Quantum Inverse Scattering Theory and Nucleon-Nucleon Potentials
The Gel’fand-Levitan and Marchenko quantum inverse scattering theory has been applied to construct nucleón nucleon (NN) potentials. Its aim was to use inversion theory as a mean to construct local and energy independent channel potentials from meson-theoretical predictions of phase shifts, or phase shift analyses results to NN data. Various derivations of the fundamental equations have been studied to facilitate calculations with existing data. A new integral equation has also been found which relates the Gel’fand-Levitan and Marchenko output kernels in a transparent way. For application, a most practical form of the theory is deduced by starting with a rational function representation of the phase shift data and by using Padé approximants for e z , therewith rational representations of the S-matrix, Jost functions and other useful quantities are determined. The excellent reproductive power was studied using both fundamental equations and with the Reid soft core potential and their phase shifts respectively. Serious results use the meson theoretical phase shifts from the Paris and the Bonn groups, and experimental phases from Arndt et al. Finally, half off-shell T-matrices were generated to compare the exact meson theoretical results with those of inversion and it is found that phase equivalent interactions have essentially the same off-shell behaviour for any physically significant range of momenta.
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