Possibility of vibrationally resolved cross section measurements for low energy charge transfer in H $+$ H$_{2}^{+}$

Charge transfer (CT) in H $+$ H$_{2}^{+}\to $ H$^{+} +$ H$_{2}$ has fundamental implications because it involves the smallest atomic ion, atom, molecular ion, and molecule possible. The current merged-beam apparatus at Oak Ridge National Laboratory (ORNL) in Oak Ridge, Tennessee, can reliably create and access low collision energies; the existing ion-atom merged beams apparatus there is currently able to benchmark the CT of these fundamental systems at energies below 0.1eV/u (Phys. Rev. A \textbf{84}, 062716, 2011). A strong contribution from v$_{i}=$2 is observed, however, the data analysis still suffers from the lack of information on the vibrational state distribution of H$_{2}^{+}$. We are exploring the possibility of inserting a three-dimensional imaging technique at the end station~of the ORNL apparatus in order to measure the vibrational state distribution of H$_{2}^{+}$ that are produced by the electron cyclotron resonance (ECR) ion source. Discussion of our initial design for the insertion of this technique in the aforementioned system will be presented here.