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Register a new userIsospin Asymmetry in Nuclei, Neutron Stars, and Heavy-Ion Collisions
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Authors
Andrew W. Steiner
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The roles of isospin asymmetry in nuclei and neutron stars are investigated using a range of potential and field-theoretical models of nucleonic matter. The parameters of these models are fixed by fitting the properties of homogeneous bulk matter and closed-shell nuclei. We discuss and unravel the causes of correlations among the neutron skin thickness in heavy nuclei, the pressure of beta-equilibrated matter at a density of 0.1 fm$^{-3}$, and the radii of moderate mass neutron stars. The influence of symmetry energy on observables in heavy-ion collisions is summarized.
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We introduce a cumulant expansion to parameterize possible initial conditions in relativistic heavy ion collisions. We show that the cumulant expansion converges and that it can systematically reproduce the results of Glauber type initial conditions. At third order in the gradient expansion, the cumulants characterize the triangularity $<r^3 cos3(phi - psi_{3,3})>$ and the dipole asymmetry $<r^3 cos(phi- psi_{1,3})>$ of the initial entropy distribution. We show that for mid-peripheral collisions the orientation angle of the dipole asymmetry $psi_{1,3}$ has a $20%$ preference out of plane. This leads to a small net $v_1$ out of plane. In peripheral and mid-central collisions the orientation angles $psi_{1,3}$ and $psi_{3,3}$ are strongly correlated. We study the ideal hydrodynamic response to these cumulants and determine the associated $v_1/epsilon_1$ and $v_3/epsilon_3$ for a massless ideal gas equation of state. $v_1$ and $v_3$ develop towards the edge of the nucleus, and consequently the final spectra are more sensitive to the viscous dynamics of freezeout. The hydrodynamic calculations for $v_3$ are compared to Alver and Roland fit of two particle correlation functions. Finally, we propose to measure the $v_1$ associated with the dipole asymmetry and the correlations between $psi_{1,3}$ and $psi_{3,3}$ by measuring a two particle correlation with respect to the participant plane, $<cos(phi_a - 3phi_b + 2Psi_{PP})>$. The hydrodynamic prediction for this correlation function is several times larger than a correlation currently measured by the STAR collaboration, $<cos(phi_a + phi_b - 2Psi_{PP})>$.
The longitudinal asymmetry arises in relativistic heavy ion collisions due to fluctuation in the number of participating nucleons. This asymmetry causes a shift in the center of mass rapidity of the participant zone. The rapidity shift as well as the longitudinal asymmetry have been found to be significant at the top LHC energy for collisions of identical nuclei. We study the longitudinal asymmetry and its effect on charged particle rapidity distribution and anisotropic flow parameters at relatively lower RHIC energies using a model calculation. The rapidity shift is found to be more pronounced for peripheral collisions, smaller systems and also for lower beam energies due to longitudinal asymmetry. A detailed study has been done by associating the average rapidity shift to a polynomial relation where the coefficients of this polynomial characterize the effect of the asymmetry. We show that the rapidity shift may affect observables significantly at RHIC energies.
We show that the phenomenology of isospin effects on heavy ion reactions at intermediate energies (few AGeV range) is extremely rich and can allow a ``direct study of the covariant structure of the isovector interaction in a high density hadron medium. We work within a relativistic transport frame, beyond a cascade picture, consistently derived from effective Lagrangians, where isospin effects are accounted for in the mean field and collision terms. We show that rather sensitive observables are provided by the pion/kaon production (pi^-/pi^+, K^0/K^+ yields). Relevant non-equilibrium effects are stressed. The possibility of the transition to a mixed hadron-quark phase, at high baryon and isospin density, is finally suggested. Some signatures could come from an expected ``neutron trapping effect.
Within the framework of the Lanzhou quantum molecular dynamics (LQMD) transport model, the isospin effect in peripheral heavy-ion collisions has been investigated thoroughly. A coalescence approach is used for recognizing the primary fragments formed in nucleus-nucleus collisions. The secondary decay process of the fragments is described by the statistical code, GEMINI. Production mechanism and isospin effect of the projectile-like and target-like fragments are analyzed with the combined approach. It is found that the isospin migration from the high-isospin density to the low-density matter takes place in the neutron-rich nuclear reactions, i.e., $^{48}$Ca+$^{208}$Pb, $^{86}$Kr+$^{48}$Ca/$^{208}$Pb/$^{124}$Sn, $^{136}$Xe+$^{208}$Pb, $^{124}$Sn+$^{124}$Sn and $^{136}$Xe+$^{136}$Xe. A hard symmetry energy is available for creating the neutron-rich fragments, in particular in the medium-mass region. The isospin effect of the neutron to proton (n/p) ratio of the complex fragments is reduced once including the secondary decay process. However, a soft symmetry energy enhances the n/p ratio of the light particles, in particular at the kinetic energies above 15 MeV/nucleon.
We discuss the sensitivity of fission barrier for heavy neutron-rich nuclei to fission paths in the two dimensional neutron-proton quadrupole plane. To this end, we use the constrained Skyrme-Hartree-Fock + BCS method, and examine the difference of fission barriers obtained with three constraining operators, that is, the neutron, proton, and mass quadrupole operators. We investigate $^{220}$U, $^{236}$U, and $^{266}$U, %from proton-rich to neutron-rich uranium isotopes, that is relevant to r-process nucleosynthesis. We find that the fission barrier heights are almost the same among the three constraining operators even for neutron-rich nuclei, indicating that the usual way to calculate fission barriers with the mass quadrupole operator is well justified. We also discuss the difference between proton and neutron deformation parameters along the fission paths.
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