA ^α _p . The fitting parameters are k = 3.57 ± 0.48 and α = 0.47 ± 0.05. The corresponding fitting parameters for ²⁴Mg, ¹²C and ⁸⁴Kr are k = 4.40 ± 0.43 and α = 0.44 ± 0.03 at 4.5 A GeV [21], k = 3.25 ± 0.12 and α = 0.40 ± 0.36 at 3.7 A GeV [6] and k = 2.64 ± 0.66 and α = 0.47 ± 0.07 at 1.7 A GeV [2], respectively. Thus our results are consistent with other reported works.

Fig. 1

Compound multiplicity distributions for different emulsion target groups in ⁸⁴Kr₃₆ with nuclear emulsion collisions at ~1 GeV per nucleon

Table 1 The value of mean compound multiplicity $\left\langle {{{N}}_{{c}} } \right\rangle$, dispersion D (N _C ) and ratio $\left\langle {{{N}}_{{c}} } \right\rangle$/D (N _C ) in ⁸⁴Kr₃₆ interactions

Table 2 A compilation of compound multiplicity for different projectile induced emulsion reactions

Fig. 2

Dependence of $\left\langle {{{N}}_{{c}} } \right\rangle$ on the mass number (A _p ) of different projectiles in nucleus–nucleus collisions

The average multiplicities of black, grey and shower particles in different ensembles of ⁸⁴Kr–nuclear emulsion interactions are presented in Table 3. For comparison, corresponding results from ⁸⁴Kr–nuclear emulsion collisions and ⁵⁶Fe–nuclear emulsion collisions at 1.7 GeV per nucleon are also tabulated in Table 3. From Table 3, it is appear that average multiplicity of black, grey and shower particles increases with the increase of target mass for both ⁸⁴Kr–nuclear emulsion and ⁵⁶Fe–nuclear emulsion interactions.

Table 3 The percentage occurrence and average multiplicities of charged particles in different target groups of ⁸⁴Kr (1.7 A GeV), ⁵⁶Fe (1.7 A GeV) and ⁸⁴Kr (~1 A GeV) interactions

Koba–Nielsen–Olesen (KNO) scaling is a well established empirical law for multiparticle production in p + p collision. KNO scaling behavior of compound multiplicity distribution is also observed in nucleus–nucleus collisions [13–18]. Figure 3 shows $\left\langle {{{N}}_{{c}} } \right\rangle$ (σ_n/σ_inel) versus N _c /$\left\langle {{{N}}_{{c}} } \right\rangle$ for ⁸⁴Kr₃₆-emulsion interactions at 1 GeV per nucleon, where σ_n denotes the partial cross section for producing n charged compound particles, σ_inel denotes the total inelastic cross section, and z = N _c /$\left\langle {{{N}}_{{c}} } \right\rangle$, respectively. From Fig. 3 it can be seen that experimental data lie on a universal curve, which can be fitted by a KNO scaling function with the form

$$ \Upphi ({\text{z)}} = \left( {{\text{Az }} + {\text{Bz}}^{3} + {\text{Cz}}^{5} + {\text{Dz}}^{7} } \right){\text{ e}}^{\text{Ez}} . $$

(1)

Fig. 3

$\left\langle {{{N}}_{{c}} } \right\rangle$ (σ_n/σ_inel) versus N _c /$\left\langle {{{N}}_{{c}} } \right\rangle$ for ⁸⁴Kr₃₆–nuclear emulsion interactions at 1 GeV per nucleon

The best fitting parameters are A = 8.34 ± 1.28, B = −(1.46 ± 2.38), C = 3.99 ± 2.76, D = 1.17 ± 0.77 and E = −(3.41 ± 0.88). The minimum fitting χ²/DOF is 1.05, which means that experimental data can be well explained by KNO scaling law. The fitting parameter value is similar as that reported in [2] for ⁸⁴Kr–emulsion interaction at 1.7 GeV per nucleon. Figure 4 shows correlations between $\left\langle {{{N}}_{{c}} } \right\rangle$ and N _s , N _h , N _g , N _b for ⁸⁴Kr–emulsion collisions at around 1 GeV per nucleon. These correlations exhibit linear relationships as follows:

$$ \left\langle {{{N}}_{{c}} } \right\rangle = (1.01 \pm 0.04){{N}}_{{b}} + (3.28 \pm 0.67), $$

(2)

$$ \left\langle {{{N}}_{{c}} } \right\rangle = (0.95 \pm 0.03){{N}}_{{g}} + (6.70 \pm 0.66), $$

(3)

$$ \left\langle {{{N}}_{{c}} } \right\rangle = (0.63 \pm 0.03){{N}}_{{s}} + (5.07 \pm 0.77), $$

(4)

$$ \left\langle {{{N}}_{{c}} } \right\rangle = (0.96 \pm 0.03){{N}}_{{h}} + (4.87 \pm 0.69). $$

(5)

Fig. 4

Dependence of $\left\langle {{{N}}_{{c}} } \right\rangle$ on N_i (i = s, h, g, b) for ⁸⁴Kr₃₆ with emulsion at ~1 GeV per nucleon

Figure 5 shows correlations between $\left\langle {{{N}}_{{s}}} \right\rangle$, $\left\langle {{{N}}_{{h}} } \right\rangle$, $\left\langle {{{N}}_{{g}} } \right\rangle$, $\left\langle {{{N}}_{{b}} } \right\rangle$ and N _c for ⁸⁴Kr–nuclear emulsion collisions at around 1 GeV per nucleon. These correlations are nicely fitted by linear relations of the form,

$$ \left\langle {{{N}}_{{b}} } \right\rangle = (0.28 \pm 0.05){{N}}_{{c}} + (0.72 \pm 0.07), $$

(6)

$$ \left\langle {{{N}}_{{g}} } \right\rangle = (0.41 \pm 0.03){{N}}_{{c}} + (1.85 \pm 0.76), $$

(7)

$$ \left\langle {{{N}}_{{s}} } \right\rangle = (0.59 \pm 0.03){{N}}_{{c}} + (4.21 \pm 0.77), $$

(8)

$$ \left\langle {{{N}}_{{h}} } \right\rangle = (0.43 \pm 0.02){{N}}_{{c}} + (2.58 \pm 0.69). $$

(9)

Fig. 5

Dependence of $\left\langle {{{N}}_{{b}} } \right\rangle$ and $\left\langle {{{N}}_{{h}} } \right\rangle$ on N _c for ⁸⁴Kr₃₆ with emulsion at ~1 GeV per nucleon

4 Conclusions

Present study reveals that mean compound particle multiplicity increases rapidly with the increase of projectile mass number. The multiplicity correlation between N _b , N _g , N _s , N _h , and average value of N _c exhibit linear relation. The compound multiplicity distribution is observed to obey KNO scaling law, which is independent of mass number and energy of the projectile.