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

Carbon-oxygen-neon mass nuclei in superstrong magnetic fields