We consider the propagation and damping of isovector excitations in heated nuclear matter within the Landau Fermi-liquid theory. Results obtained for nuclear matter are applied to calculate the Giant Dipole Resonance (GDR) at finite temperature in heavy spherical nuclei within Steinwedel and Jensen model. The centroid energy of the GDR slightly decreases with increasing temperature and the width increases as T 2 for temperatures T < 5 MeV in agreement with recent experimental data for GDR in 208 Pb and 120 Sn.The validity of the method for other Fermi fluids is finally suggested.PACS numbers: 24.30. Cz, 21.60.Ev, 21.65.+f In recent years the GDR built on highly excited states is in the center of many experimental and theoretical studies (c.f. [1] and references therein). In this context, one of the most important open problems is the behaviour of the GDR width in nonrotating nuclei as a function of temperature. There are two essentially different theoretical approaches to this problem. The first one [2] explains the temperature increasing of the width as an effect of the adiabatic coupling of the GDR to thermal shape deformations. In the second approach [3,4,5] the thermal contribution to the damping width arises from 1 an increasing nucleon-nucleon collision rate (2p2h excitations) plus a Landau spreading due to thermally allowed ph transitions [6,7,8,9].In the present work, following the ideology of the second approach, we consider isovector volume vibrations in spin-isospin symmetrical nuclear matter at finite temperature. A similar problem was considered in Refs. [7,8] within the RPA method. However the Landau damping mechanism of the dissipation of a propagating mode due to thermal smearing of Fermi distribution is too weak to be responsible for the fast increase of the observed GDR width with temperature [7,8,11]. This problem can be solved by taking into account the two-body dissipation through the collision integral of the Landau-Vlasov equation [3]. The use of a quantum kinetic equation leads to memory effects in the collision term in order to include off energy-shell contributions [12]. Moreover it was shown in Refs. [13,14], that memory effects are essentially increasing the widths of multipole resonances at small temperatures. In this Rapid Communication we calculate the isovector strength function of nuclear matter taking into account both thermal Landau damping and two-body collisional dissipation, including the quantum memory contribution.The isovector response of uniform nuclear matter is described by the linearized Landau-Vlasov equation with a collision term treated in the relaxation time approximation [4,9,14] where δf ≡ δf n −δf p and δU ≡ δU n −δU p are differences between neutron and proton distribution functions (d.f.) and mean fields respectively, δV ≡ δV n − δV p is external field (δV q = τ q δV, τ n = +1,) is the equilibrium finite temperature Fermi distribution, and the notation l ≥ 1 means that the perturbation of the d.f. δf | l≥1 in collision integral includes only Fermi ...
