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$^{+} \quad +$ 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 the only apparatus currently able to benchmark the CT of these fundamental systems at energies below 0.1eV/u (Phys. Rev. A \textbf{84}, 062716, 2011). However, the data analysis suffers from the lack of information on the initial states of H$_{2}^{+}$~which makes comparison to state-to-state calculations (PRA \textbf{67} 022708 (2003) impossible without educated guesses. 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 ion source. Our initial design for the insertion of this technique in the aforementioned system will be presented here.