Inversion schemes for momentum dependent nucleon-nucleon potentials

Some well established nucleon-nucleon (NN) potentials include a term proportional to the square of the momentum (Paris, Nijmegen). For uncoupled channels NN-potentials of this type can be obtained from NN-phase shifts via an inversion scheme based on Darboux-Crum-Krein (DCK) transformations which was developed at the institute a few years ago. Apart from the phase shifts the inversion scheme requires also the input of the momentum dependent term of the potential. By varying this term sets of phase equivalent potentials with different momentum dependence can be constructed via inversion. These sets of potentials can be used to study the influence of the non-locality on many-body observables systematically. In the first part of the thesis the inversion scheme has been implemented numerically and applied for the construction of a set of phase equivalent NN-potentials for uncoupled channels from the phase shifts of a given model potential. The main goal of the thesis was the generalization of the DCK-transformations to a matrix form which is presented in full detail. The new inversion schemes can be used to calculate momentum dependent NN-potentials for partial waves which are coupled via a tensor force. For this special case a method to find a suitable representation of the scattering data - including bound states - is given. First applications of this new inversion method for coupled channels are also presented in this work. (author)