Formulation of few-body equations without partial waves
Abstract
A formalism is developed whereby the two-body Lippmann-Schwinger equation may be solved in momentum space without partial-wave decomposition. The integral equation derived is two-dimensional 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, time-reversal invariance, and particle symmetry. The method is applied to an equation defining the auxiliary k-matrix, along with the Heitler equation, which connects the solution from the Lippmann-Schwinger equation, the t-matrix, to the k-matrix. The three-dimensional 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 two-body 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 k-matrix solutions were practically model independent.
Degree
Ph.D.
Advisors
Kim, Purdue University.
Subject Area
Nuclear physics|Atoms & subatomic particles
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