Lattice gas model with isospin-dependent interactions

Abstract

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.

Liquid-Gas Phase Transition in Nuclear Multifragmentation

“…The EOS for isospin dependent LGM in mean-field theory using the Bragg-Williams and the Bethe-Peierls approximation can be found in [144]. Phase transition aspects, much more than what we have covered here, can be found in [108,[145][146][147].…”

Application of Information Theory in Nuclear Liquid Gas Phase Transition

“…These observables were shown to be good indicators of a liquid gas phase transition, as shown in Ref. [20]. The extreme values of τ , N imf and S 2 occur at the same temperature, indicating of the onset of the phase transition, for each calculation case.…”

“…The lattice gas model was developed to describe the liquid-gas phase transition for atomic system by Lee and Yang [16]. The same model has already been applied to nuclear physics for isospin symmetrical systems in the grandcanonical ensemble [17] with a sampling of the canonical ensemble [3,4,18,19,20,21,22], and also for isospin asymmetrical nuclear matter in the mean field approximation [23]. In addition, a classical molecular dynamical model is used to compare its results with the results of lattice gas model.…”

“…The interaction constant ǫ sisj is chosen to be isospin dependent and be fixed to reproduce the binding energy of the nuclei [20]:…”

Microscopic systems with and without Coulomb interaction, fragmentation and phase transitions in finite nuclei

“…The latter, a priori more realistic choice has been used by different authors [11][12][13][14], the choice of strength is such that the classical ground state energy of finite nuclear systems is reproduced [15]. The Coulomb term in (1) is such that Z i = 0 or 1 if particle i is a neutron or a proton respectively.…”