Figure 1: Electron beams (cyan haze in top left) are routinely used to determine the molecular structures of biomolecules in cryo-electron microscopy. A new theoretical analysis has examined what happens when very short or very narrow electron beams interact with a particle. © VERONICA FALCONIERI, SRIRAM SUBRAMANIAM / NATIONAL CANCER INSTITUTE / SCIENCE PHOTO LIBRARY
Scientists should be able to achieve a new level of control over high-energy electrons interacting with a particle, according to a theoretical analysis by a RIKEN physicist and two colleagues1.
Electrons are particles, but according to quantum mechanics they also behave like waves under certain circumstances.
Electron microscopes exploit this wave-like nature of electrons to obtain high-resolution images of objects by imaging how an electron beam is scattered from an object.
The mathematics describing the interaction between high-energy electrons and a particle is highly complex. But, for conventional electron microscopes, it can be greatly simplified by the fact that the electron beam is much wider than the particle. This allows scientists to approximate the electron beam using plane waves-parallel waves that extend infinitely in both directions.
However, advances in the latest electron microscopes are causing this convenient approximation to become invalid.
For example, state-of-the-art scanning transmission electron microscopes can focus electron beams down to widths that are considerably smaller than an atom. Also, the manipulation of electron beams by light can create extremely short pulses of electrons of the order of attoseconds (10-18 second).
In these cases, experimental advances were outpacing theoretical understanding, since the theory needed to describe interactions of these extremely narrow or short electron beams with a particle was lacking.
Yuya Morimoto of the RIKEN Center for Advanced Photonics was confronted by this gap. "As an experimentalist, I've been working on creating very short electron pulses," he says. "And my team is reaching a point where we soon expect to see quite new phenomena that conventional theory can't explain."
To bridge this gap, Morimoto and two collaborators have now performed a theoretical analysis of how electron wave packets are scattered by a particle.
The theoretical analysis has important ramifications for experiments. "We've demonstrated that we can use the properties of the electron beam to control the interaction between an electron beam and a particle," explains Morimoto. "Conversely, we found that we can use the interaction between electrons and matter to monitor the quantum state of an electron beam."
In particular, the results revealed that varying the pulse width of the electron beam with certain quantum properties will significantly alter the interaction strength between the electron beam and an atom. This finding was unexpected.
"It was a big surprise for us," says Morimoto. "We'd assumed that the interaction strength wouldn't vary so much if we changed the pulse width, but we found that it changed a lot."
This ability to control the interaction strength could be used to minimize protein damage in cryoelectron microscopy and to enhance the efficiency in semiconductor manufacturing.
Yuya Morimoto (left) and collaborator Lars Madsen (right), together with Peter Hommelhoff (not shown), have performed a theoretical analysis that shows how electron scattering asymmetry can be controlled using the shaping of ultrafast electron wave packets. © 2026 RIKEN
