of pion-nucleon interactions in constituent quark models [@Mae+97]. Because of this equivalence and of the similarity with the linear Lagrangian, our discussions are set in PS case. Thus our complete non-linear Lagrangian is written as

$$\begin{aligned}
{\cal L}_S^{PS} &=&\frac 12\left( \partial _\mu S\partial ^\mu S-m_S^2S^2\right) 
+\frac 12\left( \partial _\mu {\mbox{\boldmath $\phi $}}\cdot \partial ^\mu {\mbox{\boldmath $\phi $}}
+\partial _\mu f\partial ^\mu
f\right) +f_\pi \mu ^2f+U\left( S\right)  \nonumber \\
&&+\bar Ni{\not \partial }N-\left( g+\frac{g_s}{f_\pi }S\right) \bar N\left(
f+i{\mbox{\boldmath $\tau $}}\cdot {\mbox{\boldmath $\phi $}}\gamma
_5\right) N.  \label{Lnl}\end{aligned}$$

The interaction terms in eqs (\[Lnl\]) and (\[L1\]) have the same scalar-nucleon and pion-nucleon vertices depicted in fig. 1a. However, the non-linear approach also yields extra vertices, representing seagull scalar-pion-nucleon and pion-pion-nucleon interactions, among others, displayed in fig. 1b. These results indicate that, at tree level, both Lagrangians produce the same $NN$ potential. On the other hand the extra scalar-pion-nucleon vertex represents a genuine difference between the two approaches and has consequences in processes such as pion absorption by a two-nucleon system or three body forces.

Effective Seagull
=================

The purpose of this section is to discuss the meaning of the effective seagull interaction in terms of more basic processes. In order to do this, 