FR07
Nuclear structure, reactions and stellar rates
A nucleus has no single portrait. Its masses tell us how tightly its particles are bound, its spectral lines reveal how it moves, and scattered waves probe how it interacts. Follow those clues from a single neutron to collective rotation, then calculate how a laboratory reaction feeds a star.
Follow the question you can already ask
Chapters 1–2 introduce nuclear scales and a particle in a finite well. Chapters 3–4 compare observed levels with single-neutron and collective models. Chapters 5–6 follow a neutron through a complex potential and ask how much an angular pattern tells us. Chapter 7 averages a measured reaction over a thermal distribution. Chapter 8 examines where familiar shells change near threshold; Chapter 9 walks through a published data table and a reproducible rate calculation.
Every chapter includes a worked example, a task that starts with a prediction, and exercises with explanations. Mathematical tools are introduced where they are used. The shared textbook plan supplies broader prerequisites as needed. Textbook plan
L1 · 1
What a nuclear mass tells us about binding
Calculate a binding energy from mass excesses, then distinguish average binding from the energy needed to remove the last neutron.
L2 · 2
How a finite nuclear well selects discrete levels
Match radial waves to find a binding threshold, then derive spin-orbit splitting and the number of states in each partner.
L2 · 3
Read a nuclear spectrum one neutron at a time
Use three evaluated oxygen-17 levels to derive spin-orbit splitting, test a one-neutron model and apply electric quadrupole selection rules.
L3 · 4
Paired nucleons in a rotating nucleus
Derive the erbium-166 rotational pattern, compare harmonic vibration and solve a small pairing example that connects single-particle and collective motion.
L3 · 5
Where the wave goes after a neutron meets a nucleus
Derive elastic flux loss, partial-wave amplitudes and cross sections for a complex nuclear optical potential.
L3 · 6
Why different nuclear potentials can fit the same scattering
Fit a frozen synthetic neutron record, derive Poisson deviance, and use held-out angles and a depth profile to study ambiguity.
L3 · 7
Find the collisions that burn deuterium
Derive a thermal reaction rate, locate the Gamow window and carry common calibration uncertainty through the integral.
L4 · 8
Why shells and tails change near the neutron drip line
Follow occupation-dependent shell shifts, derive a weakly bound tail and read the limited conclusion of a published oxygen-isotope calculation.
L4 · 9
Read a deuterium measurement and recalculate its thermal average
Follow the LUNA data columns, distinguish the published fit from a new fit, and check a bounded thermal-rate benchmark.
Three questions to try
- Which pattern fits an observed nuclear spectrum?
- Can different potentials explain the same angular data?
- Which measured energies control a stellar reaction rate?
The shell-filling and form-factor experiments remain in the nuclear-evidence route. Their roles here are prerequisite and comparison: neutron occupation, proton electromagnetic response and nuclear excitation spectra answer different questions. Shell filling · Form factor
Sources and reproduced scope
Evaluated level energies and published reaction measurements retain their source versions and uncertainties. Model curves, schematic figures and synthetic scattering records are identified separately. The offline benchmark files state which calculations have been reproduced.
- AME2020 nuclear reaction and separation energy tables, rct1.mas20 and rct2.mas20
Frozen March 2021 unrounded oxygen and beryllium entries, independently parsed from the mass table. Published marginal separation errors are retained. Hash marks describe extrapolation in that dated evaluation.
- M. N. Rosenbluth, High Energy Elastic Scattering of Electrons on Protons, Physical Review 79, 615 (1950)
The existing proton form-factor Lab uses one-photon Born kinematics and a fixed-momentum-transfer Rosenbluth separation. Its source documentation and numerical model remain owned by Issue 22.
- A. M. Moro, FRESCO notes, section 3.1, Optical Model
Equations 1–8: elastic-channel wave, partial-wave cross sections and complex-potential absorption. The local square-well implementation fixes a neutral projectile and centre-of-mass energy.
- Wang et al., The AME2020 atomic mass evaluation (II), Chinese Physics C 45, 030003 (2021)
Frozen March 3, 2021 mass-table format, neutron and hydrogen/deuterium rows. Mass excess and binding per nucleon are in keV; # marks extrapolated values. The course uses a three-row numerical excerpt with its original uncertainties.
- David Tong, Quantum Mechanics, Chapter 4, spherical finite potential well
Radial equation, regularity at the origin and the finite spherical well. Our bound-state threshold and tail curves are derived calculations for the stated infinite-core-mass example.
- M. Goeppert Mayer, On Closed Shells in Nuclei. II, Physical Review 75, 1969 (1949)
The spin-orbit interpretation of shell closures. The course derives the angular-momentum eigenvalues; its oscillator parameters are schematic and do not reproduce a complete experimental shell spectrum.
- TUNL, Energy Levels of A = 17 Nuclei, 1993TI07, Table 17.10
Selected oxygen-17 levels, spin/parity, energy errors and the width of the neutron-unbound 5.0848 MeV resonance. The numerical excerpt is separate from the fitted single-neutron model.
- NNDC, ENSDF adopted levels and gammas for erbium-166
Selected ground-band levels in the frozen adopted evaluation; the dataset records the evaluation date and errors. Only selected numerical facts are redistributed; model curves and artwork are original.
- M. Hjorth-Jensen, Nuclear TALENT, Electromagnetic transitions and beta decay (2017)
Multipole operators, reduced transition probabilities and angular-momentum selection. A selection rule permits a matrix element; it does not determine its size.
- J. Dobaczewski et al., Odd-even staggering, degenerate-shell seniority model
Exactly solvable degenerate-shell pairing example. Its fixed interaction and restricted shell are a teaching limit, not an isotope mass evaluation.
- R. F. Casten, Lectures on Nuclear Structure, NNPSS 2013
Collective rotational sequences and intrinsic deformation. The rigid rotor and harmonic vibrator are limiting models; the evaluated band residuals test their range.
- David Tong, Applications of Quantum Mechanics, scattering theory
Partial-wave amplitude, optical theorem, phase shifts and matching. Neutron scattering here fixes a centre-of-mass energy and a spinless central potential.
- H. Feshbach, C. E. Porter and V. F. Weisskopf, Model for Nuclear Reactions with Neutrons, Physical Review 96, 448 (1954)
Complex-potential description of elastic-channel loss. The browser implements a sharply bounded complex square well, not a global fitted optical potential.
- V. Mossa et al., The baryon density of the Universe from an improved rate of deuterium burning, Nature 587, 210–213 (2020)
Accepted manuscript, Eqs. 2–3 and Extended Data Tables 1–2: measured proton-deuteron S factors and reference thermal rates. The local subset fit and the published global fit are different calculations.
- R. Longland et al., Charged-particle thermonuclear reaction rates: I. Monte Carlo method and statistical distributions (2010), arXiv:1004.4136v1
Thermal-rate probability distributions and the need to keep common normalization errors correlated. The course derives its own first-order covariance propagation for the chosen fit.
- T. Otsuka et al., Three-body forces and the limit of oxygen isotopes, arXiv:0908.2607v3 (2010), PRL 105, 032501
Version 3, June 19, 2010; Eq. 1 and Figs. 2–4. The course reads the monopole mechanism and derives an illustrative occupation shift. It does not reproduce the many-body calculation or digitize its curves.
- NNDC, NuDat 3 user guide and terms of use
Contents, units, terms of use and changing evaluations. NuDat reports evaluated recommendations; their quoted errors do not include a model discrepancy.