Modes In Nuclear Matter Research Articles

3a-A-15 Meson Modes in nuclear matter in Schwinger Dyson formalism

3a-A-15 Meson Modes in nuclear matter in Schwinger Dyson formalism

Inhomogeneity growth in two-component fermionic systems

The dynamics of fermionic many-body systems is investigated in the framework of Boltzmann-Langevin (BL) stochastic one-body approaches. Within the recently introduced BLOB model, we examine the interplay between mean-field effects and two-body correlations, of stochastic nature, for nuclear matter at moderate temperature and in several density conditions, corresponding to stable or mechanically unstable situations. Numerical results are compared to analytic expectations for the fluctuation amplitude of isoscalar and isovector densities, probing the link to the properties of the employed effective interaction, namely symmetry energy (for isovector modes) and incompressibility (for isoscalar modes). For unstable systems, clusterization is observed. The associated features are compared to analytical results for the typical length and time scales characterizing the growth of unstable modes in nuclear matter and for the isotopic variance of the emerging fragments. We show that the BLOB model is generally better suited than simplified approaches previously introduced to solve the BL equation, and it is therefore more advantageous in applications to open systems, like heavy ion collisions.

Nuclear collective dynamics within Vlasov approach

We discuss, in an investigation based on Vlasov equation, the properties of the isovector modes in nuclear matter and atomic nuclei in relation with the symmetry energy. We obtain numerically the dipole response and determine the strength function for various systems, including a chain of Sn isotopes. We consider for the symmetry energy three parametrizations with density providing similar values at saturation but which manifest very different slopes around this point. In this way we can explore how the slope affects the collective response of finite nuclear systems. We focus first on the dipole polarizability and show that while the model is able to describe the expected mass dependence, A^{5/3}, it also demonstrates that this quantity is sensitive to the slope parameter of the symmetry energy. Then, by considering the Sn isotopic chain, we investigate the emergence of a collective mode, the Pygmy Dipole Resonance (PDR), when the number of neutrons in excess increases. We show that the total energy-weighted sum rule exhausted by this mode has a linear dependence with the square of isospin I=(N-Z)/A, again sensitive to the slope of the symmetry energy with density. Therefore the polarization effects in the isovector density have to play an important role in the dynamics of PDR. These results provide additional hints in the investigations aiming to extract the properties of symmetry energy below saturation.

Dynamics of resonances in strongly interacting systems

The effects of the propagation of particles which have a finite life-time and an according broad distribution in their mass spectrum are discussed in the context of a transport descriptions. In the first part some example cases of mesonic modes in nuclear matter at finite densities and temperatures are presented. These equilibrium calculations illustrate the dynamical range of spectral distributions to be adequately covered by non-equilibrium description of the dynamics of two nuclei colliding at high energies. The second part addresses the problem of transport descriptions which properly account for the damping width of the particles. A systematic and general gradient approximation is presented in the form of diagrammatic rules which permit to derive a self-consistent transport scheme from the Kadanoff-Baym equation. The scheme is conserving and thermodynamically consistent provided the self-energies are obtained within the phi-derivable two-particle irreducible (2PI) method of Baym. The merits, the limitations and partial cures of the limitations of this transport scheme are discussed in detail.

Analysis of Boltzmann-Langevin dynamics in nuclear matter

The Boltzmann-Langevin dynamics of harmonic modes in nuclear matter is analyzed within linear-response theory, both with an elementary treatment and by using the frequency-dependent response function. It is shown how the source terms agitating the modes can be obtained from the basic BL correlation kernel by a simple projection onto the associated dual basis states, which are proportional to the RPA amplitudes and can be expressed explicitly. The source terms for the correlated agitation of any two such modes can then be extracted directly, without consideration of the other modes. This facilitates the analysis of collective modes in unstable matter and makes it possible to asses the accuracy of an approximate projection technique employed previously.

Quantal effects on growth of instabilities in nuclear matter

The growth rates of unstable modes in nuclear matter are investigated using a quantal dispersion relation. Calculations carried out with a realistic finite range potential show that unstable modes with wave number larger than the Fermi momentum are strongly suppressed, due to the quantal effect, in the mean field evolution. The observed consequence is the shift of the most important modes towards longer wave lengths.

Effect of memory time on the agitation of unstable modes in nuclear matter.

The spontaneous agitation of collective modes in unstable nuclear matter is addressed with an extended Boltzmann-Langevin (BL) theory that incorporates a memory time in the stochastic force. The growth of the modes is then governed by effective diffusion coefficients which are renormalized by time-dependent factors, relative to the standard treatment. These correction factors deviate significantly from unity in the most unstable domain of the density-temperature phase plane, indicating the importance of including a memory time in numerical BL simulations of nuclear dynamics.

Landau damping in infinite nuclear matter

Landau damping is a form of one-body damping which is important for the study of collective motion in nuclei. There are two different approaches to the theory, one due to Landau and the other to van Kampen. The equivalence of the two methods is discussed in the context of RPA collective modes in nuclear matter.

SOUND-LIKE COLLECTIVE MODE EXCITATION WITH PION ABSORPTION IN NUCLEAR MATTER

The relativistic mean field theory consistent with bulk properties of nuclear matter is extended to study the excitations of the sound-like collective modes in nuclear matter. Corresponding relativistic mean field equations are solved numerically and self-consis-tently. The effective mass of nucleon the speed of the sound and the amplitude of the sound-like solution are calculated. When the nuclear density is near or greater than the saturation density, the sound-like non-trivial solution could be found.

The propagation and damping of the collective modes in nuclear matter

In this work we study the properties of the collective modes in nuclear matter in the four available longitudinal channels. For the calculations we selected tour different effective interactions. The particularly successful one was the finite-range interaction with density-dependent part Dl. No instabilities appeared in any channel and the Landau parameters deduced from it reproduce satisfactorily some previous microscopic calculations with the Reid soft-core potential G-matrix. The forward scattering amplitude sum rule, satisfied to a very good accuracy with Dl, is discussed in some detail.