My understanding of the two was as follows: the binding energy of a nucleus is, classically speaking, the energy needed to put together/take apart that nucleus completely (i.e. a measure of the strong force within that nucleus). However, in my mind separation energy is the energy necessary to take apart that nucleus into two (or more I suppose) specific constituent particles/nuclei.
I keep seeing these terms used, and I'm pretty sure my idea of these words are completely skewed. Could you tell me what these terms actually mean?
Answer
I believe you have the basic ideas correct.
The binding energy is the energy required to create Z separate protons and N=A-Z separate neutrons from a (A,Z) nucleus in its ground state. Another way to think about it is binding energy is the mass energy which is missing from a nucleus compared to the mass energy of the individual nucleons.
When talking about separation energy one should specify what is being separated from a nucleus. One can calculate 1-proton separation energy, 2-proton separation energy, 1-neutron s.e., etc. For example (as you suggest correctly), the 1-proton separation energy would be $$ [m(A-1,Z-1) + m(proton) - m(A,Z)]c^2$$ where $m$ is the nuclear mass.
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