the power $n$ of the potential, for fixed energy and fixed reaction amplitude $y$. They are shown in Fig. \[myfigure2\] and \[myfigure3\]. Typical energy scales for several systems are shown by Table I.

            system            power $n$   $E_n$ \[$\mu$K\]
  -------------------------- ----------- ------------------
   $^{174}$Yb$^+$+$^{87}$Rb       4            0.022
   $^{174}$Yb$^+$+$^{7}$Li        4             3.2
         He$^{*}$+Ar              6            14000
           KRb+KRb                6            22.35
          LiCs+LiCs               6             1.32

  : Typical energy scales for several systems interacting with atom-ion ($n=4$) or van der Waals ($n=6$) potential at long range.

Results for van der Waals potential
===================================

![\[KrevsE\](Color online) Reactive rate vs collision energy for distinguishable particles with van der Waals interaction at different reaction amplitudes $y$. The $s$ values are chosen to be close to $p$-wave and $d$-wave shape resonances. The dashed lines show classical approximation .](KrevsE){width="\linewidth"}

![\[KrevsT\](Color online) Same as on Figure \[KrevsE\], but averaged over thermal distribution. The shape resonances can still be seen, especially for low reactivity. The dot-dashed lines show the results obtained using parabolic approximation .](KrevsT){width="\linewidth"}

![\[KelvsT\](Color online) Thermally averaged elastic rates for the same parameters as on Figures \[KrevsE\] and \[KrevsT\]. The dashed lines show the approximate high energy result given by . The dotted lines show the low-energy $s$-wave limit. Small discrepancy is due to thermal 