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My professor explained saying that bombarding the surface with cosmic rays breaks off a few neutrons from nuclei and the nucleus, having undergone a change in energy level, emits a gamma photon. The neutrons thus emitted are typically of two categories- the fast-moving ones that have undergone little or no interaction with other nuclei, and thermal neutrons that are much slower. Apparently measuring the ratio of fast-moving and thermal neutrons tells us a lot about the surface.
He went on to say that a low value of this ratio indicates the presence of lighter elements on the surface, particularly hydrogen. (Basic mechanics tells us that momentum transfer is maximum if the colliding objects have the same mass). This technique, he says, has been instrumental in detecting the hydrogen in water present in the Southern polar caps of Mars.
1)The hydrogen in water is not free. When the neutron collides with water, it collides with the water molecule as a whole, not just the hydrogen atom. This is no different from colliding with a heavy atom of the same mass. In that case, the neutrons shouldn't slow down much, at least, that's what I think. Help?

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When the neutron collides with water, it collides with the water molecule as a whole, not just the hydrogen atom. This is no different from colliding with a heavy atom of the same mass. In that case, the neutrons shouldn't slow down much, at least, that's what I think. Help?

The de Broglie wavelength of a massive particle is given by:

$$\lambda = \frac{h}{p} = \frac{h}{mv}.$$

Planck constant $h$ is really small (6.626 $\times 10^{-34}$ J s), so we can guess that the wavelength is small as well.

The slowest (and therefore longest wavelength) neutrons here will be thermal neutrons. At a temperature of say 100 Kelvin with

$$k_B T = \frac{1}{2} m v^2$$

and a mass of 1.675 $ \times 10^{-27}$ kg that thermal velocity is 1280 m/s.

That slow, "long wavelength" neutron has a wavelength of 3 Angstroms!

So in the case of thermal neutrons with kinetic energies of ~1/100 eV, they really do just elastically scatter off of atoms or molecules; the binding energies are much larger than this, so for scattering the recoil will really be the whole molecule.

But sometimes thermal neutrons are absorbed!

Sometimes thermal neutrons will be absorbed by nuclei, some of them have huge thermal neutron cross-sections like lithium-6, boron-10 or cadmium-113. In this case it immediately becomes a nuclear process and the decay sequence localized to the nucleus in question.

But what about protons (hydrogen) scattering energetic neutrons?

For energetic neutrons, say 1 MeV with a kinetic energy of say 1.3 $\times 10^{-13}$ joules, the wavelength is now about 0.0003 Angstroms or 30 femtometer (fermi) which means it will likely be localized at one nucleus within the molecule.

Most of the time it will either elastically or inelastically scatter off of the nuclei, be it a proton (hydrogen) or an oxygen nucleus.

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The neutron collides with a nucleus, and it doesn't matter what atom or molecule that nucleus is part of. Collisions between particles of equal mass lead to more energy loss than collisions with a heavier particle, and therefore hydrogen nuclei slow down the neutrons the fastest.

The method detects elemental concentrations, not chemical species. However, if the concentration of H-nuclei is very high, then H2O is the only H-carrying species that is plausibly abundant enough.

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