Effects of neutrino trapping on thermodynamic properties of nuclear “pasta” Original Research Article

Geometrical structure of matter at subnuclear densities is investigated in the presence of a degenerate gas of neutrinos as encountered in stellar collapse. The crystalline phases with spherical, cylindrical and planar nuclei as well as with spherical and cylindrical nuclear bubbles are considered by using a compressible liquid-drop model. This model allows for uncertainties in the lepton fraction View the MathML source in addition to those in the nuclear surface tension View the MathML source and in the proton chemical potential in bulk neutron matter View the MathML source. The phase diagrams obtained at zero temperature show that only the phases with rod-like and slab-like nuclei occur at typical values of View the MathML source, View the MathML source and View the MathML source, whereas the bubble phases, especially with spherical bubbles, are at best expected at hypothetically low values of View the MathML source and/or View the MathML source. For the rod-like and slab-like nuclei, thermally induced displacements are calculated from their respective elastic constants. It is found that at temperatures appropriate to supernova cores, thermal fluctuations would destroy a layered lattice of slab-like nuclei rather than a triangular lattice of rod-like nuclei, almost independently of the nuclear models and of the degree of the neutrino degeneracy.