Recent observations of the radiation from highly magnetized neutron stars have provided a wealth of information on these objects, but they have also raised many new questions. We study various aspects of the surfaces and magnetospheres of neutron stars, including the cohesive properties and condensation of the stellar surface, formation of magnetosphere acceleration zones, and the initiation and propagation of electron-positron cascades through the magnetosphere.

We present calculations of the electronic structure of matter in strong magnetic fields ranging from B = 10^12 G to 2x10^15 G, appropriate for observed magnetic neutron stars. Our calculations are based on the density functional theory. We find that condensed matter surfaces composed of hydrogen, helium, and carbon are all bound relative to individual atoms for B = 10^12 G or higher. Condensed iron surfaces, however, are only significantly bound for B > 10^14 G. We also present Hartree-Fock calculations of the polarization-dependent photoionization cross sections of the He atom in strong magnetic fields ranging from 10^12 G to 10^14 G.

We investigate several important astrophysical implications of our calculations of the cohesive property of magnetic condensed matter. We find that for sufficiently strong magnetic fields and/or low temperatures, the neutron star surface may be in a condensed state with little gas or plasma above it; such surface condensation may lead to the formation of a charge-depleted acceleration zone ("vacuum gap") in the magnetosphere above the stellar polar cap. We quantitatively determine the conditions for surface condensation and vacuum gap formation in magnetic neutron stars. We find that condensation can occur if the thermal energy kT of the neutron star surface is less than about 8% of its cohesive energy Qs, and that a vacuum gap can form if kT is less than about 4% of Qs.

We study the conditions for the onset of pair cascades in the magnetospheres of neutron stars and the related pulsar death line/boundary. We also present Monte Carlo simulations of the full pair cascade from onset to completion. Our calculations generalize previous works to the superstrong field regime. We find that curvature radiation is a viable mechanism for the initiation of pair cascades, but that resonant and nonresonant inverse Compton scatterings are not. Additionally, we obtain the final photon spectra and pair energy distribution functions of the cascade and find significant differences between their nature in high-field neutron stars and in moderate-field neutron stars.