  Here the line shape of the up- and down-spin one-particle spectral functions
at and in the (k,energy)-plane's vicinity of their cusp singularities is
studied for the Mott-Hubbard insulator described by the 1D Hubbard model with
one fermion per site at zero and finite magnetic fields. At zero field they can
be accessed in terms of electrons by photoemission experiments. At finite
field, such functions and corresponding interplay of correlations and
magnetic-field effects refer to an involved non-perturbative many-particle
problem that is poorly understood. The Mott-Hubbard gap that separates the
addition and removal spectral functions is calculated for all spin densities
and interaction values. The qualitative differences in the one-particle
properties of the Mott-Hubbard insulator and corresponding doped insulator are
also investigated. The relation of our theoretical results and predictions to
both condensed-matter and ultracold spin-1/2 atom systems is discussed.
