Nuclear Reaction - How to determine variables as much as possible

May 2019
Hey Guys,
exercise: "It is desired to study the first excited state of 16O which is at energy of 6.049 MeV.
Using the (alpha, n) reaction on target of 13C, what is the minimum energy of incident alphas which will populate the excited state?

So, i suggest to define first the reaction equation:
alpha + 13C -> 16O + n where E(16O) = 6,049 MeV

Because we are searching the minimum energy of the alpha, i would define the Q value = 0
(with kinetic energy of particle i = Ti)

-> Tc + Ta = To +Tn
-> Tc + Ta - Tn = 6,049 MeV

How i get more information about the system?
If iam using a change of the system from lab-frame(momentum of 13C = 0) to Center of Mass frame(Sum(momentum) = 0 of final products)), i get the following relation:

E(alpha) = ((En)^2 + 12*En + 36MeV - (m(alpha)c)^2 - ((m(c))*c^2)^2)/2m(c)*c^2

Does somebody know a "trick" to get there more informations of the system to finally get the min. E of alphas?

Best Regards,
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