A new extended target decomposition scheme

The conventional decomposition from a distributed target is to seek a solution of average single target M^T, which preserves symmetry parameters A₀, C, and D and a part which consists solely of non-symmetric parameters B₀^T-B^T, E^T, and F^T. These parameters with index T are determined easily from four equations. The novel feature is to create a variable A₀^T in addition to the four non-symmetric target parameters of the old scheme. The new variable A₀^N extracts out of the general symmetry-preserving A₀ a special target variable A₀^T, such that A₀=A₀^T+A₀^N. The A₀^T now becomes part of the average single target parameters: A₀^T, B₀^T, B^T, C, D, E^T, F^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 A₀^T which before was A₀, "the generator and preservator of target symmetry". It is kind of ironic that the "symmetry-preserving" generator A₀ itself is not preserved in the new scheme, but is split into A₀^T and A₀^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^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 A₀ is split, one part A₀^T contributing to the average single target M^T and one new part A₀^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 A₀^N.