Elasticity of neutron star mantle: improved compressible liquid drop model for cylindrical phases

Neutron stars are the densest objects in the Universe. They have microscopically homogeneous core and heterogeneous crust. In particular, there may be a specific layer inside neutron stars, the mantle, which consists of substantially non-spherical nuclei immersed in a background of relativistic degenerate electrons and quasi-free neutrons. In this paper we reconsider transverse shear modulus for cylindrical phases of the mantle within the framework of compressible liquid drop model. We demonstrate that transverse shear affects the shape of nuclear clusters: their cross-section becomes elliptical. This effect reduces respective elastic constant. Using a simple model we perform all derivations analytically and obtain the expression for the transverse shear modulus, which can be useful for astrophysical applications.