Interaction between two non-threshold bound states

A general non-threshold BPS (F, D$_p$) (or (D$_{p - 2}$, D$_p$)) bound state can be described by a boundary state with a quantized world-volume electric (or magnetic) flux and is characterized by a pair of integers $(m, n)$. With this, we calculate explicitly the interaction amplitude between two such non-threshold bound states with a separation $Y$ when each of the states is characterized by a pair of integers ($m_i, n_i$) with $i = 1, 2$. With this result, one can show that the non-degenerate (i.e., $m_i n_i \neq 0$) interaction is in general attractive for the case of (D$_{p - 2}$, D$_p$) but this is true and for certain only at large separation for the case of (F, D$_p$). In either case, this interaction vanishes only if $m_1/ n_1 = m_2/ n_2$ and $n_1 n_2 > 0$. We also study the analytic structure of the corresponding amplitude and calculate in particular the rate of pair production of open strings in the case of (F, D$_p$).