with mass $m_s$ yields a central $NN$ potential proportional to $e^{-m_sr}/r$, whereas the spatial dependence of TPEP is closer to $\left( e^{-\mu r}/r\right) ^2$, $\mu $ being the pion mass [@Rob+; @Kai+]. Moreover, the TPEP is proportional to $g^4$, where $g$ is the $\pi N$ coupling constant, whereas the exchange of a sigma is proportional to $g^2$. In spite of all these problems, the use of an effective scalar field may be useful in problems where simplicity is more important than precision. As far as the former is concerned an effective scalar field allows calculations at tree level, whereas the exchange of two pions involves loop integrations.

If one is willing to use an effective scalar field in a calculation, there are two possibilities at hand. The first one consists in employing the usual sigma field of the linear model, which is the chiral partner of the pion. The other possibility is to use a scalar field in the framework of non-linear Lagrangians, which is chiral invariant and appears naturally when the non-linear fields are obtained from the linear ones [@Wei]. These two scalars fields couple differently to pions and nucleons and hence lead to predictions which do not overlap 