Broad Overview
When interrogating atom by electron-impact, the energy of the projectile plays a major role on the mechanism of the processes that can occur. Whereas the projectile interacts with each electron of the target and its nucleus, there is a Coulomb repulsive interaction between the electrons of the target, as well as a Coulomb attractive interaction between each electron of the target with the nucleus. Possible resulting processes include single excitation, double excitation, partial and/or complete fragmentation involving the (e,Ne) schemes, where N is the number of electrons emerging from the collision zone. Thus, the (e,2e) process is a few-body atomic process involving energy transfers from an incident electron to matter resulting in a single ionized electron from the target and a scattered electron.
For slow incident electrons, the projectile has the time to see all the details of the target structure. Thus, it can interact more than once with the target. This process is characterized by large momentum transfers to the target and by small impact parameters. Perturbatively, this means that not only the first-Born approximation but also higher orders in the Born series are important when describing the (e,2e) process. Moreover, exchange between the slow incident electron and the electrons of the targets have to be accounted exactly.
For fast incident electrons, exchange between the incident electron and the electrons of the targets can be ignored in the theoretical formulation when detecting ionized electrons with low kinetic energy. In this case, the projectile mostly interacts once with the target. This process is characterized by small momentum transfers to the target and by large impact parameters. Therefore, the first-Born approximation provides a significant account for the triply differential cross section. However, it may turn out that for some kinematics (for instance when two-electron doubly-excited states are accessible) one would need at least the second-Born approximation to improve agreement between experiment and theory.
Some Open Questions
Our interest is on highly correlated processes such as the correlated (e,2e) process of helium where the residual ion remains in its excited states. For any kinematics, a state-of-art calculation of the first-Born approximation, that includes exactly the electron correlations in both the initial and final states, is required. All existing second-Born approximation rely on the closure approximation or/and its variants which may breakdown for certain kinematics and geometries. A cleaner second-Born calculation that includes all significant intermediate states is thus of great interest in atomic physics.
When interrogating atom by electron-impact, the energy of the projectile plays a major role on the mechanism of the processes that can occur. Whereas the projectile interacts with each electron of the target and its nucleus, there is a Coulomb repulsive interaction between the electrons of the target, as well as a Coulomb attractive interaction between each electron of the target with the nucleus. Possible resulting processes include single excitation, double excitation, partial and/or complete fragmentation involving the (e,Ne) schemes, where N is the number of electrons emerging from the collision zone. Thus, the (e,2e) process is a few-body atomic process involving energy transfers from an incident electron to matter resulting in a single ionized electron from the target and a scattered electron.
For slow incident electrons, the projectile has the time to see all the details of the target structure. Thus, it can interact more than once with the target. This process is characterized by large momentum transfers to the target and by small impact parameters. Perturbatively, this means that not only the first-Born approximation but also higher orders in the Born series are important when describing the (e,2e) process. Moreover, exchange between the slow incident electron and the electrons of the targets have to be accounted exactly.
For fast incident electrons, exchange between the incident electron and the electrons of the targets can be ignored in the theoretical formulation when detecting ionized electrons with low kinetic energy. In this case, the projectile mostly interacts once with the target. This process is characterized by small momentum transfers to the target and by large impact parameters. Therefore, the first-Born approximation provides a significant account for the triply differential cross section. However, it may turn out that for some kinematics (for instance when two-electron doubly-excited states are accessible) one would need at least the second-Born approximation to improve agreement between experiment and theory.
Some Open Questions
Our interest is on highly correlated processes such as the correlated (e,2e) process of helium where the residual ion remains in its excited states. For any kinematics, a state-of-art calculation of the first-Born approximation, that includes exactly the electron correlations in both the initial and final states, is required. All existing second-Born approximation rely on the closure approximation or/and its variants which may breakdown for certain kinematics and geometries. A cleaner second-Born calculation that includes all significant intermediate states is thus of great interest in atomic physics.