Abstract
Recent progress in few-body problem physics based on the three-body Faddeev equations is reviewed for three-related fields. The first field involves the description of light nuclear reactions in terms of multi-channel three-body Faddeev equations. The second field is the investigation of the two- and three-body threshold behaviors for the NNπ system using the three-body Faddeev equations, where the π D and the NN′ or N-(Nπ ) scattering lengths are calculated, and also we show that the NN′ potential has a long range term of 1/r 2 form. The third is a new Coulomb treatment in terms of a generalized screening range to describe on-shell Coulomb amplitudes which is useful in the threebody Faddeev equations. This procedure reproduces both of the Coulomb phase shift and the wave function from the electron-electron to the heavy-ion-heavy-ion systems.
Highlights
1.1 Nuclear reactions In the numerical approach to the light nuclear reactions, the exchange dynamics of a few-nucleons or the light nuclear-clusters are dominant for large momentum transfer and the details of the nuclear force frequently appear
Beside the alpha-particle, realistic nuclei are constructed by the proton, neutron, d, t, 3He, 12C, 16O, 20Ne, 24Mg, 28Si, 32S, and so on. Those structures can be seen by cooling the A-nucleons with the anti-symmetrized molecular dynamics (AMD)-method [2], or by the Jacobi-coordinate based AMD (JAMD) [3]
Each three-cluster dynamics is described by the three-body Faddeev equations; for M ≥ 2, the equations are mixed via the two-cluster subsystem with a common spectator particle
Summary
1.1 Nuclear reactions In the numerical approach to the light nuclear reactions, the exchange dynamics of a few-nucleons or the light nuclear-clusters are dominant for large momentum transfer and the details of the nuclear force frequently appear. Beside the alpha-particle, realistic nuclei are constructed by the proton, neutron, d, t, 3He, 12C, 16O, 20Ne, 24Mg, 28Si, 32S, and so on Those structures can be seen by cooling the A-nucleons with the anti-symmetrized molecular dynamics (AMD)-method [2], or by the Jacobi-coordinate based AMD (JAMD) [3]. One can say that the A-body Faddeev equations are the most powerful method for light nuclear reactions, the increase in numerical cost and the advances in hardware are always put in the balance. At this stage, the three-cluster Faddeev equations can represent A-nucleon reaction systems by using the coupled-channel method with the three-cluster potentials which will be presented in the section 2
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