doc/src/Eqs/pair_dipole_sf2.tex

   1 \documentclass[12pt]{article}
   2
   3 \begin{document}
   4
   5 \begin{eqnarray*}
   6 T_{pq} = T_{ij} & = & \frac{q_j}{r^3} \left[ 1 -
   7   3\left(\frac{r}{r_c}\right)^{\!2} +
   8   2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p_i}\times\vec{r}) \\
   9 T_{qp} = T_{ji} & = & - \frac{q_i}{r^3} \left[ 1 -
  10   3\left(\frac{r}{r_c}\right)^{\!2} +
  11   2\left(\frac{r}{r_c}\right)^{\!3} \right] (\vec{p_j}\times\vec{r}) \\
  12 T_{pp} = T_{ij} & = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
  13   e3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \times \vec{p_j}) + \\
  14   & & \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
  15   3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_j}\bullet\vec{r})
  16   (\vec{p_i} \times \vec{r}) \\
  17 T_{pp} = T_{ji} & = & -\frac{1}{r^3}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
  18   3\left(\frac{r}{r_c}\right)^{\!4}\right](\vec{p_j} \times \vec{p_i}) + \\
  19   & & \frac{3}{r^5}\left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
  20   3\left(\frac{r}{r_c}\right)^{\!4}\right] (\vec{p_i} \bullet \vec{r})
  21   (\vec{p_j} \times \vec{r}) \\
  22 \end{eqnarray*}
  23
  24 \end{document}