THE TRANSITION MATRIX FOR NUCLEON-NUCLEON SCATTERING
As part of a study of the influence of off-the-energyshell effects on the optical potential for nucleon-nucleus scattering, a method is presented for the calculation, via the reactance matrix, of the nucleon-nucleon transition matrix in terms of an internucleon potential and the scattering amplitude. The singular integral equations for the partial-wave amplitudes of the reactance matrix are reduced to a Fredholm form which contains the scattering amplitude parametrically. The iteration solution of the Fredholm equations is shown to be generally unreliable; however, the zeroth-order iteration approximates the exact solution quite well near the energy-shell. The replacement of the kernals of the integral equations by separable functions is discussed; the validity of such an approximation is illustrated. The requirement that the solutions of the (exact) Fredholm equations be consistant with the original singular integral equations yields a solution for the scattering amplitude ia terms of the resolvent kernels of the Fredholm equations. The entire of a hard-core being present is the nucleon-nucleon interaction. (auth)
- Research Organization:
- Brown Univ., Providence
- NSA Number:
- NSA-15-015186
- OSTI ID:
- 4042171
- Report Number(s):
- TID-12165
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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