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Register a new userLocalization and clustering in the nuclear Fermi liquid
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Using the framework of nuclear energy density functionals we examine the conditions for single-nucleon localization and formation of cluster structures in finite nuclei. We propose to characterize localization by the ratio of the dispersion of single-nucleon wave functions to the average inter-nucleon distance. This parameter generally increases with mass and describes the gradual transition from a hybrid phase in light nuclei, characterized by the spatial localization of individual nucleon states that leads to the formation of cluster structures, toward the Fermi liquid phase in heavier nuclei. Values of the localization parameter that correspond to a crystal phase cannot occur in finite nuclei. Typical length and energy scales in nuclei allow the formation of liquid drops, clusters, and halo structures.
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Axial breathing modes are studied within the nuclear energy--density--functional theory to discuss the modification of the nucleon effective mass produced beyond the mean--field approximation. This analysis is peformed with the subtracted second random--phase--approximation (SSRPA) model applied to two nuclei, $^{48}$Ca and $^{90}$Zr. Analyzing the centroid energies of axial breathing modes obtained with the mean--field--based random--phase approximation and with the beyond--mean--field SSRPA model, we estimate the modification (enhancement) of the effective mass which is induced beyond the mean field. This is done by employing a relation, obtained with the Landaus Fermi liquid theory, between the excitation frequency of axial modes to $sqrt{m/m^*}$, where $m$ ($m^*$) is the bare (effective) mass. Such an enhancement of the effective mass is discussed in connection with the renormalization of single--particle excitation energies generated by the energy--dependent SSRPA self-energy correction. We find that the effective beyond--mean--field compression of the single--particle spectrum produced by the self--energy correction is coherent with the increase of the effective mass estimated from the analysis of axial breathing modes.
An electron localization measure was originally introduced to characterize chemical bond structures in molecules. Recently, a nucleon localization based on Hartree-Fock densities has been introduced to investigate $alpha$-cluster structures in light nuclei. Compared to the local nucleonic densities, the nucleon localization function has been shown to be an excellent indicator of shell effects and cluster correlations. Using the spatial nucleon localization measure, we investigate the emergence of fragments in fissioning heavy nuclei. To illustrate basic concepts of nucleon localization, we employ the self-consistent energy density functional method with a quantified energy density functional optimized for fission studies. We study the particle densities and spatial nucleon localization distributions along the fission pathways of $^{264}$Fm, $^{232}$Th and $^{240}$Pu. We demonstrate that the fission fragments are formed fairly early in the evolution, well before scission. We illustrate the usefulness of the localization measure by showing how the hyperdeformed state of $^{232}$Th can be understood in terms of a quasimolecular state made of $^{132}$Sn and $^{100}$Zr fragments. Compared to nucleonic distributions, the nucleon localization function more effectively quantifies nucleonic clustering: its characteristic oscillating pattern, traced back to shell effects, is a clear fingerprint of cluster/fragment configurations. This is of particular interest for studies of fragment formation and fragment identification in fissioning nuclei.
The short-range and tensor components of the bare nucleon-nucleon interaction induce a sizeable depletion of low momenta in the ground state of a nuclear many-body system. The self-consistent Greens function method within the ladder approximation provides an textit{ab-initio} description of correlated nuclear systems that accounts properly for these effects. The momentum distribution predicted by this approach is analyzed in detail, with emphasis on the depletion of the lowest momentum state. The temperature, density, and nucleon asymmetry (isospin) dependence of the depletion of the Fermi sea is clarified. A connection is established between the momentum distribution and the time-ordered components of the self-energy, which allows for an improved interpretation of the results. The dependence on the underlying nucleon-nucleon interaction provides quantitative estimates of the importance of short-range and tensor correlations in nuclear systems.
A brief introduction of the relationship of string percolation to the Quantum Chromo Dynamics (QCD) phase diagram is presented. The behavior of the Polyakov loop close to the critical temperature is studied in terms of the color fields inside the clusters of overlapping strings, which are produced in high energy hadronic collisions. The non-Abelian nature of the color fields implies an enhancement of the transverse momentum and a suppression of the multiplicities relative to the non overlapping case. The prediction of this framework are compared with experimental results from the SPS, RHIC and LHC for $pp$ and AA collisions. Rapidity distributions, probability distributions of transverse momentum and multiplicities, Bose-Einstein correlations, elliptic flow and ridge structures are used to evaluate these comparison. The thermodynamical quantities, the temperature, and energy density derived from RHIC and LHC data and Color String Percolation Model (CSPM) are used to obtain the shear viscosity to entropy density ratio ($eta/s$). It was observed that the inverse of ($eta/s$) represents the trace anomaly $Delta =(varepsilon-3P)/T^{4}$. Thus the percolation approach within CSPM can be successfully used to describe the initial stages in high energy heavy ion collisions in the soft region in high energy heavy ion collisions. The thermodynamical quantities, temperature and the equation of state are in agreement with the lattice QCD calculations. Thus the clustering of color sources has a clear physical basis although it cannot be deduced directly from QCD.
We present two novel relations between the quasiparticle interaction in nuclear matter and the unique low momentum nucleon-nucleon interaction in vacuum. These relations provide two independent constraints on the Fermi liquid parameters of nuclear matter. Moreover, the new constraints define two combinations of Fermi liquid parameters, which are invariant under the renormalization group flow in the particle-hole channels. Using empirical values for the spin-independent Fermi liquid parameters, we are able to compute the major spin-dependent ones by imposing the new constraints as well as the Pauli principle sum rules.
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