Is the proton to neutron mass ratio different while they are free versus when they are bound inside a nucleus?
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However, it is hard to say anything about the masses of individual protons/neutrons in the nucleus, because you can only determine the total mass of the nucleus, but not the mass of a single proton/neutron inside the nucleus.
The above quote states the truth, there is no way to measure individual nucleons in the nucleus. But there is the mathematics developed to describe particles in those dimensions, special relativity and quantum mechanics. One can model mathematically the nucleus as a collective bound state of protons and neutrons.
Special relativity tells us that the invariant mass of the free particles is the length of the four vector .
In the nucleus the proton and neutron are not free, and quantum mechanics describes them as virtual particles which means that their four vectors are variable in length (see Feynman diagrams page), within the limits of the integration which will give measurable quantities. This means that the virtual masses of protons and neutrons will be different at a given time, but this will depend on the model used to fit observed data, as the periodic table and the binding energy curve.
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