>Magister Scientiae - MSc / Measurements of nuclear level lifetimes are an important aspect of experimental nuclear physics. Such measurements determine transition matrix elements for nuclear structure research and also provide the widths of relevant excited states in nuclei that are of astrophysical interest. In the latter, the measured widths are used to obtain reaction rates in main sequence stars such as the Sun and in binary-star systems where the accretion of material from one star to another provides an opportunity to study extreme stellar environments such as novae and x-ray bursts. This thesis work describes the design and simulation of a new experimental set up at iThemba LABS that will allow for highprecision femtosecond-level lifetime measurements of nuclear states using the Doppler Shift Attenuation Method (DSAM). We use the Solid Edge computer-aided design (CAD) software to design a new scattering chamber with a cooled target ladder specifically for such measurements using inverse-kinematic transfer reactions with ion implanted targets. The light charged ejectiles from the reaction will be detected with a ΔE - E silicon telescope, while Doppler shifted rays will be registered using a high-purity and 100% efficient germanium (HPGe) detector. We also describe preliminary Monte Carlo simulation codes that are being developed in a relativistically invariant framework to optimize the experimental set up and to obtain predicted lineshapes of γ rays from several astrophysically relevant states in nuclei using this experimental set up. / National Research Foundation (NRF)