= Solution
Interpret the displayed <semi-empirical mass formula> as an equation for mass energy, using $c=1$ for the mass terms. Its seven contributions are as follows.
The term $Z(m_p+m_e)$ is the rest energy of the $Z$ <protons> and $Z$ atomic <electrons>; $(A-Z)m_n$ is the rest energy of the <neutrons>. Including $Zm_e$ makes this an atomic-mass approximation. Small atomic electronic binding energies are neglected.
The volume contribution $-a_vA$ represents the short-range attractive <strong interaction>. Saturation gives each nucleon roughly a fixed number of neighbors, so the <nuclear binding energy> is approximately proportional to $A$; binding lowers the mass. The surface contribution $+a_sA^{2/3}$ restores the binding missing from <nucleons> near the surface. Approximately constant nuclear density gives radius proportional to $A^{1/3}$ and area proportional to $A^{2/3}$, explaining that power and the positive mass correction.
The <Coulomb potential energy> contribution $+a_cZ^2/A^{1/3}$ is positive because <proton> charges repel. A sphere's electrostatic self-energy scales as $Z^2/R$, and $R\propto A^{1/3}$. The more refined proton-pair count $Z(Z-1)$ differs from the $Z^2$ approximation explicitly used here.
The <nuclear symmetry energy> contribution $+a_a(Z-A/2)^2/A$ penalizes unequal <neutron> and <proton> populations. By the <Pauli exclusion principle>, filling one species' higher-momentum states is energetically more expensive than balancing the two <Fermi seas>; nuclear interactions also contribute to the empirical coefficient. The stated convention is equivalent to $23.285(N-Z)^2/A$ MeV, since $Z-A/2=(Z-N)/2$. It must not be combined with the usual coefficient near $23$ MeV without this factor of four.
Finally, <nuclear pairing> favors paired <protons> and paired <neutrons>. In the mass formula,
$$
\boxed{\Delta M_{\rm pair}c^2=
\begin{cases}
-a_pA^{-1/2}&Z,N\text{ both even},\\
0&A\text{ odd},\\
+a_pA^{-1/2}&Z,N\text{ both odd}.
\end{cases}}
$$
The signs reverse when this correction is written as a contribution to positive <nuclear binding energy>. This smooth <liquid-drop model> omits detailed nuclear shell corrections.
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