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A method suggested by Koltun of matching two-nucleon energies and wave-function logarithmic derivatives is employed to deduce nuclear matrix elements directly from the energy dependence of N-N scattering phase shifts without specifying the N-N potential function. Tensor coupling is treated exactly and expressed directly in terms of the scattering data. Both the 1968 Yale and 1962 Hamada-Johnston phase shifts were used. The matrix elements were also computed by numerical integration of the coupled Schrodinger radial equations with a HJ potential. Results are compared and discussed. The agreement obtained between the two methods improves with increasing nuclear size (Decreasing oscillator energy h(omega)/2 pi. (Author)