After the calculation we analyze the wave packet to get the energy dependent reaction probability. To calculate this quantity we use the method taken from Ref. [33]. The energy dependent reaction probability is defined as
Eq. (13) can also be derived rigorously rather than with the hand-waving argument presented here. However, the proof is elaborate, albeit straightforward. Therefore, we will only outline it here[81]. First, take a plane wave along the SF z-axis, expand it into spherical Bessel functions[82] and rotate it to the BF-frame. Then, project the plane wave onto a specific (J,M) state and normalize this state. Next, write the spherical Bessel functions in their asymptotic expression and take the inner product with the initial wave packet. As in Ref. [80] one gets two integrals, one of which is negligible. Neglegting this integral¸ one obtains Eq. (13), apart from a complex factor which disappears in calculating P_{r}(E).
By taking the surface not at r_{s}, but at R_{s} we can use this method also to calculate P_{nr}(E), the non-reaction probability. This last quantity is interesting, because we can use it to assess the convergence of the calculation. If the results are converged, P_{r}(E) + P_{nr}(E) are equal to 1.