The Formation of a Rational S Matrix Using Phase Shifts from Elastic Scattering
Abstract
Three linear methods for constructing a rational S matrix from phase shifts are presented and compared. Applications to ^{1}S_{0} neutronproton elastic scattering data and to potential model problems show them to be efficient and in some cases superior to the NewtonRaphson (NR) and LevenbergMarquardt (LM) methods. The relative power of the three methods is seen to depend upon the smoothness of the data. One exacting test we have made is to take as data some phase shifts computed to high accuracy from a spinaveraged NN potential of Malfliet and Tjon (MTV). We truncate the MTV potential at different ranges R. The known analytic structure resulting from the truncation, including Gamow state poles, is stably reproduced. One method, which we designate as KKH, is superior in this problem with smooth data. In another class of problems, when even small random noise is injected into our neutronproton data, another method, which we label HY, is superior.' In this ease, LM, NR, and KKH are sometimes completely ineffective. Slight improvements are sometimes made with NR or LM iterations after the other methods have achieved their optimum parameter values. Therefore, we recommend that all five methods be programmed together as different options. Such a program should contain a number of important rational function checks.
 Publication:

Journal of Computational Physics
 Pub Date:
 October 1988
 DOI:
 10.1016/00219991(88)900617
 Bibcode:
 1988JCoPh..78..481Y