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We have investigated collisions between transversely polarized electrons and Ar, in which the Ar is simultaneously ionized and excited to the Ar+*[3p4(+D)4p] states. The Stokes parameters of the fluorescence emitted in the following transitions was measured: (+D)4s 2D/2−(1D)4p 2F7/2 (461.0 nm), (1D)4s 2D5/2 −(1D)4p 2F5/2 (463.7 nm), (1P)3d 2D5/2−(1D)4p 2D5/2 (448.2 nm), and (1D)4s 2D3/2−(1D)4p 2P3/2 (423.7 nm). We develop the angular momentum algebra necessary to extract from these data, starting from the overall atomic J multipoles, the partitioning of orbital angular momentum into the 1D core electric quadrupole and hexadecapole moments, and the outer 4p electric quadrupole moment. The magnetic dipole of the outer electron is also determined. This procedure requires the assumption of good LS coupling for these states, which is justified. We recouple these individual core- and outer-electron moments to calculate the initial electric quadrupoles, hexadecapoles, and hexacontatetrapoles of the initial excited-state manifold. The detailed time structure of the electron-atom collision is considered, as well as the time evolution of the excited ionic state. The Rubin-Bederson hypothesis is thus shown to hold for the initial ionic L and S terms. The consequences of the breakdown of LS coupling are considered. From the circular polarization data, estimates of the relative importance of direct and exchange excitation cross section are made. We discuss experimental issues related to background contributions, Hanle depolarization of the fluorescence signal, and cascade contributions. Nonlinearity of the equations relating the Stokes parameters to the subshell multipole moments complicates the data analysis. Details of the Monte Carlo terrain-search algorithm used to extract multipole data is discussed, and the implications of correlation between the various subshell multipole moments is analyzed. The physical significance of the higher-order multipole moments is discussed, and graphical representations of the effects of these multipoles on the excited ionic charge clouds is presented.