  The properties of $\isotope[12]{C}$, $\isotope[16]{O}$, and
$\isotope[20]{Ne}$ nuclei in strong magnetic fields $B\simeq 10^{17}\,$G are
studied in the context of strongly magnetized neutron stars and white dwarfs.
The SKY3D code is extended to incorporate the interaction of nucleons with the
magnetic field and is utilized to solve the time-independent Hartree-Fock
equations with a Skyrme interaction on a Cartesian three-dimensional grid. The
numerical solutions demonstrate a number of phenomena, which include a
splitting of the energy levels of spin-up and -down nucleons, spontaneous
rearrangment of energy levels in $\isotope[16]{O}$ at a critical field, which
leads to jump-like increases of magnetization and proton current in this
nucleus, and evolution of the intrinsically deformed $\isotope[20]{Ne}$ nucleus
towards a more spherical shape under increasing field strength. Many of the
numerical features can be understood within a simple analytical model based on
the occupation by the nucleons of the lowest states of the harmonic oscillator
in a magnetic field.
