Tunneling phenomenon has been studied since the time of Sir Isaac Newton. In the case of neutron tunneling phenomenon, it is the quantum mechanics wave-particle duality which manifests itself. In this case, particularly, the neutron wave-packet under total reflection condition suffers the so-called frustrated total reflection as known in standard optics. More accurately, this tunneling phenomenon shows itself via sharp dips in the plateau of total reflection. The prerequisite to observe such quantum mechanics phenomenon lies within a thin film Fabry-Perot resonator configuration. This thin film Fabry-Perot resonator geometry consists of two reflecting mirrors separated by a transparent material from a neutron optics viewpoint. In view of the specific neutron scattering properties related to the spin of the neutron wave-packet. As a direct proof, isotopic nickel based thin films Fabry-Perot resonator have been fabricated by depositing thin film of nickel by ion beam sputtering. The vacuum chamber was pumped down to the pressure of 10-8 mbar and deposition was performed at pressure of 2x10-4 mbar. The deposition rate was kept at 1.5 nm / minute and thickness layers were monitored by a calibrated quartz microbalance. Unpolarized neutron reflectometry measurements were carried out at the ORPHEE reactor using the time-of-flight EROS reflectometer. The incidence neutron wavelength varied between 3 – 25 Å. The grazing angle and angular resolution were of the order of 0.8˚ and 0.05 respectively. The software program, a Matlab routine for the simulation of specular X-ray and neutron reflectivity data with matrix technique, was employed to simulate the phenomenon and thereafter the experimentally obtained data and calculated (theoretical) data were compared. From the analysis of the comparison, a conclusion was drawn about the agreement between experimental data and theoretical data. The tunneling phenomenon has been observed in nanostructured isotopic nickel based thin film Fabry-Perot resonator. It manifested itself by the existence of dips, tunneling resonances, in the total reflection plateau due to quasi-bound states in the isotopic nickel based thin film Fabry-Perot resonator. In total, there were 7 tunneling resonances. The full widths at half maximum of these dips were found to decrease with increasing momentum wave vector transfer (Q) and this correlated to the neutron lifetime in the nanostructured isotopic nickel based thin film Fabry-Perot resonator. / Physics / M. Sc. (Physics)