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 Y-L in addition to those in the nuclear surface tension E-surf and in the proton chemical potential in bulk neutron matter mu ((0))(p). The phase diagrams obtained at zero temperature show that only the phases with rod-like and slab-like Iluclei occur at typical values of Y-L, E-surf and mu ((0))(p). whereas the bubble phases, especially with spherical bubbles, are at best expected at hypothetically low values of Y-L and/or E-surf 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. (C) 2001 Elsevier Science B.V, All rights reserved. [References: 19]
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