Spin polarization of molecular photoelectrons in the case of rotationally resolved photoionization spectra

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Abstract
A theoretical derivation of the differential photoionization cross section taking into account the spin polarization of photoelectrons is presented. This cross section corresponds to rotationally resolved transitions from an initial rotational level of the neutral molecule to a final rotational level of the ion. The final-state wave function of the ion-plus-electron system is written in the Hund’s-case (c) coupling scheme, and the parities of this state and of the initial-state wave functions are explicitly introduced. Two equivalent expressions for the cross section are obtained that correspond to two coupling schemes of the angular momenta involved in the problem. One is a transferred-momentum-coupling scheme, and the other is the final-state (ion-plus-electron) total-angular-momentum-coupling scheme. Their respective advantages in analyzing the experimental results are highlighted. Each term in the transition moment and cross-section expressions contains a multiplicative factor of a simple form that determines if a contribution to these expressions is zero or not, thus playing the role of a selection-rule factor. Our expressions apply to the single-photon process as well as to multiphoton processes in cases in which only the last (one-photon) ionization step is considered explicitly. The paper ends with derivation of explicit formulas for the total cross section and the angle-integrated spin-polarization parameter in a particular case. The photoionization of the HI molecule was the model for these particular formulas.