Critical behavior of the isotope yield distributions in the Multifragmentation Regime of Heavy Ion Reactions

Isotope yields have been analyzed within the framework of a Modified Fisher Model to study the power law yield distribution of isotopes in the multifragmentation regime. Using the ratio of the mass dependent symmetry energy coefficient relative to the temperature, $a_{sym}/T$, extracted in previous work and that of the pairing term, $a_{p}/T$, extracted from this work, and assuming that both reflect secondary decay processes, the experimentally observed isotope yields have been corrected for these effects. For a given I = N - Z value, the corrected yields of isotopes relative to the yield of $^{12}C$ show a power law distribution, $Y(N,Z)/Y(^{12}C) \sim A^{-\tau}$, in the mass range of $1 \le A \le 30$ and the distributions are almost identical for the different reactions studied. The observed power law distributions change systematically when I of the isotopes changes and the extracted $\tau$ value decreases from 3.9 to 1.0 as I increases from -1 to 3. These observations are well reproduced by a simple de-excitation model, which the power law distribution of the primary isotopes is determined to $\tau^{prim} = 2.4 \pm 0.2$, suggesting that the disassembling system at the time of the fragment formation is indeed at or very near the critical point.Comment: 5 pages, 5 figure

The Isospin Dependence Of The Nuclear Equation Of State Near The Critical Point

We discuss experimental evidence for a nuclear phase transition driven by the different concentration of neutrons to protons. Different ratios of the neutron to proton concentrations lead to different critical points for the phase transition. This is analogous to the phase transitions occurring in 4He-3He liquid mixtures. We present experimental results which reveal the N/A (or Z/A) dependence of the phase transition and discuss possible implications of these observations in terms of the Landau Free Energy description of critical phenomena.Comment: 14 pages, 18 figure

Universal Behavior of Lyapunov Exponents in Unstable Systems

We calculate the Lyapunov exponents in a classical molecular dynamics framework. The system is composed of few hundreds particles interacting either through Yukawa (Nuclear) or Slater-Kirkwood (Atomic) forces. The forces are chosen to give an Equation of State that resembles the nuclear and the atomic $^4He$ Equation Of State respectively near the critical point for liquid-gas phase transition. We find the largest fluctuations for an initial "critical temperature". The largest Lyapunov exponents $\lambda$ are always positive and can be very well fitted near this "critical temperature" with a functional form $\lambda\propto |T-T_c|^{-\omega}$, where the exponent $\omega=0.15$ is independent of the system and mass number. At smaller temperatures we find that $\lambda\propto T~ ^{0.4498}$, a universal behavior characteristic of an order to chaos transition.Comment: 11 pages, RevTeX, 3 figures not included available upon reques

A novel approach to Isoscaling: the role of the order parameter m = (N-Z)/A

Isoscaling is derived within a recently proposed modified Fisher model where the free energy near the critical point is described by the Landau O(m^6) theory. In this model m = (N-Z)/A is the order parameter, a consequence of (one of) the symmetries of the nuclear Hamiltonian. Within this framework we show that isoscaling depends mainly on this order parameter through the 'external (conjugate) field' H. The external field is just given by the difference in chemical potentials of the neutrons and protons of the two sources. To distinguish from previously employed isoscaling relationships, this approach is dubbed: m - scaling. We discuss the relationship between this framework and the standard isoscaling formalism and point out some substantial differences in interpretation of experimental results which might result. These should be investigated further both theoretically and experimentally.Comment: 14 pages, 5 figure

The Quantum Nature of a Nuclear Phase Transition

In their ground states, atomic nuclei are quantum Fermi liquids. At finite temperatures and low densities, these nuclei may undergo a phase change similar to, but substantially different from, a classical liquid gas phase transition. As in the classical case, temperature is the control parameter while density and pressure are the conjugate variables. At variance with the classical case, in the nucleus the difference between the proton and neutron concentrations acts as an additional order parameter, for which the symmetry potential is the conjugate variable. Different ratios of the neutron to proton concentrations lead to different critical points for the phase transition. This is analogous to the phase transitions occurring in $^{4}$He-$^{3}$He liquid mixtures. We present experimental results which reveal the N/Z dependence of the phase transition and discuss possible implications of these observations in terms of the Landau Free Energy description of critical phenomena.Comment: 5 pages, 4 figure

Chaos driven fusion enhancement factor at astrophysical energies

We perform molecular dynamics simulations to assess the screening effects by bound target electrons in low energy nuclear reactions in laboratories. Quantum effects corresponding to the Pauli and Heisenberg principle are enforced by constraints. We show that the enhancement of the average cross section and of its variance is due to the perturbations induced by the electrons.This gives a correlation between the maximum amplitudes of the inter-nuclear oscillational motion and the enhancement factor. It suggests that the chaotic behavior of the electronic motion affects the magnitude of the enhancement factor.Comment: 4 pages, 3 figure

Vlasov Description Of Dense Quark Matter

We discuss properties of quark matter at finite baryon densities and zero temperature in a Vlasov approach. We use a screened interquark Richardson's potential consistent with the indications of Lattice QCD calculations. We analyze the choices of the quark masses and the parameters entering the potential which reproduce the binding energy (B.E.) of infinite nuclear matter. There is a transition from nuclear to quark matter at densities 5 times above normal nuclear matter density. The transition could be revealed from the determination of the position of the shifted meson masses in dense baryonic matter. A scaling form of the meson masses in dense matter is given.Comment: 15 pages 4 figure

Analysis of fragment yield ratios in the nuclear phase transition

The critical phenomena of the liquid-gas phase transition has been investigated in the reactions 78,86Kr+58,64Ni at beam energy of 35 MeV/nucleon using the Landau free energy approach with isospin asymmetry as an order parameter. Fits to the free energy of fragments showed three minima suggesting the system to be in the regime of a first order phase transition. The relation m =-{\partial}F/{\partial}H, which defines the order parameter and its conjugate field H, has been experimentally verified from the linear dependence of the mirror nuclei yield ratio data, on the isospin asymmetry of the source. The slope parameter, which is a measure of the distance from a critical temperature, showed a systematic decrease with increasing excitation energy of the source. Within the framework of the Landau free energy approach, isoscaling provided similar results as obtained from the analysis of mirror nuclei yield ratio data. We show that the external field is primarily related to the minimum of the free energy, which implies a modification of the source concentration \Delta used in isospin studies