Nuclear isospin diffusivity

The isospin diffusion and other irreversible phenomena are discussed for a two-component nuclear Fermi system. The set of Boltzmann transport equations, such as that employed for reactions, is linearized, for weak deviations of a system from uniformity, in order to arrive at nonreversible fluxes linear in the nonuniformities. Besides the diffusion driven by a concentration gradient, also the diffusion driven by temperature and pressure gradients is considered. Diffusivity, conductivity, heat-conduction, and shear-viscosity coefficients are formally expressed in terms of the responses of distribution functions to the nonuniformities. The linearized Boltzmann-equation set is solved, under the approximation of constant form factors in the distribution-function responses, to find concrete expressions for the transport coefficients in terms of weighted collision integrals. The coefficients are calculated numerically for nuclear matter, using experimental nucleon-nucleon cross sections. The isospin diffusivity is inversely proportional to the neutron-proton cross section and is also sensitive to the symmetry energy. At low temperatures in symmetric matter, the diffusivity is directly proportional to the symmetry energy.

Figure 1

Isospin diffusion coefficient $D_I$ in symmetric matter, for $U_i=0$, at different indicated densities, as a function of the temperature $T$. In the high-temperature limit, the diffusion coefficient exhibits the behavior $D_I\propto \sqrt{T}∕n$. Correspondingly, at high temperatures in the figure, the largest coefficient values are obtained for the lowest densities and the lowest coefficient values are obtained for the highest densities. In the low-temperature limit, the diffusion coefficient exhibits the behavior $D_I\propto n^{3∕2}∕T^2$ and the order of the results in density reverses.

Figure 2

Isospin diffusion coefficient $D_I$ at normal density $n=n_0=0.16{\text{fm}}^{-3}$ and different indicated asymmetries $\delta$, for $U_i=0$, as a function of the temperature $T$. An increase in the asymmetry generally causes a decrease in the coefficient, as discussed in the text.

Figure 3

Thermal conductivity $\kappa$ in symmetric nuclear matter, at different indicated densities in units of $n_0$, as a function of temperature $T$. The conductivity increases as density increases.

Figure 4

Shear viscosity $\eta$ in symmetric nuclear matter, at different indicated densities in units of $n_0$, as a function of temperature $T$. The viscosity increases as density increases.

Figure 5

Mean-field enhancement factor of the diffusion coefficient in symmetric nuclear matter, $R\equiv D_I\left(U_i\right)∕D_I(U_i=0)$, at a fixed density $n$, as a function of temperature $T$. The solid and dashed lines, respectively, represent the factors for the assumed linear and quadratic dependence of the interaction symmetry energy on density. The lines from top to bottom are for densities $n=2n_0,n_0,0.5n_0$, and $0.1n_0$, respectively. At normal density the results for the two dependencies coincide.