Decay of proton to neutron

Question

Decay of proton to neutron is--

1. Possible only inside nucleus

2)Not possible

3. Always possible as it is associated with Beta+ decay

I thought that mass should be conserved here, but we know that neutron mass is more than proton,so how in any emission can proton decay into a neutron? [The correct answer given here is 2,i.e(possible only inside nucleus)]

One analogy that i came with is maybe, according to Einstein's equation, we should give some energy to make this decay happen, so that the extra mass is provided by energy, according to E=mc^2.

Is that the correct analogy? I'm still not convinced that decay of proton to neutron should happen,can someone please explain it in detail.

Answer 1

Mass is not a conserved quantity where one has to use special relativity to describe the data. Mass is the "length" of the four vector $(E,p_x,p_y,p_z)$ that, in the case of a nucleus, describes each nucleon in the nucleus. Energy and momentum are the conserved quantities.

The free neutron decays because there exists a lower energy state for its constituents that form another bound state, the proton, and release the energy in an electron and an antineutrino, the Feynman diagram:

The proton and neutron differ in their quark content, as you can see in the diagram.

Feynman diagrams can be read with the time going the other direction, i.e. a proton going to a neutron, with the appropriate changes in charges and lepton numberss, but are not possible until, as you say the energy is supplied.

This has a probability to happen in nuclear decays, where there are lower energy states to which the nucleus can break down, and in the beta plus decay , part of the energy is used to turn a proton structure to a neutron structure.

It is the decay of a nucleus, explained by a change in the proton structure when energetically possible, not really a decay of the proton.