Semi-empirical mass formula
Nuclear physics · Physics
Study notes
Worked example: Estimate the binding energy per nucleon of iron-56 (Z=26, A=56) with the SEMF. Step 1: Volume: 15.8×56 = 884.8 MeV. Step 2: Surface: −18.3×56^{2/3} = −18.3×14.63 = −267.7 MeV. Step 3: Coulomb: −0.714×26×25/56^{1/3} = −0.714×650/3.83 = −121.2 MeV. Step 4: Asymmetry: A−2Z = 4; −23.2×16/56 = −6.6 MeV. Step 5: Pairing (even-even): +12/√56 = +1.6 MeV. Step 6: Total B = 884.8−267.7−121.2−6.6+1.6 = 490.9 MeV; B/A = 8.77 MeV — matches the measured 8.79 MeV! Conclusion: five terms capture the most-bound nucleus in nature — the peak everything fuses or fissions toward.