Measurements of the density matrix for collisionally produced H atoms for electron transfer collision of H+ on He will be continued. By fully modeling the collision region and calculating the transition amplitudes of the Stark-mixed hydrogenic states, the n=3 density matrix with 14 independent parameters, associated with the newly formed hydrogen atoms, can be fit to the measured signals. Significant improvements in the measuring apparatus and in the analysis associated with the fit of the density matrix to the optical signals will be utilized in the further measurements. The resulting changes have so far produced measured values of the density matrix that are in striking agreement with theory, for the most part. Important differences do remain, and further tests and extension are warranted-especially for the n=2 manifold and for the differential measurement. Because of significant, recent advances in atomic theory the measurement program is now directed toward a detailed understanding of differences and similarities between the calculated density matrix and the measured one.