Observations of triple coincidence polarization correlations of the sequential cascading photons (667.8 nm 3 1 D ! 2 1 P and 58.4 nm 2 1 P ! 1 1 S transitions) and the scattered electrons from electron impact excitation of the 3 1 D state of helium have determined the amplitudes and relative phases of the magnetic substates. The ambiguity of electron-photon coincidence measurements, which determine only the cosine of the sum of the phases between the m 62 amplitudes, is resolved. The measured amplitudes and phases at 60 eV incident energy and 40 ± scattering angle confirm the convergent close coupling values. [S0031-9007 (97)04277-4] PACS numbers: 34.80.DpFundamental studies of quantum physics frequently concern the symmetry and invariances of dynamical systems. The continuous symmetries of space, time, and rotation lead to the conservation of linear momentum, energy, and angular momentum which lead to the well known structure of atoms and their associated scattering properties. The reflection and rotational symmetries of an electronic charge distribution for a specific electronically excited state of an atom are revealed by choosing a reference axis or frame and determining the state multipoles. For example, the selection of an axis of cylindrical symmetry and detection of a nonisotropic population of the radiated photons determines the polarization of the atomic state. The selection of planar symmetry and detection of the radiated photons in coincidence with the scattered electron leads generally to knowledge of the atomic alignment and orientation. The alignment is defined as the nonisotropic population of magnetic substates of equal M with ͗M͘ 6͗J 2 ͘͞3 and determines the shape and size of the electronic charge cloud. The orientation is defined as the nonisotropic population of the 1M and 2M magnetic substates and determines the angular momentum transferred during the excitation process. Work of this type has been reviewed [1,2] and forms part of the quest for quantum mechanically complete measurements [1][2][3][4][5] to determine the scattering amplitudes and relative phases for a unique state and specific scattering dynamics.Studies of the 2 1 P state characterization with the detection of two particles (the scattered electron and the single 2 1 P to 1 1 S photon) are extensive and essentially complete [2]. However, the complete characterization of the amplitudes and relative phases for higher angular momentum states requires a lowering of the scattering symmetry and hence the detection of an increasing number of photons. For the 3 1 D state of helium studied here, the polarization requires specification of only an axis of symmetry and has been measured frequently since about 1964 [6]. However, angular and polarization correlation analyses, requiring a plane of symmetry and hence the detection of two outgoing particles (the scattered energy loss electron and either the 3 1 D to 2 1 P or 2 1 P to 1 1 S photon), have been made only since about 1987 [7][8][9][10]. Similar measurements of the correlations of th...