Self-Assessment Quiz — Chapter 33

Test your understanding of the major open questions and frontier facilities before moving to the capstone. Try to answer each question before checking the solutions at the end.

Q1. (Multiple Choice) The neutron drip line has been experimentally established up to which element?

(a) Helium ($Z = 2$) (b) Oxygen ($Z = 8$) (c) Neon ($Z = 10$) (d) Calcium ($Z = 20$)

Q2. (Multiple Choice) Approximately how many bound nuclear species are predicted to exist?

(a) ~3,400 (b) ~5,000 (c) ~7,000 (d) ~10,000

Q3. (True/False) The proton drip line is more difficult to reach experimentally than the neutron drip line for most elements.

Q4. (Short Answer) What is the nuclear equation of state, and why is it difficult to determine at densities above $2\rho_0$?

Q5. (Multiple Choice) Which of the following observations directly constrains the nuclear equation of state at high density?

(a) Alpha decay half-lives of actinide nuclei (b) Neutron star mass-radius measurements from NICER (c) The binding energy of $^{208}$Pb (d) The spectrum of hydrogen

Q6. (Multiple Choice) The current experimental disagreement about the predicted proton magic number for superheavy elements is between:

(a) $Z = 82$ and $Z = 92$ (b) $Z = 114$ and $Z = 120$ (c) $Z = 126$ and $Z = 164$ (d) $Z = 100$ and $Z = 110$

Q7. (True/False) The currently synthesized superheavy elements have already reached the predicted center of the island of stability at $N = 184$.

Q8. (Short Answer) Name two pieces of evidence that confirmed neutron star mergers as a site of the r-process.

Q9. (Multiple Choice) Neutrinoless double beta decay ($0\nu\beta\beta$), if observed, would demonstrate that:

(a) Protons can decay (b) The neutrino is a Majorana particle and lepton number is violated (c) Dark matter interacts with nuclei (d) The Standard Model is complete

Q10. (True/False) The nuclear matrix elements for $0\nu\beta\beta$ are precisely known, so the main experimental challenge is just building a large enough detector.

Q11. (Multiple Choice) In direct dark matter detection, spin-independent WIMP-nucleus scattering cross sections scale approximately as:

(a) $A^{1/3}$ (b) $A$ (c) $A^2$ (d) $Z^2$

Q12. (Short Answer) What is the "neutrino fog" (or "neutrino floor"), and why does it matter for dark matter searches?

Q13. (Multiple Choice) ITER is designed to achieve a plasma energy gain factor of:

(a) $Q = 1$ (breakeven) (b) $Q = 5$ (c) $Q = 10$ (d) $Q = 50$

Q14. (True/False) The NIF ignition experiment in December 2022 achieved engineering breakeven — the fusion energy exceeded the total electrical energy used to power the laser system.

Q15. (Short Answer) The proton spin puzzle refers to the discovery that quark spins contribute only about 30% of the proton's total spin. What accounts for the remaining ~70%?

Q16. (Multiple Choice) Which facility is specifically designed to resolve the proton spin puzzle?

(a) FRIB (b) ITER (c) The Electron-Ion Collider (EIC) (d) LEGEND-1000

Q17. (Multiple Choice) FRIB's primary capability is:

(a) Colliding electrons with protons at high energy (b) Producing rare isotopes via heavy-ion beam fragmentation at 400 kW (c) Detecting gravitational waves from neutron star mergers (d) Confining deuterium-tritium plasma in a tokamak

Q18. (True/False) Ab initio nuclear structure calculations can now reach nuclei in the tin region ($A \sim 100$–$140$) starting from the underlying nuclear force.

Q19. (Short Answer) Name three career paths available to nuclear physics graduates outside of academic research.

Q20. (Multiple Choice) Which statement best summarizes the central message of this chapter?

(a) Nuclear physics is a completed science with no remaining open questions (b) Nuclear physics is primarily a historical field, with all major facilities now shut down (c) Nuclear physics is defined by fundamental open questions that connect to astrophysics, cosmology, particle physics, and energy policy (d) The only remaining question in nuclear physics is whether fusion energy will work

Solutions

Q1. (c) Neon ($Z = 10$). The neutron drip line has been experimentally established only up to $Z = 10$.

Q2. (c) ~7,000. Current theoretical models predict approximately 7,000 bound nuclear species between the proton and neutron drip lines.

Q3. False. The proton drip line is relatively well known up to $Z \approx 90$. The neutron drip line is the frontier — known only to $Z = 10$.

Q4. The nuclear equation of state is the relationship between pressure, energy density, and composition of nuclear matter. At densities above $2\rho_0$, it is difficult to determine because: (1) no terrestrial experiment can sustain such densities in equilibrium; (2) the nuclear force at high density is sensitive to many-body effects, three-nucleon forces, and possibly phase transitions to exotic matter (hyperons, quark matter); and (3) different theoretical models that agree at $\rho_0$ diverge dramatically at higher densities.

Q5. (b) NICER mass-radius measurements directly constrain the EOS because the mass-radius relationship of neutron stars is determined by the EOS through the TOV equation.

Q6. (b) $Z = 114$ and $Z = 120$. Different theoretical models (Skyrme HF, relativistic mean field, macroscopic-microscopic) predict different proton shell closures in the superheavy region.

Q7. False. The most neutron-rich known superheavy isotopes have $N \approx 175$–$177$, which is 7–9 neutrons short of the predicted magic number $N = 184$.

Q8. (1) The gravitational wave signal GW170817, detected by LIGO/Virgo, confirmed a binary neutron star merger. (2) The associated kilonova (AT2017gfo) showed infrared emission consistent with the radioactive decay of r-process elements (particularly lanthanides), confirming that heavy elements were synthesized in the merger ejecta.

Q9. (b) The observation of $0\nu\beta\beta$ would prove that neutrinos are Majorana particles (identical to their antiparticles) and that lepton number is violated ($\Delta L = 2$).

Q10. False. The nuclear matrix elements for $0\nu\beta\beta$ are a major source of uncertainty — different theoretical calculations disagree by factors of 2–3. Reducing this uncertainty is an active area of nuclear theory research.

Q11. (c) $A^2$. For spin-independent (coherent) scattering, the WIMP interacts coherently with all nucleons, and the cross section scales as the square of the mass number.

Q12. The neutrino fog is the irreducible background from coherent elastic neutrino-nucleus scattering (CE$\nu$NS) by solar, atmospheric, and diffuse supernova neutrinos. As dark matter detectors become more sensitive, they will begin detecting these neutrino-induced nuclear recoils, which are indistinguishable from WIMP scattering events. This sets a practical floor on dark matter detection sensitivity.

Q13. (c) $Q = 10$. ITER is designed to produce 500 MW of fusion power from 50 MW of input heating power.

Q14. False. NIF achieved scientific ignition — fusion energy exceeded the laser energy delivered to the target. But the total electrical energy consumed by the laser system was approximately 300 MJ, far more than the 3.15 MJ of fusion energy produced. Engineering breakeven was not achieved.

Q15. The remaining ~70% comes from gluon spin (~40%, measured primarily at RHIC) and orbital angular momentum of quarks and gluons (~30%, poorly constrained experimentally and targeted by the EIC).

Q16. (c) The Electron-Ion Collider (EIC) at Brookhaven National Laboratory, designed for polarized electron-proton/ion collisions to probe nucleon structure.

Q17. (b) FRIB produces rare isotopes by fragmenting intense heavy-ion beams (up to 400 kW) on production targets and separating the fragments with the ARIS separator.

Q18. True. Methods like coupled-cluster theory and in-medium similarity renormalization group (IM-SRG), using chiral EFT interactions, have extended ab initio calculations to medium-mass nuclei including the tin region.

Q19. Any three of: medical physics, nuclear engineering/reactor operations, national security/nonproliferation, nuclear forensics, science policy (DOE, NRC, IAEA), data science/industry, defense/intelligence.

Q20. (c) Nuclear physics is defined by fundamental open questions that connect to astrophysics, cosmology, particle physics, and energy policy.