  This is a study of quasi-discrete Bogoliubov quasi-particles in a spherically
symmetric harmonic trap. We first evaluate analytically the aymptotic energy
shifts of the high energy modes and find them to have $1/sqrt(n)$ dependence on
the number of radial nodes, $n$, consistent with earlier semiclassical
discussions. To address the question of the widths or decay rates, we attempt
to clarify previous discussions by deriving an implicit equation for the widths
from an assumption of exponential decay. Numerically, we study the trends in
the behavior of the widths as a function of temperature, energy, particle
number and scattering lengths. In particular, we find that the width due to
Landau decay rises rapidly at low $n$ and then declines, while the Beliaev
decay rate rises slowly with $n$. As temperature goes to zero, Beliaev decay
reaches a constant (>0 for n>0), while the Landau decay rate goes to zero. The
decay rate is approximately linear in the s-wave scattering length.
