We address a long standing problem concerning the scale behaviour of parton densities in the low x, low Q 2 domain. We emphasize the important role of absorptive corrections at low x and use knowledge of diffractive deep inelastic scattering to exclude the absorptive effect from conventional deep inelastic data. In this way we obtain a significantly different low x behaviour of the gluon density, which is now much better described by linear DGLAP evolution. Accounting also for a second power correction, which arises from the freezing of α s at low Q 2 , leads to an essentially flat behaviour of the low x gluon density.

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We study the nuclear isentropic equation of state for a stellar matter composed of nucleons, hyperons, and Δ-resonances. We investigate different snapshots of the evolution of a neutron star, from its birth as a lepton-rich protoneutron star in the aftermath of a supernova explosion to a lepton-poor regime when the star starts cooling to a catalyzed configuration. We use a relativistic model within the mean-field approximation to describe the hot stellar matter and adopt density-dependent couplings adjusted by the DDME2 parameterization. We use baryon-meson couplings for the spin-1/2 baryonic octet and spin-3/2 decuplet determined in a unified manner relying on SU(6) and SU(3) symmetry arguments. We observe that Λ is the dominant exotic particle in the star at different entropies for both neutrino-free and neutrino-trapped stellar matter. For a fixed entropy, the inclusion of new particles (hyperons and/or delta resonances) in the stellar matter decreases the temperature. Also, an increase in entropy per baryon (1 to 2) with decreasing lepton number density (0.4 to 0.2) leads to an increase in stellar radii and a decrease in its mass due to neutrino diffusion. In the neutrino transparent matter, the radii decrease from entropy per baryon 2 to T = 0 without a significant change in stellar mass.

The presence of nuclear pasta is expected to modify the transport properties in the mantle of neutron stars. The non-spherical geometry of the pasta nuclear clusters leads to anisotropies in the collision frequencies, impacting the thermal and electrical conductivity. We derive analytical expressions for the anisotropic collision frequencies using the Boltzmann equation in the relaxation time approximation. The average parallel, perpendicular and Hall electrical conductivities are computed in the high-temperature regime above crustal melting, considering incoherent elastic electron-pasta scattering and randomly oriented pasta structures. Numerical values are obtained at different densities and temperatures by using the IUFSU parametrization of the non-linear Walecka model to determine the crustal structure. We find that the anisotropy of the collision frequencies grows with the length of the pasta structures and, independently of the magnetic field, the presence of rod and slab phases decreases the conductivity by more than one order of magnitude. Our numerical results indicate that, even if the pasta structures might survive above the crustal melting point, no strong anisotropies are to be expected in the conduction properties in this temperature regime, even in the presence of a very high magnetic field.