Chapter 4 Further Reading — The Semi-Empirical Mass Formula

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Textbook Treatments

K. S. Krane, Introductory Nuclear Physics (Wiley, 1987), Chapter 3. The standard treatment. Krane derives each SEMF term clearly and discusses the valley of stability and drip lines. His Table 3.2 remains a useful reference for fitted parameters. Despite the book's age, this chapter has held up well — the SEMF itself hasn't changed.
S. S. M. Wong, Introductory Nuclear Physics, 2nd ed. (Wiley, 2004), Chapter 3. Similar in scope to Krane but somewhat more modern. Wong includes a useful discussion of the Coulomb exchange correction and the Wigner energy.
B. Povh, K. Rith, C. Scholz, F. Zetsche, and W. Rodejohann, Particles and Nuclei, 7th ed. (Springer, 2015), Chapter 2. A concise, clear treatment at a slightly lower level than Krane. Good for first exposure.
P. Ring and P. Schuck, The Nuclear Many-Body Problem (Springer, 1980; reprinted 2004), Chapter 2. Advanced treatment embedding the SEMF in the broader context of Hartree-Fock theory and the nuclear density functional. For students ready to go deeper into the many-body physics underlying the SEMF.
A. Bohr and B. R. Mottelson, Nuclear Structure, Vol. I (Benjamin, 1969; reprinted World Scientific, 1998), Chapter 2. The magisterial treatment by the master. Bohr and Mottelson derive the liquid drop model in the context of nuclear collective motion and connect it to the statistical properties of nuclear matter. Dense but rewarding.

C. F. von Weizsäcker, "Zur Theorie der Kernmassen," Zeitschrift für Physik 96, 431–458 (1935). The paper that launched the semi-empirical mass formula. Weizsäcker derived the volume, surface, Coulomb, and asymmetry terms and showed that the formula reproduces the trend of nuclear binding energies. In German; a milestone of nuclear physics.
H. A. Bethe and R. F. Bacher, "Nuclear Physics A. Stationary States of Nuclei," Reviews of Modern Physics 8, 82–229 (1936). The legendary "Bethe Bible" — the first comprehensive review of nuclear physics. Section IV contains the most influential early treatment of the mass formula, refining Weizsäcker's work and establishing the five-term form that we still use. This 148-page review is a masterpiece of scientific writing.
H. A. Bethe, "Energy Production in Stars," Physical Review 55, 434–456 (1939). Bethe's Nobel Prize-winning paper on the CNO cycle and pp chain. The connection between the SEMF (specifically the B/A curve) and stellar energy production is made explicit.

W. J. Huang, M. Wang, F. G. Kondev, G. Audi, and S. Naimi, "The AME 2020 atomic mass evaluation (I). Evaluation of input data, and adjustment procedures," Chinese Physics C 45, 030002 (2021). The current standard for nuclear mass data. The AME2020 includes evaluated masses for 3,557 nuclides (2,457 experimentally measured, 1,100 estimated from systematics). This is the dataset against which the SEMF should be tested.
M. Wang, W. J. Huang, F. G. Kondev, G. Audi, and S. Naimi, "The AME 2020 atomic mass evaluation (II). Tables, graphs and references," Chinese Physics C 45, 030003 (2021). The companion paper with the actual mass tables. Available online at the AMDC (Atomic Mass Data Center): https://www-nds.iaea.org/amdc/
G. Audi, F. G. Kondev, M. Wang, W. J. Huang, and S. Naimi, "The NUBASE2020 evaluation of nuclear physics properties," Chinese Physics C 45, 030001 (2021). Nuclear properties (half-lives, spins, parities, decay modes) for all known nuclides. Essential companion to the mass tables.

P. Möller, A. J. Sierk, T. Ichikawa, and H. Sagawa, "Nuclear ground-state masses and deformations: FRDM(2012)," Atomic Data and Nuclear Data Tables 109–110, 1–204 (2016). The Finite Range Droplet Model — the most widely used macroscopic-microscopic mass model. Achieves RMS residuals of 0.56 MeV over 2,353 nuclei. The FRDM extends the SEMF with finite-range surface energy, Coulomb redistribution, and Strutinsky shell corrections.
S. Goriely, N. Chamel, and J. M. Pearson, "Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas," Physical Review C 88, 061302(R) (2013). The HFB mass models (HFB-24 through HFB-31) are the leading microscopic mass models, based on Skyrme density functional theory. They achieve RMS residuals of 0.5–0.6 MeV without explicitly fitting to individual nuclei.
V. M. Strutinsky, "Shell effects in nuclear masses and deformation energies," Nuclear Physics A 95, 420–442 (1967). The original paper on the Strutinsky shell correction method — the mathematical framework for separating smooth (macroscopic) and oscillating (shell) contributions to nuclear binding energy.

M. Goeppert Mayer, "On Closed Shells in Nuclei," Physical Review 75, 1969–1970 (1949). The one-page paper in which Goeppert Mayer pointed out the empirical evidence for magic numbers. She received the Nobel Prize (1963) for the shell model that explained them.
O. Haxel, J. H. D. Jensen, and H. E. Suess, "On the 'Magic Numbers' in Nuclear Structure," Physical Review 75, 1766 (1949). The independent discovery of the role of spin-orbit coupling in producing the magic numbers, published nearly simultaneously with Goeppert Mayer's work.

National Nuclear Data Center (NNDC), Brookhaven National Laboratory: https://www.nndc.bnl.gov/ — Interactive chart of nuclides, nuclear wallet cards, evaluated nuclear data. The NuDat database allows searching binding energies, separation energies, and nuclear properties for any nuclide.
Atomic Mass Data Center (AMDC): https://www-nds.iaea.org/amdc/ — The official source for the Atomic Mass Evaluation tables.
IAEA Nuclear Data Services: https://www-nds.iaea.org/ — Comprehensive nuclear data including cross sections (ENDF), decay data, and reaction data.
FRIB Mass Explorer: https://massexplorer.frib.msu.edu/ — Interactive visualization of nuclear masses from various mass models, including comparisons to experimental data. An excellent tool for exploring the SEMF's predictions and limitations.

A. Pais, Inward Bound: Of Matter and Forces in the Physical World (Oxford, 1986), Chapter 15. A historian's account of the development of the liquid drop model and the mass formula, placing Weizsäcker's and Bethe's work in the context of 1930s nuclear physics.
J. Pearson, "The quest for a microscopic nuclear mass formula," Hyperfine Interactions 132, 59–74 (2001). A readable review of the progression from the SEMF to modern microscopic mass models, by one of the leading practitioners.