  We investigate an asteroseismic model of non-rotating paramagnetic neutron
star with core-crust stratification of interior pervaded by homogeneous
internal and dipolar external magnetic field, presuming that neutron degenerate
Fermi-matter of the star core is in the state of Pauli's paramagnetic permanent
magnetization caused by polarization of spin magnetic moments of neutrons along
the axis of magnetic field of collapsed massive progenitor. The magnetic
cohesion between metal-like crust and permanent-magnet-like core is considered
as playing a main part in the dynamics of starquake. Focus is laid on the
post-quake relaxation of the star by node-free torsional vibrations of highly
conducting crustal solid-state plasma, composed of nuclei embedded in the
degenerate Fermi-gas of relativistic electrons, about axis of magnetic field
frozen in the immobile paramagnetic core. Two scenarios of these axisymmetric
seismic vibrations are examined, in first of which these are considered as
maintained by combined action of Lorentz magnetic and Hooke's elastic forces
and in second one by solely Lorentz force. Based on the energy variational
method of magneto-solid-mechanical theory of elastic continuous medium, the
spectral formulae for the frequency and lifetime of this toroidal mode are
obtained and discussed in the context of theoretical treatment of recently
discovered quasi-periodic oscillations of the X-ray outburst flux from SGR
1806-20 and SGR 1900+14 as being produced by above seismic vibrations.
