1 \documentclass[12pt
]{article
}
6 E & = & LJ(r)
\qquad \qquad \qquad r < r_
{\rm in
} \\
7 & = & S(r) * LJ(r)
\qquad \qquad r_
{\rm in
} < r < r_
{\rm out
} \\
8 & = &
0 \qquad \qquad \qquad \qquad r > r_
{\rm out
} \\
9 E & = & C(r)
\qquad \qquad \qquad r < r_
{\rm in
} \\
10 & = & S(r) * C(r)
\qquad \qquad r_
{\rm in
} < r < r_
{\rm out
} \\
11 & = &
0 \qquad \qquad \qquad \qquad r > r_
{\rm out
} \\
12 LJ(r) & = &
4 \epsilon \left[ \left(
\frac{\sigma}{r
}\right)^
{12} -
13 \left(
\frac{\sigma}{r
}\right)^
6 \right] \\
14 C(r) & = &
\frac{C q_i q_j
}{ \epsilon r
} \\
15 S(r) & = &
\frac{ \left[r_
{\rm out
}^
2 - r^
2\right]^
2
16 \left[r_
{\rm out
}^
2 +
2r^
2 -
3{r_
{\rm in
}^
2}\right]}
17 { \left[r_
{\rm out
}^
2 -
{r_
{\rm in
}}^
2\right]^
3 }