An J=1→J=1 atomic system in Samarium with incident laser resonant radiation has been investigated. A linearly polarized laser at 686nm excites atoms from the level 4ƒ[superscript]66s[superscript]2 [superscript]7F[subscript]1 to a excited level 4ƒ[superscript]66s6p [superscript]9F[subscript]1 via the process of optical pumping. When an external magnetic field is applied to the atom-laser interaction and the decay fluorescence collected, a level-crossing profile appears. Theoretical predictions of the level-crossing profile can be made using spherically irreducible tensors to describe the density matrix which take advantage of the symmetry of the atomic system. By comparing theory with experimental data, a discussion is made of the various parameters and external factors that can affect this system, which show that Doppler broadening is the major influence. An additional investigation is made into the evolution of the J=1→J=1 atomic system with increasing laser exposure. Comparisons of the experimental data with theoretical predictions are made by analyzing the FWHM of the overall level-crossing profile, the FWHM of the dip about B = 0 and the relative depth of the dip. By charting the progress of these parameters with increasing laser exposure, it can be seen that the theory and experimental data agree qualitatively. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1320338 / Thesis (Ph.D.) -- University of Adelaide, School of Chemistry and Physics, 2008