  The Busch-formula relates the energy-spectrum of two point-like particles
interacting in a 3-D isotropic Harmonic Oscillator trap to the free scattering
phase-shifts of the particles. This formula is used to find an expression for
the \it shift \rm in the spectrum from the unperturbed (non-interacting)
spectrum rather than the spectrum itself. This shift is shown to be
approximately $\Delta=-\delta(k)/\pi\times dE$, where $dE$ is the spacing
between unperturbed energy levels. The resulting difference from the
Busch-formula is typically 1/2% except for the lowest energy-state and small
scattering length when it is 3%. It goes to zero when the scattering length
$\rightarrow \pm \infty$.
  The energy shift $\Delta$ is familiar from a relatedproblem, that of two
particles in a spherical infinite square-well trap of radius $R$ in the limit
$R\rightarrow \infty$. The approximation ishowever as large as 30% for finite
values of $R$, a situation quite different from the Harmonic Oscillator case.
  The square-well results for $R\rightarrow \infty$ led to the use ofin-medium
(effective) interactions in nuclear matter calculations that were $\propto
\Delta$ and known as the \it phase shift approximation \rm.Our results indicate
that the validity of this approximation depends on the trapitself, a problem
already discussed by DeWitt more than 50 years ago for acubical vs spherical
trap.
