\Lambda \left( \frac{%
\Lambda ^2}{\mu ^2}-1\right) e^{-\Lambda r}$$ and its derivatives are given by $$\begin{aligned}
\frac{\partial U\left( \mu r,\Lambda \right) }{\partial r_\alpha } &=&\mu 
\frac{r_\alpha }rU_1\left( \mu r,\Lambda \right) , \\
\frac{\partial ^2U\left( \mu r,\Lambda \right) }{\partial r_\alpha \partial
r_\beta } &=&\frac{\mu ^2}3\left[ \delta _{\alpha \beta }\left( U\left( \mu
r,\Lambda \right) -G\left( r\right) \right) \right.  \nonumber \\
&&\left. +\left( \frac{3r_\alpha r_\beta }{r^2}-\delta _{\alpha \beta
}\right) U_2\left( \mu r,\Lambda \right) \right] ,\end{aligned}$$ where $$\begin{aligned}
U_1\left( \mu r,\Lambda \right) &=&-\left( \frac 1{\mu r}+1\right) \frac{%
e^{-\mu r}}{\mu r}+\frac{\Lambda ^2}{\mu ^2}\left( 1+\frac 1{\Lambda r}%
\right) \frac{e^{-\Lambda r}}{\Lambda r}  \nonumber \\
&&+\frac 12\left( \frac{\Lambda ^2}{\mu ^2}-1\right) e^{-\Lambda r}, \\
U_2\left( \mu r,\Lambda \right) &=&\left( 1+\frac 3{\mu r}+\frac 3{\mu ^2r^2}%
\right) \frac{e^{-\mu r}}{\mu r}-\frac{\Lambda ^3}{\mu ^3}\left( 1+\frac 3{%
\Lambda r}+\frac 3{\Lambda ^2r^2}\right) \frac{e^{-\Lambda r}}{\Lambda r} 
\nonumber \\
&&-\frac 12\frac \Lambda \mu \left( \frac{\Lambda ^2}{\mu ^2}-1\right)
\left( 1+\frac 1{\Lambda r}\right) e^{-\Lambda r}, \\
G\left( r\right) &=&\frac 12\frac \mu \Lambda \left( \frac{\Lambda ^2}{\mu ^2%
}-1\right) ^2e^{-\Lambda r}.\end{aligned}$$

Substituting these results into the potential, we have

$$\begin{aligned}
W^{ijk} &=&\frac 43\left( \frac{g\mu }{2m}\right) ^4\frac m{\left( 4\pi
\right) ^2}\frac{m_s}\mu {\mbox{\boldmath $\tau $}}^{(i)}\cdot {%
\mbox{\boldmath $\tau $}}^{(j)}  \nonumber \\
&&\times \left\{ \left( 1-\lambda \right) \left[ {\mbox{\boldmath $\sigma $} 
}^{(i)}\cdot {\mbox{\boldmath$\sigma $}}^{(j)}U\left( m_sr_{kj},\Lambda
