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\begin{document}

\begin{eqnarray}

U_A &=& - \frac{A}{6} \left[

	\frac{2 a_1 a_2}{r^2-\left(a_1+a_2\right)^2}

	+ \frac{2 a_1 a_2}{r^2 - \left(a_1 - a_2\right)^2}

	+ \mathrm{ln}

				\left( 

					\frac{r^2-\left(a_1+a_2\right)^2}{r^2-\left(a_1-a_2\right)^2}

				\right)

\right] \nonumber \\

\nonumber \\

U_R &=& \frac{A}{37800}  \frac{\sigma^6}{r}

\left[ \frac{}{} \right. \nonumber \\

	&&\qquad		\frac{r^2-7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)}

					{\left(r-a_1-a_2\right)^7} \nonumber \\

	&&\qquad		+\frac{r^2+7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)}

					{\left(r+a_1+a_2\right)^7} \nonumber \\

	&&\qquad		-\frac{r^2+7r\left(a_1-a_2\right)+6\left(a_1^2-7a_1a_2+a_2^2\right)}

					{\left(r+a_1-a_2\right)^7} \nonumber \\

	&&\qquad	\left.	-\frac{r^2-7r\left(a_1-a_2\right)+6\left(a_1^2-7a_1a_2+a_2^2\right)}

					{\left(r-a_1+a_2\right)^7}

\right] \nonumber \\

\nonumber \\

U &=& U_A + U_R, \qquad r < r_c \nonumber

\end{eqnarray}

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\begin{document}

\begin{eqnarray}

	U &=& \frac{2 ~ a^3 ~ \sigma^3 ~ A}{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}