Scaling Functions and Superscaling in Medium and Heavy Nuclei

The scaling function $f(\psi')$ for medium and heavy nuclei with $Z\neq N$ for which the proton and neutron densities are not similar is constructed within the coherent density fluctuation model (CDFM) as a sum of the proton and neutron scaling functions. The latter are calculated in the cases of $^{62}$Ni, $^{82}$Kr, $^{118}$Sn, and $^{197}$Au nuclei on the basis of the corresponding proton and neutron density distributions which are obtained in deformed self-consistent mean-field Skyrme HF+BCS method. The results are in a reasonable agreement with the empirical data from the inclusive electron scattering from nuclei showing superscaling for negative values of $\psi'$, including those smaller than -1. This is an improvement over the relativistic Fermi gas (RFG) model predictions where $f(\psi')$ becomes abruptly zero for $\psi'\leq -1$. It is also an improvement over the CDFM calculations made in the past for nuclei with $Z\neq N$ assuming that the neutron density is equal to the proton one and using only the phenomenological charge density.Comment: 4 pages, 1 figure, ReVTeX, accepted for publication in Phys. Rev.

Surface properties of neutron-rich exotic nuclei: A source for studying the nuclear symmetry energy

We study the correlation between the thickness of the neutron skin in finite nuclei and the nuclear symmetry energy for isotopic chains of even-even Ni, Sn, and Pb nuclei in the framework of the deformed self-consistent mean-field Skyrme HF+BCS method. The symmetry energy, the neutron pressure and the asymmetric compressibility in finite nuclei are calculated within the coherent density fluctuation model using the symmetry energy as a function of density within the Brueckner energy-density functional. The mass dependence of the nuclear symmetry energy and the neutron skin thickness are also studied together with the role of the neutron-proton asymmetry. A correlation between the parameters of the equation of state (symmetry energy and its density slope) and the neutron skin is suggested in the isotopic chains of Ni, Sn, and Pb nuclei.Comment: 13 pages, 10 figures. Accepted for publication in Phys. Rev.

Superscaling in Nuclei: A Search for Scaling Function Beyond the Relativistic Fermi Gas Model

We construct a scaling function $f(\psi^{\prime})$ for inclusive electron scattering from nuclei within the Coherent Density Fluctuation Model (CDFM). The latter is a natural extension to finite nuclei of the Relativistic Fermi Gas (RFG) model within which the scaling variable $\psi^{\prime}$ was introduced by Donnelly and collaborators. The calculations show that the high-momentum components of the nucleon momentum distribution in the CDFM and their similarity for different nuclei lead to quantitative description of the superscaling in nuclei. The results are in good agreement with the experimental data for different transfer momenta showing superscaling for negative values of $\psi^{\prime}$, including those smaller than -1.Comment: 16 pages, 5 figures, submitted for publication to Phys. Rev.

Superscaling and Neutral Current Quasielastic Neutrino-Nucleus Scattering beyond the Relativistic Fermi Gas Model

The superscaling analysis is extended to include quasielastic (QE) scattering via the weak neutral current of neutrinos and antineutrinos from nuclei. The scaling function obtained within the coherent density fluctuation model (used previously in calculations of QE inclusive electron and charge-changing (CC) neutrino scattering) is applied to neutral current neutrino and antineutrino scattering with energies of 1 GeV from $^{12}$C with a proton and neutron knockout (u-channel inclusive processes). The results are compared with those obtained using the scaling function from the relativistic Fermi gas model and the scaling function as determined from the superscaling analysis (SuSA) of QE electron scattering.Comment: 10 pages, 6 figures, published in Phys. Rev.

Symmetry energy of deformed neutron-rich nuclei

The symmetry energy, the neutron pressure and the asymmetric compressibility of deformed neutron-rich even-even nuclei are calculated on the examples of Kr and Sm isotopes within the coherent density fluctuation model using the symmetry energy as a function of density within the Brueckner energy-density functional. The correlation between the thickness of the neutron skin and the characteristics related with the density dependence of the nuclear symmetry energy is investigated for isotopic chains of these nuclei in the framework of the self-consistent Skyrme-Hartree-Fock plus BCS method. Results for an extended chain of Pb isotopes are also presented. A remarkable difference is found in the trend followed by the different isotopic chains: the studied correlations reveal a smoother behavior in the Pb case than in the other cases. We also notice that the neutron skin thickness obtained for $^{208}$Pb with SLy4 force is found to be in a good agreement with recent data.Comment: 14 pages, 10 figures, 2 tables, accepted for publication in Physical Review

Effects of turbulent mixing on critical behaviour in the presence of compressibility: Renormalization group analysis of two models

Critical behaviour of two systems, subjected to the turbulent mixing, is studied by means of the field theoretic renormalization group. The first system, described by the equilibrium model A, corresponds to relaxational dynamics of a non-conserved order parameter. The second one is the strongly non-equilibrium reaction-diffusion system, known as Gribov process and equivalent to the Reggeon field theory. The turbulent mixing is modelled by the Kazantsev-Kraichnan "rapid-change" ensemble: time-decorrelated Gaussian velocity field with the power-like spectrum k^{-d-\xi}. Effects of compressibility of the fluid are studied. It is shown that, depending on the relation between the exponent \xi and the spatial dimension d, the both systems exhibit four different types of critical behaviour, associated with four possible fixed points of the renormalization group equations. The most interesting point corresponds to a new type of critical behaviour, in which the nonlinearity and turbulent mixing are both relevant, and the critical exponents depend on d, \xi and the degree of compressibility. For the both models, compressibility enhances the role of the nonlinear terms in the dynamical equations: the region in the d-\xi plane, where the new nontrivial regime is stable, is getting much wider as the degree of compressibility increases. In its turn, turbulent transfer becomes more efficient due to combined effects of the mixing and the nonlinear terms.Comment: 25 pages, 4 figure

Scaling Function, Spectral Function and Nucleon Momentum Distribution in Nuclei

The link between the scaling function extracted from the analysis of (e,e') cross sections and the spectral function/momentum distribution in nuclei is revisited. Several descriptions of the spectral function based on the independent particle model are employed, together with the inclusion of nucleon correlations, and effects of the energy dependence arising from the width of the hole states are investigated. Although some of these approaches provide rough overall agreement with data, they are not found to be capable of reproducing one of the distinctive features of the experimental scaling function, namely its asymmetry. However, the addition of final-state interactions, incorporated in the present study using either relativistic mean field theory or via a complex optical potential, does lead to asymmetric scaling functions in accordance with data. The present analysis seems to indicate that final-state interactions constitute an essential ingredient and are required to provide a proper description of the experimental scaling function.Comment: 29 pages, 13 figures, accepted for publication in Physical Review

Effects of Turbulent Mixing on the Critical Behavior

Effects of strongly anisotropic turbulent mixing on the critical behavior are studied by means of the renormalization group. Two models are considered: the equilibrium model A, which describes purely relaxational dynamics of a nonconserved scalar order parameter, and the Gribov model, which describes the nonequilibrium phase transition between the absorbing and fluctuating states in a reaction-diffusion system. The velocity is modelled by the d-dimensional generalization of the random shear flow introduced by Avellaneda and Majda within the context of passive scalar advection. Existence of new nonequilibrium types of critical regimes (universality classes) is established.Comment: Talk given in the International Bogolyubov Conference "Problems of Theoretical and Mathematical Physics" (Moscow-Dubna, 21-27 August 2009

Superscaling in dilute Fermi gas and its relation to general properties of the nucleon momentum distribution in nuclei

The superscaling observed in inclusive electron scattering is described within the dilute Fermi gas model with interaction between the particles. The comparison with the relativistic Fermi gas (RFG) model without interaction shows an improvement in the explanation of the scaling function $f(\psi ')$ in the region $\psi ' < -1$, where the RFG result is $f(\psi ') = 0$. It is found that the behavior of $f(\psi ')$ for $\psi ' < -1$ depends on the particular form of the general power-law asymptotics of the momentum distribution $n(k)\sim 1/ k^{4+m}$ at large $k$. The best agreement with the empirical scaling function is found for $m\simeq 4.5$ in agreement with the asymptotics of $n(k)$ in the coherent density fluctuation model where $m = 4$. Thus, superscaling gives information about the asymptotics of $n(k)$ and the NN forces.Comment: 6 pages, 5 figures, accepted for publication in Physical Review

Effects of turbulent mixing on critical behaviour: Renormalization group analysis of the Potts model

Critical behaviour of a system, subjected to strongly anisotropic turbulent mixing, is studied by means of the field theoretic renormalization group. Specifically, relaxational stochastic dynamics of a non-conserved multicomponent order parameter of the Ashkin-Teller-Potts model, coupled to a random velocity field with prescribed statistics, is considered. The velocity is taken Gaussian, white in time, with correlation function of the form $\propto \delta(t-t') /|{\bf k}_{\bot}|^{d-1+\xi}$, where ${\bf k}_{\bot}$ is the component of the wave vector, perpendicular to the distinguished direction ("direction of the flow") --- the $d$-dimensional generalization of the ensemble introduced by Avellaneda and Majda [1990 {\it Commun. Math. Phys.} {\bf 131} 381] within the context of passive scalar advection. This model can describe a rich class of physical situations. It is shown that, depending on the values of parameters that define self-interaction of the order parameter and the relation between the exponent $\xi$ and the space dimension $d$, the system exhibits various types of large-scale scaling behaviour, associated with different infrared attractive fixed points of the renormalization-group equations. In addition to known asymptotic regimes (critical dynamics of the Potts model and passively advected field without self-interaction), existence of a new, non-equilibrium and strongly anisotropic, type of critical behaviour (universality class) is established, and the corresponding critical dimensions are calculated to the leading order of the double expansion in $\xi$ and $\epsilon=6-d$ (one-loop approximation). The scaling appears strongly anisotropic in the sense that the critical dimensions related to the directions parallel and perpendicular to the flow are essentially different.Comment: 21 page, LaTeX source, 7 eps figures. arXiv admin note: substantial text overlap with arXiv:cond-mat/060701