Speaker: Wayne Polyzou (University of Iowa)
Title: The three-nucleon problem in Poincar\'e invariant quantum mechanics
Abstract:
I discuss a formulation of the three-nucleon problem that is suitable
for constructing realistic models of scattering reactions with beam
energies in the few GeV range. Scattering at these energies requires
a Poincar\'e invariant quantum treatment. Since the dynamics at these
energies is dominated by a finite number of degrees of freedom, it is
possible to model the dynamics using an exact unitary representation
of the Poincar\'e group on a few-particle Hilbert space. For the
three-nucleon case this representation can be constructed to have
cluster properties and satisfy a spectral condition. I show how
high-precision NN interactions, like AV18 or CD-Bonn, can be
reinterpreted as generating exact two-body unitary representations of
the Poincar\'e group that fit experimental two-body scattering data
and how cluster separability determines the structure of the
three-body dynamics up to three-body interactions. Low-energy
calculations using these realistic interactions illustrate the
difference between Galilean symmetric and Poincar\'e symmetric
calculations of the triton binding energy and the polarization
observable $A_y$. Scattering calculations up to 2 GeV, using a
Malfliet-Tjon interaction, are used to test the convergence of the
multiple scattering series and determine regions of the three-body
phase space which are sensitive to differences in the relativistic and
non-relativistic treatment. Exclusive breakup experiments at 508 MeV
are consistent with the predictions of this relativistic model.