Formulation of FewBody Equations Without Partial Waves.
Abstract
A formalism is developed whereby the twobody LippmannSchwinger equation may be solved in momentum space without partialwave decomposition. The integral equation derived is twodimensional and so is amenable to direct numerical solution. A major component of the method is the reduction of the integral equation taking advantage of symmetries common in atomic and nuclear systems, such as parity conservation, timereversal invariance, and particle symmetry. The method is applied to an equation defining the auxiliary kmatrix, along with the Heitler equation, which connects the solution from the LippmannSchwinger equation, the tmatrix, to the kmatrix. The threedimensional technique is then applied to the NN system, for both the bound state (deuteron) and scattering problems. In calculating numerical results for the NN system, special numerical techniques are developed which include the angular variables appearing in the two body equations. In order to verify the soundness of our numerical techniques, the deuteron binding energy and phase shifts for twobody total angular momentum up to 30 are presented and compared to the partial wave results. Finally, a global comparison of some recent realistic NN interactions is presented. It is found that, even though the potential inputs tended to be vastly different, even for low momenta, the kmatrix solutions were practically model independent.
 Publication:

Ph.D. Thesis
 Pub Date:
 1994
 Bibcode:
 1994PhDT........58R
 Keywords:

 Physics: Nuclear; Physics: Atomic