In contrast to l-mixing described in Sec. 4.1, a more rigorous approach to PAD calculations does not limit the description of the detachment orbital to a few l components. Given sufficiently general implementation, expansion of the Dyson orbital in a single-center basis (as in the l-mixing model) is not necessary. Instead, partial-wave expansion is reserved for the final state, described by the wave function of the emitted photoelectron, 𝜓 , where k is linear momentum. The anisotropy parameter for a given transition can then be calculated from the transition-dipole matrix elements 𝜓 𝑟𝑌 , Φ defined within the electric-dipole and sudden-detachment approximations. In the above, Dyson orbital Φ is defined as: