  We propose a new, more realistic, description of the perturbed gravitational
potential of spiral galaxies, with spiral arms having Gaussian-shaped groove
profiles. We investigate the stable stellar orbits in galactic disks, using the
new perturbed potential. The influence of the bulge mass on the stellar orbits
in the inner regions of a disk is also investigated. The new description offers
the advantage of easy control of the parameters of the Gaussian profile of its
potential. We find a range of values for the perturbation amplitude from 400 to
800 km^2 s^{-2} kpc^{-1} which implies a maximum ratio of the tangential force
to the axisymmetric force between 3% and 6%, approximately. Good
self-consistency of arm shapes is obtained between the Inner Lindblad resonance
(ILR) and the 4:1 resonance. Near the 4:1 resonance the response density starts
to deviate from the imposed logarithmic spiral form. This creates bifurcations
that appear as short arms. Therefore the deviation from a perfect logarithmic
spiral in galaxies can be understood as a natural effect of the 4:1 resonance.
Beyond the 4:1 resonance we find closed orbits which have similarities with the
arms observed in our Galaxy. In regions near the center, in the presence of a
massive bulge, elongated stellar orbits appear naturally, without imposing any
bar-shaped potential, but only extending the spiral perturbation a little
inward of the ILR. This suggests that a bar is formed with a half-size around 3
kpc by a mechanism similar to that of the spiral arms. The potential energy
perturbation that we adopted represents an important step in the direction of
self-consistency, compared to previous sine function descriptions of the
potential. Our model produces a realistic description of the spiral structure,
able to explain several details that were not yet understood.
