Deviation from the single-particle model in the angular distribution of thorium ${\mathit{L}}_3$ x rays in proton-impact ionization

Angular distributions of ${\mathit{L}}_3$ x-ray transitions, including electric-dipole-forbidden ones, were measured for 1-, 2-, and 3-MeV proton impact on a thorium target, where the excitation and detection systems were cylindrically symmetric. A sophisticated spectrum-analysis technique was applied, where both the Lorentzian broadening of the transitions and the Si(Li) detector response function with various tailing features were taken into account. The anisotropy-parameter ratios are expected to be independent of the ionization process, and to be characteristic of the x-ray transitions in the independent-particle model. The ratios of the anisotropy parameters of the electric-dipole-allowed transitions were in disagreement with this expectation, even when the higher-order multipole contributions were taken into account. These results follow the same trend as earlier angular distribution and angular correlation measurements. Additionally, the electric-dipole-forbidden ${\mathit{LtL}}_3$${\mathit{M}}_2$) and Ls(${\mathit{L}}_3$${\mathit{M}}_3$) transitions had a ${\mathit{P}}_4$(cos(θ)) term, which is not expected within the framework of the single-particle-model predictions. Possible causes for this discrepancy are explored.