What would happen if the half-life of a neutron was much more less than it is now? How could this affect the nuclei?
The halflife of the neutron is set by three things (more or less):
- the mass difference between the neutron and the proton,
- the number (two) of light particles that accompany the decay and
- the strength of the weak interaction.
Changing number (3) effects the lifetime of all weak mediated processes, but all of them in the same sense.
Changing (1) reconfigures the entire table of the nuclides.
Changing (2) requires a complete re-write of our understanding of small scale physics and could do essentially anything.
For the lifetime of the neutron to be different, the weak interaction coupling constant would be different. As far as nuclei are concerned the unstable ones with beta decays would have different lifetimes. In general all weak interaction mediated decays would have different lifetimes.
Ryan is correct. In addition I would point to beta decay, in one form of which a neutron is transformed into a proton, inside the nucleus. This is called $\beta^-$ decay and is accompanied by the emission of an electron $e^-$ by the affected nucleus.