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IL NUOVO CIMENTO VOL. 110 A, N. 11 Novembre 1997 NOTE BREVI

Correlation between conditional moments

in nuclear diffractive excitation

and electromagnetic dissociation at high energy

FU-HULIU

Department of Physics, Shanxi Teacher University - Linfen, Shanxi 041004, PRC (ricevuto il 7 Novembre 1997; approvato il 22 Dicembre 1997)

Summary. — The conditional moments of the charge distributions of the projectile

fragments in sulphur fragmentation are obtained using the simple Monte Carlo partition method. Thus, the logarithmic correlations between the conditional moments can be observed. The results of nuclear diffractive excitation, electro-magnetic dissociation and Monte Carlo method have been compared. PACS 25.70 – Low and intermediate energy heavy-ion reactions.

Nuclear fragmentation (hot-nuclei multifragmentation) in relativistic nucleus-nucleus collisions is an important experimental phenomenon. Campi [1] introduced the critical behaviour method in the study of hot-nuclei multifragmentation. He regards the hot-nuclei multifragmentation as a critical phenomenon and identifies the single-event moment (called the conditional moment) as follows:

Mkj4

!

dkQ nj(d) , (1)

where nj

(d) 40, 1, 2, R, is the number of fragments of charge d appearing in the event j. The sum includes all the fragments, excluding the heaviest one produced in the event. Campi also introduced the normalized moment

Skj4 Mk j

OM1j.

(2)

According to the discussion in ref. [2], by omitting the limited condition d c dmaxin

formula (1), the situation for correlation behaviour is not affected. We have included the heaviest fragment in the following version of formula (1):

Mkj4

!

dmax

dk_{Q n}j_{(d) .}

(3)

According to formulas (1) and (2), or (2) and (3), the correlations between ln S3and

ln S2, as well as ln S5 and ln S2 for high-energy interactions of nuclei with emulsion

were obtained in refs. [1-4].

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In this paper, we study the correlation between conditional moments in diffractive excitation (DE) and electromagnetic dissociation (EMD) of sulphur nuclei using the simple Monte Carlo partition method and compare the calculated results with the experimental data of refs. [5] and [6].

Up to now, three kinds of interactions in high-energy nucleus-nucleus emulsion collisions have been found in experiment. They are nuclear reaction, electromagnetic dissociation and elastic collision. Most of nuclear reactions events are diffractive excitation.

According to the discussions in refs. [5] and [6], potential DE events are those interactions showing no visible target excitation (the number of target fragments is zero), when the interactions are examined in the emulsion using the optical microscopes. Let ui denote the emission angle of the i-th charged shower particle in

event, the DE event obeys the constraint condition of

!

charged shower particles of sin u D0.4 are classified as non-DE ones. The EMD events are generated in collisions involving impact parameters large enough so that no nuclear interactions occur. Extremely strong electromagnetic fields from the heavy nuclei are produced for a very short time at the projectile; such events typically consist of projectile nucleus. The fragmentation cone was defined by u Guc4 PfOPbeam, where

Pf and Pbeam are the Fermi momentum (estimated to be 200 MeVOc) and projectile

momentum. The EMDs were then picked up using the criterion that the total charge of the projectile fragments inside this cone is the charge of projectile nucleus.

According to the raw data of refs. [5] and [6], the normalized moments have been calculated event by event in this paper. The correlations between ln S3 and ln S2

Fig. 1. – Correlations between ln S3 and ln S2 in32S fragmentation at 200 GeVON in the case of

inclusion of the heaviest fragment. Top, middle and bottom panels correspond to the DE, EMD and MC events, respectively.

CORRELATION BETWEEN CONDITIONAL MOMENTS IN NUCLEAR DIFFRACTIVE EXCITATION ETC. 1363

Fig. 2. – As for fig. 1, but excluding the heaviest fragment.

calculated using formulas (2), (3) and (1), (2) are shown in figs. 1 and 2, respectively. Up, middle and down figures correspond to the experimental DE and EMD events and the simple MC simulation events, respectively, where the simple MC simulation is similar to the simple partition method and only based on the charge conservation.

From fig. 1 one can see that the logarithmic correlations between the conditional moments are observed. The slopes of correlation lines for DE, EMD and MC events in fig. 1 are 1.823, 1.741 and 1.985, respectively. The calculated slope is similar to the two slopes of experimental correlation lines, and the distribution region of simulation events in ln S3-ln S2plane is similar to that of DE and EMD events. There is no obvious

difference among DE, EMD and MC events when the heaviest fragment is included. From fig. 2 one can also see that the logarithmic correlations between the conditional moments are observed. The slopes of the correlation lines for DE, EMD and MC events in fig. 2 are 2.080, 2.028 and 2.005, respectively. The calculated slope is similar to the experimental data and the distribution region of simulation events in ln S3-ln S2 plane is wider than that of DE and EMD events. When the heaviest

fragment is excluded the difference between experimental events and simulation events is obvious. It is a reflection of the liquid-gas phase transition of the concerned system that the experimental events are mainly distributed in the low ln S2region.

A lot of light fragments will appear in high-energy nuclear fragmentation if the liquid-gas phase transition happens. Thus, the value of ln S2is low. In other words, the

probabilities of experimental events with low ln S2are greater than normal ones such

as the simple MC events. This phenomenon can be reflected in the conditional moment distribution rather than in the conditional moment correlation [4]. In correlation plane, this phenomenon can be reflected in the region of low ln S2.

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In conclusion, when the heaviest fragment is excluded, we suggest that the conditional moment distribution or events distribution in ln S3-ln S2plane could be used

in the liquid-gas phase transition studies. The probabilities of events with low ln S2are

greater than normal ones if the liquid-gas phase transition happens. * * *

This Project is supported by China National Education Committee Foundation of Scholarly Exchange, Shanxi Provincial Foundation of Scholarly Exchange and Shanxi Provincial Foundation of Leading Man in Science.

R E F E R E N C E S

[1] CAMPIX., J. Phys. A, 19 (1987) L917.

[2] LIU HONG-MIN, SA BEN-HAO, ZHENG YU-MING et al., High Energy Phys. Nucl. Phys. (in Chinese), 15 (1991) 1053.

[3] LIUFU-HUand SUNHAN-CHENG, Can. J. Phys., 73 (1995) 365. [4] LIUFU-HU, Chin. J. Nucl. Phys., 17 (1995) 200.

[5] BAHK S. Y., CHANG S. D., CHEONB. G. et al., Phys. Rev. C, 43 (1991) 1410 and references quoted therein.