Linear Least-Squares Analysis and Effective Interactions
In the following we exhibit a few results from the application of the method of singular value analysis (SVA), a particular form of linear least-squares analysis,1 to two sets of experimental two-body matrix elements, the 63 Chung-Wildenthal (CW) matrix elements2 for the 1d5/2, 2s1/2, 1d3/2 shells (A ≈ 20–40) and the best 84 matrix elements from the work of Schiffer and True (ST).3 The latter cover the atomic weight range of A ≈ 40 to 200 and nine shells from 1d3/2 to 1i13/2. Our purpose is the extraction of a first-order set of strength parameters for an effective interaction of minimum rank and simple form for each set or both sets of data. The ranges, being non-linear in their effects, are investigated separately. In this work we consider mainly local potential forms. (This is not a limitation of the approach.) The SVA method is well-suited to this problem since it was developed for and extensively applied to the analysis of satellite trajectories and the like,1 where similar over-determined problems arise.
KeywordsMatrix Element Effective Interaction Minimum Rank Tensor Force Satellite Trajectory
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