IL NUOVO CIMENTO VOL. 110 A, N. 6 Giugno 1997 NOTE BREVI
Final-state energy spectrum in relativistic nuclear
electromagnetic dissociation
FU-HULIU
Institute of High Energy Physics, Academia Sinica P.O. Box 918(3), Beijing 100 039, PRC
(ricevuto il 2 Gennaio 1995; approvato il 23 Luglio 1997)
Summary. — The final-state energy spectrum in the electromagnetic dissociation is calculated by a simple method. The final-state energy curves obtained from the calculation are in agreement with the experimental data of 28Si into p 127Al at an
energy of 14.6 GeVON.
PACS 25.70 – Low and intermediate energy heavy-ion reactions.
In high-energy heavy-ion collisions, two main interaction processes were found: nuclear reactions and electromagnetic dissociation (EMD or ED). The latter is caused by the electromagnetic excitation of nuclei in peripheral heavy-ion collisions. Such EMD can be very important at high energies, due to the relativistic enhancement of the Coulomb field of the target, as seen in the rest frame of the projectile. The fragment charge, partial cross-section, transverse momentum and final-state energy of the EMD process have been measured in a number of experiments at a variety of beam energies [1-4].
In the centre-of-mass frame of collisions, both the projectile and the target move toward the centre-of-mass with given velocities. It is generally believed that this corresponds to a collision of two photons with given momenta with photon energy distributions given by the Weizsäcker-Williams (WW) method. But the final-state energy (Ef) spectrum measured in the E814 experiment is not well reproduced in both low- and high-Ef region by the calculation based on the WW method. Maybe we need some additional mechanisms to explain the Efspectrum.
In this note, we report a modelling calculation of the Efspectrum in the EMD and compare it with the experimental data of the E814 Collaboration [4].
We assume that the virtual photons presented isotropic emission in the electromagnetic field plane of the moving target with high velocity in the rest frame of the projectile, and the components Px and Py of the virtual photons momentum obey Gaussian distribution having same standard deviation s, i.e.
fPx , y(Px , y) 41Ok2 p s Q exp [2P2x , yO2s2] . (1)
We know that the momentum P 4
k
P2x 1P2y obeys Rayleigh distribution. For the
FU-HU LIU 662
Fig. 1. – Final-state energy distributions in the EMD of relativistic28Si into p 127Al for Pb, Sn,
Cu and Al targets.
virtual photon, the energy (Eg) equals P due to its zero mass in the rest frame. Therefore, we have the virtual-photon energy distribution:
fg(Eg) 4EgOs2Q exp [2Eg2O2 s2] . (2)
Let E * denote the total excitation energy and Q denote the combination energy of the last proton in the projectile; we have
E * 4Eg1 Q . (3)
Let Epdenote the energy of the emitted proton; we have E * 4Ef1 Ep. (4)
From eqs. (2), (3) and (4), we have the following Efdistribution: f (Ef) 4 (Ef1 Ep2 Q) Os2Q exp [2(Ef1 Ep2 Q)2O2 s2] . (5)
Here, we treat the energy of the emitted proton as a constant due to direct emission.
FINAL-STATE ENERGY SPECTRUM IN RELATIVISTIC NUCLEAR ELECTROMAGNETIC DISSOCIATION 663
We now compare the results of this calculation to data on the EMD of relativistic 28
Si into p 127Al. To this purpose, we normalize the data of the E814 Collaboration which using a28
Si beam at 14.6 GeVON at Brookhaven National Laboratory, incident on targets of Pb, Sn, Cu and Al, respectively [4]. The final-state energy curves obtained from the calculation are displayed for comparison with the data (histograms with error bars) in fig. 1. For four targets, the same two parameters are taken in this comparison. We take s 45.2 MeVOc and Ep2 Q 4 2 12.0 MeV. From fig. 1 one can see that the agreement between the theoretical and experimental curves is very nice, which means that the hypotheses of the model are reasonable.
High-energy heavy-ion collisions is a very complex process. We need more and better models to explain the nuclear reaction and electromagnetic dissociation. The present note has shown that at relativistic energies it is possible to explain the interaction properties with general physics.
* * *
I am grateful to Profs. LIN-KAI DING and HAN-CHENG SUN for their discussions.
This work was supported in part by the National Natural Science Foundation of China.
R E F E R E N C E S
[1] BRECHTMANNC. and HEINRICHW., Z. Phys. A, 330 (1988) 407.
[2] FU-HULIUet al., in Proceedings of the 1988 Changsha Symposium on High Energy Nuclear Emulsion, Journal of Human Education Institute (Natural Science Edition) (in Chinese),
Special Issue, No. 2 (1988).
[3] SINGHG., SENGUPTAK. and JAINP. L., Phys. Rev. C, 41 (1990) 999. [4] E814 COLLABORATION(J. BARRETTEet al.), Phys. Rev. C, 45 (1992) 2427.
