We propose a model that provides a unified description of nuclear equation

We model the disassembly of an excited nuclear system formed as a result of a heavy ion collision. We find that, as the beam energy in central collisions in varied, the dissociating system crosses a liquidgas coexistence curve, resulting in a first-order phase transition. Accessible experimental signatures are identified: a peak in the specific heat, a power-law yield for composites, and a maximum in the second moment of the yield distribution. [S0031-9007(97) PACS numbers: 25.70. Pq, 21.65. + f, 24.10.Pa, 64.60.My Nuclear matter is a fictitious arbitrarily large N Z system in which the Coulomb interaction is switched off. Mean-field theory for nuclear matter has been applied many times, and it is well known that such a system shows a van-der-Waals-type liquid-gas phase transition. It was suggested in the early 1980s [1,2] that in heavy ion collisions at intermediate energies one might be able to probe this liquid-gas phase transition region. In heavy ion collisions, matter would be heated as well as compressed. This compressed blob would then expand passing through the liquid-gas coexistence phase. One might be able to extract information about this region from selected experimental data. Earlier, the Purdue group had conjectured that the breakup of large nuclei by energetic protons would show signatures of critical phenomena [2].There are several complications which make the study of phase transitions in nuclei difficult. The systems are small, thus singularities get replaced by broad peaks. The collision is over quickly. The existence of thermal equilibrium has sometimes been questioned and replaced by quite complicated transport equation approaches. Often one has been content to do calculations where the objective is to fit the experimental data. Once this is achieved the question of a possible liquid-gas phase transition is not addressed. There are models where such questions are irrelevant, or at least very indirect, such as various models based on sequential decays. The literature on calculations for fragment yields in intermediate energy heavy ion collisions is huge. We will not attempt to mention all approaches.In this paper we will focus on the liquid-gas phase transition using a lattice gas model [3]. Previously we have used the model to fit data on central collisions [3], on peripheral collisions [4], and for central Au on Au collisions [5]. The model gives a fair description of data in those instances-does it say anything definite about the experimental signature of liquid-gas phase transitions?In the lattice gas model we place n nucleons in N cubes, where n is the number of nucleons in the disassembling system, and N͞n r 0 ͞r f , where r 0 is the normal nuclear density, and the disassembly is to be calculated at r f , the "freeze-out" density beyond which nucleons are too far apart to interact. An attractive nearestneighbor interaction is assumed. We place the n nucleons in N cubes by Monte Carlo sampling using the Metropolis algorithm. Once the nucleons have been placed we also ascribe to each...

In this paper we continue the investigation of the lattice gas model. The main improvement is that we use two strengths for bonds: one between like particles and another between unlike particles to implement the isospin dependence of nuclear force. The main effect is the elimination of unphysical clusters, such as the dineutron or diproton. It is therefore a better description of a nuclear system. The equation of state in mean field theory is obtained for nuclear matter as well as for N Z systems. Through numerical and analytical calculation we show that the new model maintains all the important features of the older model. We study the effect of the Coulomb interaction on multifragmentation of a compound system of Aϭ86, Zϭ40, and also for Aϭ197, Zϭ79. For the first case the Coulomb interaction has small effect. For the latter case the effect is much more pronounced but typical signatures of the lattice gas model such as a minimum ͑maximum͒ in the value of (S 2 ) are still obtained but at a much lower temperature.

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We develop here a simple yet versatile model for nuclear fragmentation in heavy ion collisions. The model allows us to calculate thermodynamic properties such as phase transitions as well as the distribution of fragments at disassembly. In spite of its simplicity the model gives very good fit to recent data taken at the Michigan National Superconducting Cyclotron Laboratory.The model is an extension of a lattice gas model which itself has strong overlaps with percolation models which have been used in the past to compare with nuclear fragmentation data.