3 research outputs found
Practical approximation scheme for the pion dynamics in the three-nucleon system
We discuss a working approximation scheme to a recently developed formulation
of the coupled piNNN-NNN problem. The approximation scheme is based on the
physical assumption that, at low energies, the 2N-subsystem dynamics in the
elastic channel is conveniently described by the usual 2N-potential approach,
while the explicit pion dynamics describes small, correction-type effects.
Using the standard separable-expansion method, we obtain a dynamical equation
of the Alt-Grassberger-Sandhas (AGS) type. This is an important result, because
the computational techniques used for solving the normal AGS equation can also
be used to describe the pion dynamics in the 3N system once the matrix
dimension is increased by one component. We have also shown that this
approximation scheme treats the conventional 3N problem once the pion degrees
of freedom are projected out. Then the 3N system is described with an extended
AGS-type equation where the spin-off of the pion dynamics (beyond the 2N
potential) is taken into account in additional contributions to the driving
term. These new terms are shown to reproduce the diagrams leading to modern
3N-force models. We also recover two sets of irreducible diagrams that are
commonly neglected in 3N-force discussions, and conclude that these sets should
be further investigated, because a claimed cancellation is questionable.Comment: 18 pages, including 5 figures, RevTeX, Eps
Why is the three-nucleon force so odd?
By considering a class of diagrams which has been overlooked also in the most
recent literature on three-body forces, we extract a new contribution to the
three-nucleon interaction which specifically acts on the triplet odd states of
the two nucleon subsystem. In the static approximation, this 3N-force
contribution is fixed by the underlying 2N interaction, so in principle there
are no free parameters to adjust. The 2N amplitude however enters in the 3NF
diagram in a form which cannot be directly accessed or constrained by NN
phase-shift analysis. We conclude that this new 3N-force contribution provides
a mechanism which implies that the presence of the third nucleon modifies the
p-wave (and possibly the f-wave) components of the 2N subsystem in the
triplet-isotriplet channels.Comment: 10 Pages, 7 figures, RevTeX, twocolumn, epsf (updated version with
minor changes
The pion-three-nucleon problem with two-cluster connected-kernel equations
It is found that the coupled piNNN-NNN system breaks into fragments in a
nontrivial way. Assuming the particles as distinguishable, there are indeed
four modes of fragmentation into two clusters, while in the standard three-body
problem there are three possible two-cluster partitions and conversely the
four-body problem has seven different possibilities. It is shown how to
formulate the pion-three-nucleon collision problem through the
integral-equation approach by taking into account the proper fragmentation of
the system. The final result does not depend on the assumption of separability
of the two-body t-matrices. Then, the quasiparticle method a' la
Grassberger-Sandhas is applied and effective two-cluster connected-kernel
equations are obtained. The corresponding bound-state problem is also
formulated, and the resulting homogeneous equation provides a new approach
which generalizes the commonly used techniques to describe the three-nucleon
bound-state problem, where the meson degrees of freedom are usually suppressed.Comment: 20 pages, REVTeX, with 3 COLOR figures (PostScript