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Near and on the surface of the Moon, there is not only radiation emanating from the Sun (solar wind, CME, SPE), but also deep space (cosmic) radiation. The cosmic radiation also interacts with the nuclei of the elements comprising the lunar surface minerals and causes secondary radiation, like gamma and neutron radiation. This would affect the radiation dose calculation for astronauts while walking on the Moon.

Have there been any measurements on neutron radiation performed by the Surveyor (or later) missions?

Is it possible to derive an upper bound on neutron radiation energies and flux from models of interaction of nuclei with cosmic radiation?

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Have there been any measurements on neutron radiation performed by the Surveyor (or later) missions?

The Lunar Reconnaissance Orbiter (LRO) has several instruments designed to determine the radiation environment of the moon.

The Cosmic Ray Telescope for the Effects of Radiation (CRaTER) was specifically designed to "...characterize the lunar radiation environment and its biological impacts..."

The Lunar Exploration Neutron Detector (LEND) instrument is a dedicated neutron detector and has the capability to measure up to ~15 MeV neutrons.

So the answer is yes.
[I am not at work (still snowed-in after Janus) so I do not have access to most journal publications. Thus, I am unable to elaborate further on the results/conclusions of the neutron radiation surveys.]

Is it possible to derive an upper bound on neutron radiation energies and flux from models of interaction of nuclei with cosmic radiation?

The Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) spacecraft has a dedicated neutron detector to measure energies above 20 MeV.

So far as I can tell, the detectors can go up to $> 10^{3}$ GeV/nucleon, but I am not sure if they are pointed at the moon. I do know it is one of the few space born cosmic ray detectors (most cosmic ray detectors require a great deal of mass, which places significant limits on space-based missions). They have characterized the absolute flux of protons and helium up to ~1.2 TeV, electrons up to ~600 GeV, anti-proton energy spectrum up to ~200 GeV. There are several detailed observations in the arXiv eprint 0904.4692 showing the observed cosmic ray spectrum.

Unfortunately, I do not know the answer to your second question, but my best guess as a good start would be to look into results from PAMELA.

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