  We present a theoretical study of degeneracy breaking due to short-ranged
impurities in finite, single-wall, metallic carbon nanotubes. The effective
mass model is used to describe the slowly varying spatial envelope
wavefunctions of spinless electrons near the Fermi level at two inequivalent
valleys (K-points) in terms of the four component Dirac equation for massless
fermions, with the role of spin assumed by pseudospin due to the relative
amplitude of the wave function on the sublattice atoms (``A'' and ``B''). Using
boundary conditions at the ends of the tube that neither break valley
degeneracy nor mix pseudospin eigenvectors, we use degenerate perturbation
theory to show that the presence of impurities has two effects. Firstly, the
position of the impurity with respect to the spatial variation of the envelope
standing waves results in a sinusoidal oscillation of energy level shift as a
function of energy. Secondly, the position of the impurity within the hexagonal
graphite unit cell produces a particular 4 by 4 matrix structure of the
corresponding effective Hamiltonian. The symmetry of this Hamiltonian with
respect to pseudospin flip is related to degeneracy breaking and, for an
armchair tube, the symmetry with respect to mirror reflection in the nanotube
axis is related to pseudospin mixing.
