\documentstyle[12pt]{article}

\begin{document}

\begin{eqnarray}
	U &=& \frac{2 ~ a^3 ~ \sigma^3 ~ A_{cs}}{9 \left( a^2 - r^2 \right)^3} 
 \left[ 1 - \frac{\left(5 ~ a^6+45~a^4~r^2+63~a^2~r^4+15~r^6\right) \sigma^6}
 {15 \left(a-r\right)^6 \left( a+r \right)^6} \right], ~~ r < r_c \nonumber
\end{eqnarray}

\end{document}