The Energy dependence of the pi N amplitude and the three nucleon interaction

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.

Note:

RevTex file, 36 pages, 10 figures available from authors: phira@flinders.edu.au

nuclear physics
three-body problem
partial wave analysis: coupled channel
nuclear force
binding energy
tritium
pi nucleon: elastic scattering
elastic scattering: pi nucleon
scattering amplitude: energy dependence
energy dependence: scattering amplitude

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