Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The energy dependence of the $\pi N$ amplitude and the three-nucleon
  interaction   By calculating the contribution of the $\pi-\pi$ three-body force to the
three-nucleon binding energy in terms of the $\pi N$ amplitude using
perturbation theory, we are able to determine the importance of the energy
dependence and the contribution of the different partial waves of the $\pi N$
amplitude to the three-nucleon force. A separable representation of the
non-pole $\pi N$ amplitude allows us to write the three-nucleon force in terms
of the amplitude for $NN\rightarrow NN^*$, propagation of the $NNN^*$ system,
and the amplitude for $NN^*\rightarrow NN$, with $N^*$ being the $\pi N$
quasi-particle amplitude in a given state. The division of the $\pi N$
amplitude into a pole and non-pole gives a procedure for the determination of
the $\pi NN$ form factor within the model. The total contribution of the
three-body force to the binding energy of the triton for the separable
approximation to the Paris nucleon-nucleon potential (PEST) is found to be very
small mainly as a result of the energy dependence of the $\pi N$ amplitude, the
cancellation between the $S$- and $P$-wave $\pi N$ amplitudes, and the soft
$\pi NN$ form factor.

1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
2
The categories of this paper are: math
0
The categories of this paper are: hep-ph
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex