Ejecta binding energy of an initially uniform core ($E_{\mathrm{ej}}=C(M_{\mathrm{Fe}}^{5/3}-M_c^{5/3})$)

For an initial uniform mass density $\rho$, integrate the gravitational work of the outer spherical shells from enclosed mass $M_c$ to $M_{\mathrm{Fe}}$. Since $r(m)=[3m/(4\pi \rho ){]}^{1/3}$, the positive unbinding cost is $C(M_{\mathrm{Fe}}^{5/3}-M_c^{5/3})$, with $C=(3G/5)(4\pi \rho /3{)}^{1/3}$. This includes shell–core interactions. It does not equal the final compact object's much greater binding energy. Dissociation, later recombination and overlying stellar layers add separate energy accounting.