Two separate investigations are presented, both linked by a common interest in the occupancy of the valence neutron orbitals and their relation to nuclear structure studies. A study of the change in neutron occupancy in the 0Î½2Î² decay of 136 Xe â 136 Ba has been performed. The neutron occupancies of 136 Ba have been probed us- ing the (p,d) and ( 3 He,Î±) neutron-removal reactions and the (d,p) and (Î±, 3 He) neutron-addition reactions, performed at the Institut Physique Nucl Ìeaire, Orsay. The same reactions have been performed on 134 Ba as an additional consistency check. Spectroscopic factors were extracted through a DWBA analysis and the valence orbital occupancies were extracted using the Macfarlane and French sum rules. The change in neutron occupancy that occurs during 0Î½2Î² decay was then determined and compared to those calculated by using the interacting shell model and the interacting boson model. The comparison showed that while the various models were able to qualitatively describe the change in occupancy, quantitatively there are significant differences between the models. These are the same models that are used to determine the nuclear matrix elements used in determining the rate of 0Î½2Î² decay. An additional systematic study of the valence neutron occupancies on the seven even stable tin isotopes is presented. The occupancies were probed in two sets of experiments. The first measurement used the low Q-value (p,d) and (d,p) reactions performed at the Maier-Leibnitz-Laboratory, Munich, to extract spec- troscopic information for low-j orbitals. The second measurement used the high Q-value ( 3 He,Î±) and (Î±, 3 He) reactions at the Institut Physique Nucl Ìeaire, Orsay to extract spectroscopic information for high-j states. Absolute cross sections were determined and the amount transferred angular momenta was identified by comparison of angular distributions to those calculated using a DWBA analysis. The spectroscopic factors were used in conjunction with the Macfarlane-French sum rules to determine the valence neutron occupancies. These measurements not only qualitatively test the robustness of sum rules in transfer reactions but also provide information about the neutron occupancy of 116 Sn and 124 Sn, two nu- clei of relevance to 0Î½2Î² decay. The measured occupancies of these two isotopes were compared to those obtained from recent theoretical calculations.