Why 3He(n,p)3H nuclear reaction proceeds but 3He(n,gamma)4He heavily suppressed? The neutron capture reaction 3He(n,p)3H is very useful for neutron detection as the Q value of ~700keV is converted to kinetic energies in the produced p and 3H. These charged products can then ionize gas mixed in with 3He in a gas chamber and then be detected. The cross-section for this reaction is massive at ~kilobarns for thermal neutrons (~2000m/s).
My question is: why does the reaction 3He(n,gamma)4He not occur very often? The Q-value for this is ~20MeV! This is because the 4He nucleus is so tightly bound. A quick literature search for this puts the cross-section at ~microbarns.
Am I missing something? Is there some selection rule I'm not aware of?
 A: It's because the lowest-energy excited state in $^4$He is at 20.2 MeV and has spin-parity $0^+$.  (I think that this link selects $^4$He from the chart of isotopes; click "list of levels" or "level scheme.")  A $0^+\to0^+$ transition cannot emit a photon, because the photon must carry off one unit of angular momentum.  That state is just wide enough to overlap with the energy of an unbound $^3$He and neutron at rest.
You get the same sort of effect in $^6$Li(n,$\alpha$)$^3$H.  (Though tonight I can't find an associated excitation in $^7$Li, grrr.) For this reason, enriched lithium is also used to dope scintillators for neutron detection or for neutron shielding where it's important to have a low gamma background.
All the heavier nuclei have internal transitions and emit 1–10 MeV of photons after neutron capture.  Usually the photons come from a cascade of internal transitions and don't have anything like a line spectrum.
The $^3$He nucleus has a fairly large magnetic moment and can pick up a nuclear spin from an electron-polarized alkali vapor, like optically pumped rubidium or potassium.  Since the $^3$He+n capture passes through a $0^+$ state, polarized $^3$He will prefer to absorb one neutron spin state.  This is a common method for polarizing beams of thermal or cold neutrons.
