A new extended target decomposition scheme

The conventional decomposition from a distributed target is to seek a solution of average single target M/sup T/, which preserves symmetry parameters A/sub 0/, C, and D and a part which consists solely of non-symmetric parameters B/sub 0//sup T/-B/sup T/, E/sup T/, and F/sup T/. These parameters with index T are determined easily from four equations. The novel feature is to create a variable A/sub 0//sup T/ in addition to the four non-symmetric target parameters of the old scheme. The new variable A/sub 0//sup N/ extracts out of the general symmetry-preserving A/sub 0/ a special target variable A/sub 0//sup T/, such that A/sub 0/=A/sub 0//sup T/+A/sub 0//sup N/. The A/sub 0//sup T/ now becomes part of the average single target parameters: A/sub 0//sup T/, B/sub 0//sup T/, B/sup T/, C, D, E/sup T/, F/sup T/, G, and H. In this scheme C, D, G, and H, the target symmetry and coupling parameters, are still preserved intact. What is new in the scheme is A/sub 0//sup T/ which before was A/sub 0/, "the generator and preservator of target symmetry". It is kind of ironic that the "symmetry-preserving" generator A/sub 0/ itself is not preserved in the new scheme, but is split into A/sub 0//sup T/ and A/sub 0//sup N/! That was why this new decomposition took so long in coming to development. The physical interpretation of the new scheme is a decomposition of the distributed target into a single average target M/sup T/ and an N-target (N here standing for non-symmetry) and a background cloud of spherical particles. The C, D, G, and H still are preserved intact but the symmetry generator A/sub 0/ is split, one part A/sub 0//sup T/ contributing to the average single target M/sup T/ and one new part A/sub 0//sup N/ (N stands for new here!) forms a background cloud of elementary spheres. An example is shown consisting of a cloud of dipoles being averaged into a single dipole, a non-symmetrical N-target, and a new background cloud of elementary spheres, determined by A/sub 0//sup N/.<>