Electron beam induced electron capture? Would it be possible to induce electron capture/fission by firing an electron beam at a heavy-element target? I know pelletrons/Van de Graff generators/accelerators can produce electrons of around 25MeV, and particle accelerators can improve on that further. If it is possible, how hard would you have to shoot the electrons to get them to enter the nucleus (or at least pass through the other electrons) with consistency? 
I understand that electron capture is one of the slower nuclear reactions, so if electrons are moving too fast it may actually be inhibited. However, on the flip side, more electrons would be spending time near the nucleus, and there may be a critical speed at which fired electrons are sufficiently slowed by passage through the electron shells so that they spend significant time near the nucleus before being either captured or ejected from the atom. I have no idea how to calculate that speed.
Thoughts? Could this work?
 A: A proposal exists, with calculations,  for induced electron capture using antineutrinos from an ion beam. I searched the CERN document server and there is nothing there to show that an experiment  has taken up the proposal.
Your proposal cannot work on neutral atoms as target because the energy needed to penetrate the orbitals of the electrons about the nucleons would not have the necessary resonant energy for electron capture where the energies are kev.
There exists a technique to scatter electrons off a nucleus and study the nuclear reactions :

The principle of the technique is based around the ion trapping phenomenon which is observed at electron storage ring facilities, which has an adverse effect on the performance of electron storage rings.
The novel idea to be employed at SCRIT is to use the ion trapping to allow short-lived RI's to be made a target, as trapped ions on the electron beam, for the scattering experiments. This idea was first given a proof-of-principle study using the electron storage ring of Kyoto University, KSR; this was done using a stable nucleus of 133Cs as a target in an experiment of 120MeV electron beam energy, 75mA typical stored beam current and a 100 seconds beam lifetime. The results of this study were favorable with elastically scattered electrons from the trapped Cs being clearly visible.

It has taken years to produce results.

The first elastic electron scattering has been successfully performed at the self-confining radioactive-isotope ion target (SCRIT) facility, the world’s first electron scattering facility for SCRIT technique achieved high luminosity (over $10 ^27$ $cm^{−2}$ $s^{−1}$ , sufficient for determining the nuclear shape) with only $10^8$ target ions. While 132Xe used in this time as a target is a stable isotope, the charge density distribution was first extracted from the momentum transfer distributions of the scattered electrons by comparing the results with those calculated by a phase shift calculation.

It is a complicated experiment. Maybe in the future they might try to study  induced electron capture fission.
