New collective mode due to collisional coupling

Abstract

Starting from a nonmarkovian conserving relaxation time approximation for collisions we derive coupled dispersion relations for asymmetric nuclear matter. The isovector and isoscalar modes are coupled due to asymmetric nuclear meanfield acting on neutrons and protons differently. A further coupling is observed by collisional correlations. The latter one leads to the appearance of a new soft mode besides isoscalar and isovector modes in the system. We suggest that this mode might be observable in asymmetric systems. This soft mode approaches the isovector mode for high temperatures. At the same time the isovector mode remains finite and approaches a constant value at higher temperatures showing a transition from zero sound like damping to first sound. The damping of the new soft mode is first sound like at all temperatures.The investigation of collective excitations in asymmetric nuclear matter is of current interest for experiments with nuclei far from β-stability, [1] and citations therein. We consider here a Fermi gas model consisting of a number of different species (neutrons, protons, etc) interacting with the own specie and with other ones. The interaction between different sorts of particles is important to consider if we want to include friction between different streams of isospin components. Especially the isospin current may not be conserved by this way. We neglect explicitly shell effects and concentrate only on bulk matter properties. Let us start with a set of coupled quantum kinetic equations for the reduced density operator ρ a for the specie awhere E = P 2 /2m denotes the kinetic energy operator and U the mean field operator and the external field which is assumed to be a nonlinear function of the density. We have approximated the collision integral by a non-Markovian relaxation time [8]. The memory effects condensed in the frequency dependent relaxation time turned out to be necessary to reproduce damping of zero sound [2,3]. It accounts for the fact that during a two particle collision a collective mode can couple to the scattering process. Consequently, the dynamical relaxation time represents the physical content of a hidden three particle process and is equivalent to the memory effects.We have further assumed the relaxation with respect to the local equilibriumρ b of any specie in the system. The relaxation of the actual distribution of specie a is driven by the local equilibrium of all the other components. The cross coupling is realized by nondiagonal relaxation times τ ab . We specify the local equilibrium by a small deviation of the chemical potential of specie a [4] compared with the global equilibrium (2) with < k|E|k ′ >= ǫ(k). The equilibrium distributions < k|ρ 0 a |k ′ >= f a (k)δ kk ′ are the corresponding Fermi functions with chemical potential µ a and the normalization to density n a = 2 dp (2π) 3 f a (p). The local equilibrium specified by δµ a is determined if we impose the density balance to be fulfilled separately for each specie current J a which reads in Wigner coordinat...

Quasiparticle parametrization of mean fields, Galilei invariance, and universal conserving response functions

“…As a result the response has been used successfully to describe collective excitations like giant resonances [7][8][9][10][11] also in multicomponent systems [12][13][14][15][16][17][18]. In fact, the velocity dependence of the quasiparticle mean field induces the appearance of multipole forces and when treated in random phase approximation (RPA) produces multiple pairing forces [19].…”

Momentum conservation and local field corrections for the response of interacting Fermi gases

“…There are two distinguishable cases, the single component case where we have to include momentum conservation and obtain divergent conductivity and the multicomponent case where we should expect Mermin-like formulae in order to render the conductivity finite. In order to bring these two extreme cases together the response function for multicomponent systems should be considered [6].In this letter we want to restrict to the one -component situation. In [2] we have derived the density, current and energy response χ, χ J , χ E of an interacting quantum system…”

“…However one should note that this formula is valid only for the extension to a multicomponent system [6] (at least a two-component system) since it makes no sense to speak of conductivity in a single component system where the conductivity should be infinite. Clearly the Mermin formula does not distinguish these cases and cannot be sufficient to describe the response.…”

Dynamical local field, compressibility, and frequency sum rules for quasiparticles

“…A toy example of Imf = sin (aω)/(ω 2 − 4π 2 /a 2 ) and the corresponding real part obtained from the Kramers Kronig relation (22) shows that indeed (37) can hold simultaneously with the Kramers Kronig relation.…”

“…We restrict here to a one component system though the generalization to multicomponent systems is straight forward 37,38 and considered in different approaches [39][40][41] .…”