  We review briefly the fundamental equations of a semi-microscopic
core-particle coupling method that makes no reference to an intrinsic system of
coordinates. We then demonstrate how an intrinsic system can be introduced in
the strong coupling limit so as to yield a completely equivalent formulation.
It is emphasized that the conventional core-particle coupling calculation
introduces a further approximation that avoids what has hitherto been the most
time-consuming feature of the full theory, and that this approximation can be
introduced either in the intrinsic system, the usual case, or in the laboratory
system, our preference. A new algorithm is described for the full theory that
largely removes the difference in complexity between the two types of
calculation. Comparison of the full and approximate theories for some
representative cases provides a basis for the assessment of the accuracy of the
traditional approach. We find that for well-deformed nuclei, e.g. 157Gd and
157Tb, the core-coupling method and the full theory give similar results.
