Philosophiae Doctor - PhD / This thesis describes research work undertaken to study neutron pairing correlations in 136Ba via the 138Ba(p, t) pair transfer reaction and to perform high-precision spectroscopy of low-lying states in 136Cs using the 138Ba(d, ) reaction. The aim of this project was to provide useful spectroscopic information relevant for matrix element calculations of 136Xe neutrinoless double beta decay. This work is relevant because neutrinoless double beta decays are standard-model-forbidden lepton number violating processes, which if observed, would establish the Majorana nature of the neutrinos and also determine the absolute mass scale of the light Majorana neutrinos. Our experiments show a signi cant fragmentation of the two-neutron transfer (p, t) strength to excited 0+ states in 136Ba, which could signi cantly affect future matrix element calculations. Additionally we obtain information on 65 new states in 136Cs observed in this work. It is anticipated that these new information will play a vital role in improving the precision of calculated matrix elements for 136Xe double beta decays.