Abstract
We study the binding energy of the three-nucleon system in relativistic models that use two different relativistic treatments of the potential that are phase equivalent to realistic NN interactions. One is based on a unitary scale transformation that relates the non-relativistic center-of-mass Hamiltonian to the relativistic mass (rest energy) operator and the other uses a non-linear equation that relates the interaction in the relativistic mass operator to the non-relativistic interaction. In both cases Lorentz-boosted interactions are used in the relativistic Faddeev equation to solve for the three-nucleon binding energy. Using the same realistic NN potentials as input, the solution of the relativistic three-nucleon Faddeev equation for 3 H shows slightly less binding energy than the corresponding nonrelativistic result. The effect of the Wigner spin rotation on the binding is very small.
Highlights
For up to 300 MeV proton energy, proton-deuteron scattering measurements have been analyzed with rigorous three-nucleon (3N) Faddeev calculations [1] based on the CD-Bonn potential [2] and the Tucson-Melbourne 3N force (3NF) [3]
In the following we want to demonstrate some recent results: in Section 2 we introduce the relativistic nucleonnucleon potentials constructed by the momentum scale transformation [17] (MST) and Coester-PieperSerduke scheme (CPS) methods, in Section 3 the construction of the boosted potentials is discussed, in Section 4 we give numerical results for the triton binding energy based on the Poincareinvariant Faddeev equation and in Section 5 we summarize
A phase-shift equivalent 2N potential vr in the relativistic 2N Schrodinger equation is related to the potential v in the nonrelativistic Schrodinger equation by the momentum scale transformation scheme and the Coester-PieperSerduke scheme
Summary
For up to 300 MeV proton energy, proton-deuteron (pd) scattering measurements have been analyzed with rigorous three-nucleon (3N) Faddeev calculations [1] based on the CD-Bonn potential [2] and the Tucson-Melbourne 3N force (3NF) [3]. Because the result may depend on the transformation of the nonrelativistic potential to a relativistic potential, a momentum scale transformation [17] (MST) was introduced without any additional parameters. This scale transformation method is not equivalent to the construction of a relativistic potential from a field theory. In the following we want to demonstrate some recent results: in Section 2 we introduce the relativistic nucleonnucleon potentials constructed by the MST and CPS methods, in Section 3 the construction of the boosted potentials is discussed, in Section 4 we give numerical results for the triton binding energy based on the Poincareinvariant Faddeev equation and in Section 5 we summarize
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