This in fact measures the beta-decay-rate of the neutron, as each neutron is assumed to decay into a single proton, an invisible neutrino and an electron.
So if you have a bunch of neutrons in a bottle, why can't they form a nucleus and then an atom. When some of them decay to protons and electrons you have all required parts.
The nuclear force binding an atom has a very short distance. So, I guess the question is how close can a neutron get to another neutron?
This is an excellent question!
Electron capture by a proton requires some energy to be converted into a neutron and a neutrino. We don't have this energy available here so that the inverse reaction is not possible.
Note that sometimes, it is possible that a neutron directly decays into an hydrogen atom. This can be observed.
It is a combination of the uncertainty principle (that implies that the neutrons have some momentum when located in a zone of 1fm) and the range and strength of the nuclear force. Two neutrons (or two protons) cannot form and bound state as the above-mentioned small amount of momentum cannot be compensated by the strong force.
Does it help (I am a bit out of my field with your questions ;) )?
It does, thank you :)
You are welcome! :)