Isospin Diffusion and the Nuclear Symmetry Energy in Heavy Ion Reactions

Abstract

Using symmetric 112Sn+112Sn, 124Sn+124Sn collisions as references, we probe isospin diffusion in peripheral asymmetric 112Sn+124Sn, 124Sn+112Sn systems at an incident energy of E/A=50 MeV. Isoscaling analyses imply that the quasiprojectile and quasitarget in these collisions do not achieve isospin equilibrium, permitting an assessment of isospin transport rates. We find that comparisons between isospin sensitive experimental and theoretical observables, using suitably chosen scaled ratios, permit investigation of the density dependence of the asymmetry term of the nuclear equation of state.

Density dependence of the symmetry energy from neutron skin thickness in finite nuclei

“…Sometimes modeled forms of the symmetry energy, such as eq. (16), are implied to deduce L. Simulations of isospin diffusion data with isospin-and momentum-dependent transport models [8,13,57,58,94] have allowed to estimate L in a range between 50 and 110 MeV. Improved quantum molecular dynamics simulations describing both isospin diffusion data and double ratios of neutron and proton spectra, support a similar range of L values for a symmetry energy at saturation between 28 and 34 MeV [16].…”

Isospin diffusion observables in heavy-ion reactions

“…Recently, constraints on the density dependence of the symmetry energy were obtained from measurements of isospin diffusion in peripheral nuclear collisions [6,8]. In this paper, we identify a set of experimental observables, specifically observables constructed with yield ratios of mirror nuclei, that provide consistent measures of the isospin diffusion and extend those experimental investigations to a wider range of rapidity, transverse momentum and impact parameter.In a heavy ion collision involving a projectile and a target with different proton fractions, Z/A, the symmetry energy tends to propel the system towards isospin equilibrium so that the difference between neutron and proton densities is minimized [7].The isospin asymmetry A Z N − = δ of a projectile-like residue produced in a peripheral collision reflects the exchange of nucleons with the target; significant diffusion rates should lead to larger isospin asymmetries for collisions with neutron-rich targets and smaller isospin asymmetries for collisions with proton-rich targets [6].To isolate the isospin diffusion effects from similar effects caused by preequilibrium emission, Coulomb or sequential decays, relative comparisons involving different targets are important. In recent studies, isospin diffusion has been measured by "comparing" A+B collisions of a neutron-rich (A) nucleus and a proton-rich (B) nucleus to symmetric collisions involving two neutron-rich nuclei (A+A) and two proton-rich (B+B) nuclei under the same experimental conditions [6].…”

“…Ratios of the mass seven mirror nuclei yields are analyzed to show the rapidity, transverse momentum and impact parameter dependence of isospin diffusion. [4][5][6][7] for its determination. Recently, constraints on the density dependence of the symmetry energy were obtained from measurements of isospin diffusion in peripheral nuclear collisions [6,8].…”

“…To do this, one can measure an observable X that is linearly dependent on the residue asymmetry, i.e. X = a⋅δ+b, and constructs the corresponding isospin transport ratio R i (X) ( )Then, trivial substitution provides that R i (X)=R i (δ) and one dispenses with most of the uncertainty associated with determining δ from measurements of X.The above idea has been adopted to study the isospin diffusion using the isoscaling (B+B) [6]. The isoscaling parameter α can be obtained from the isotope yield ratios from two reactions, which are similar in all aspects except in their isospin compositions:…”

Transport properties of isospin asymmetric nuclear matter using the time-dependent Hartree-Fock method

“…For example, collisions at Fermi energies give access to contact times which are short enough to induce only a partial charge equilibration [12] and thus can be used to determine equilibration times [13]. Alternatively, charge equilibration has also been studied with deep inelastic collisions at lower energies, but with large isospin asymmetry in the entrance channel [14][15][16].…”