Lowest mean transverse energy obtainable from a photocathode

In plain words

Electrons leave a cathode with some random sideways energy that blurs the beam; how low it can go, and what sets the floor, is open.

Precise statement

The intrinsic normalized emittance of a photoemission source is eps_n = $\sigma_x$ sqrt(MTE/(m c^2)), with sigma_x the rms source size and MTE the mean transverse energy of emitted electrons. Values of approximately $5\,\mathrm{meV}$ were reported around 2020 from near-threshold photoemission of cryogenically cooled single-crystal Cu(100). Determine the lowest achievable MTE at quantum efficiency $\ge 10^{-5}$ and the physics that sets it (lattice temperature, surface roughness and work-function variation, electron-phonon and electron-electron scattering, multiphoton emission).

What would settle it

MTE measurements versus temperature, photon energy and surface preparation on candidate cathodes, matched by a photoemission model including the surface.

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