The Pion three nucleon problem with two cluster connected kernel equations

Canton, L.

doi:10.1103/PhysRevC.58.3121

The Pion three nucleon problem with two cluster connected kernel equations

L. Canton
(
- INFN, Padua
)

Jun, 1998

20 pages

Published in:

Phys.Rev.C 58 (1998) 3121-3142

e-Print:

nucl-th/9806061 [nucl-th]

DOI:

10.1103/PhysRevC.58.3121

Report number:

DFPD-98-TH-22

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Abstract:

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.

nuclear physics
many-body problem: (3nucleon pi)
model: cluster
integral equations
fragmentation
pseudoparticle
bound state: (3nucleon)
Feynman graph
scattering amplitude

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