  The self-similar infall model (SSIM) is normally discussed in the context of
radial orbits in spherical symmetry. However it is possible to retain the
spherical symmetry while permitting the particles to move in Keplerian
ellipses, each having the squared angular momentum peculiar to their 'shell'.
The spherical 'shell', defined for example by the particles turning at a given
radius, then moves according to the radial equation of motion of a 'shell'
particle. The 'shell' itself has no physical existence except as an ensemble of
particles, but it is convenient to sometimes refer to the shells since it is
they that are followed by a shell code. In this note we find the distribution
of squared angular momentum as a function of radius that yields the NFW density
profile for the final dark matter halo. It transpires that this distribution is
amply motivated dimensionally. An effective 'lambda' spin parameter is roughly
constant over the shells. We also study the effects of angular momentum on the
relaxation of a dark matter system using a three dimensional representation of
the relaxed phase space.
