$q $}}^2+m_s^2},\end{aligned}$$

where the arrows indicate that the normalization of the spinors were also changed. Using these results and keeping only terms of the order ${\bf p}/m$, we get the non-relativistic amplitude

$$\begin{aligned}
t^{ijk}(\lambda ) &=&\frac{g^4}{\left( 2m\right) ^2} {\mbox{\boldmath $\tau$}}^{(i)}\cdot {\mbox{\boldmath $\tau $}}^{(j)} \; {\mbox{\boldmath $\sigma $} }^{(i)}\cdot {\bf k }\; \frac 1{{\bf k}^2+\mu ^2}  \nonumber \\
&&\times {\mbox{\boldmath $\sigma $} }^{(j)}\cdot \left[ \left( \frac 1m -%
\frac \lambda{gf_\pi }\right) {\bf k } +\frac \lambda {gf_\pi }{\bf q}%
\right] \frac 1{{\bf q}^2+m_s^2},\end{aligned}$$

where ${\bf k }={\bf p}_i-{\bf {p'}}_i$and ${\bf q}= {\bf  p'} _k- {\bf p}_k$. The full non-relativistic amplitude $t_{3N}$ is given by the permutation over all indices $ijk.$

In momentum space the three body potential $W$ is defined by $$\left\langle {\mbox{\boldmath $p $}}_1^{\prime }{\mbox{\boldmath $p $}}%
_2^{\prime }{\mbox{\boldmath $p $}}_3^{\prime }\left| W\right| {%
\mbox{\boldmath $p $}}_1{\mbox{\boldmath $p $}}_2{\mbox{\boldmath $p $}}%
_3\right\rangle =-(2\pi )^3\delta ^3\left( {\mbox{\boldmath $p $}}_1^{\prime
}+{\mbox{\boldmath $p $}}_2^{\prime }+{\mbox{\boldmath $p $}}_3^{\prime }-{%
\mbox{\boldmath $p $}}_1-{\mbox{\boldmath $p $}}_2-{\mbox{\boldmath $p $}}%
_3\right) t_{3N}.  \label{W3N}$$

We apply Fourier transform to (\[W3N\]) in order to obtain the potential in configuration space and we have

$$\left\langle {\mbox{\boldmath $r $}}_1^{\prime }{\mbox{\boldmath $r $}}%
_2^{\prime }{\mbox{\boldmath $r $}}_3^{\prime }\left| W\right| {%
\mbox{\boldmath $r $}}_1{\mbox{\boldmath 