Quiz — Chapter 10: Exotic Nuclei

Instructions. Choose the best answer for each question. Answers are provided at the end.

Q1. Approximately how many bound nuclear species are predicted to exist between the proton and neutron drip lines?

(a) 300 (b) 3,300 (c) 7,000 (d) 50,000

Q2. The neutron drip line has been experimentally determined for elements up to approximately:

(a) Helium ($Z = 2$) (b) Neon ($Z = 10$) (c) Calcium ($Z = 20$) (d) Tin ($Z = 50$)

Q3. Which production method is best suited for studying nuclei with half-lives shorter than 1 millisecond?

(a) ISOL (Isotope Separation On-Line) (b) Projectile fragmentation (in-flight separation) (c) Neutron activation (d) Spallation followed by chemical separation

Q4. A halo nucleus is characterized by all of the following EXCEPT:

(a) Very low nucleon separation energy (b) Valence nucleons in low angular momentum orbits ($\ell = 0$ or $1$) (c) A deformed nuclear core (d) An anomalously large matter radius

Q5. The two-neutron separation energy of $^{11}$Li is approximately:

(a) 369 keV (b) 8 MeV (c) 28 MeV (d) 0.5 eV

Q6. Why are neutron halos more spatially extended than proton halos with similar separation energies?

(a) Neutrons are lighter than protons (b) Neutrons do not experience the Coulomb barrier that confines protons (c) The strong force is weaker for neutrons (d) Neutrons have spin 1, allowing larger orbital radii

Q7. The parity inversion in $^{11}$Be refers to the fact that:

(a) The ground state has positive parity instead of the expected negative parity (b) The ground state has negative parity instead of the expected positive parity (c) The first excited state has the same parity as the ground state (d) The parity quantum number is not well-defined for halo nuclei

Q8. Which physical mechanism is primarily responsible for the evolution of shell structure far from stability?

(a) The Coulomb interaction between protons (b) The tensor component of the nuclear force and three-nucleon forces (c) Relativistic corrections to the nuclear potential (d) The weak interaction

Q9. The island of inversion refers to a region where:

(a) Protons and neutrons exchange roles in the shell model (b) Nuclear shapes invert from prolate to oblate (c) Deformed intruder configurations become the ground state, contrary to the standard shell model prediction (d) The sign of the nuclear binding energy changes

Q10. In the island of inversion around $N = 20$, the intruder configuration involves:

(a) Promoting protons from the $sd$ shell to the $fp$ shell (b) Promoting neutrons from the $sd$ shell to the $fp$ shell (c) Removing neutrons from the $p$ shell (d) Adding neutrons to the $g$ shell

Q11. A Borromean nucleus is defined as a three-body system where:

(a) All three pairwise subsystems are bound (b) Exactly one pairwise subsystem is bound (c) No pairwise subsystem is bound, yet the three-body system is bound (d) The nucleus can only exist at very high temperatures

Q12. Which of the following is a confirmed Borromean nucleus?

(a) $^{12}$C (b) $^{208}$Pb (c) $^{6}$He (d) $^{56}$Fe

Q13. Proton radioactivity was first observed from a ground state in:

(a) $^{4}$He (b) $^{151}$Lu (c) $^{238}$U (d) $^{11}$Li

Q14. The $N = 34$ shell closure was confirmed by measuring which quantity in $^{54}$Ca?

(a) The nuclear charge radius (b) The beta-decay half-life (c) The energy of the first $2^+$ excited state (d) The neutron capture cross section

Q15. Why is the neutron-rich frontier important for nuclear astrophysics?

(a) Neutron-rich nuclei are needed for nuclear fusion reactors (b) The r-process path runs through neutron-rich nuclei whose properties are largely unmeasured (c) Neutron-rich nuclei are used in medical imaging (d) All stable nuclei are neutron-rich

Q16. FRIB's primary beam power of 400 kW is significant because:

(a) It determines the maximum beam energy (b) Higher beam power produces higher rates of rare isotopes (c) It allows the accelerator to operate continuously without cooling (d) It is needed to overcome the Coulomb barrier

Q17. The narrow momentum distribution observed for $^{9}$Li fragments after $^{11}$Li breakup is evidence for a halo because:

(a) Narrow momentum implies large spatial extent, via the uncertainty principle (b) Narrow momentum implies the neutrons are tightly bound (c) All nuclear fragmentation produces narrow momentum distributions (d) The momentum distribution directly measures the nuclear charge

Q18. Which newly established magic number was confirmed by measuring $E(2^+_1) = 2.563$ MeV in $^{52}$Ca?

(a) $N = 16$ (b) $N = 20$ (c) $N = 32$ (d) $N = 50$

Q19. The oxygen neutron drip line occurs at $^{24}$O ($N = 16$) rather than at $^{28}$O ($N = 20$). This is because:

(a) The Coulomb interaction destabilizes oxygen isotopes with $N > 16$ (b) The $N = 20$ shell closure disappears in oxygen, replaced by a gap at $N = 16$ due to three-nucleon forces (c) $^{28}$O undergoes spontaneous fission (d) The pairing interaction is zero for $N > 16$ in oxygen

Q20. Two-proton radioactivity has been observed in $^{45}$Fe. This occurs because:

(a) $^{45}$Fe has too few neutrons for nuclear stability (b) The one-proton daughter $^{44}$Mn is more unbound than $^{45}$Fe itself, so sequential emission is energetically forbidden, but two-proton emission to $^{43}$Cr is allowed (c) The Coulomb barrier for two-proton emission is lower than for one-proton emission (d) $^{45}$Fe is a Borromean nucleus

Answers

  1. (c) ~7,000 bound species are predicted; only ~3,300 have been observed.

  2. (b) The neutron drip line is experimentally known up to neon ($Z = 10$).

  3. (b) In-flight separation has no diffusion delay, enabling study of nuclei with sub-microsecond half-lives. ISOL requires milliseconds for diffusion from the target.

  4. (c) Halo nuclei are characterized by low separation energy, low-$\ell$ valence orbits, and large matter radius. A deformed core is not a defining feature of halos.

  5. (a) $S_{2n}(^{11}\text{Li}) = 369.15 \pm 0.65$ keV.

  6. (b) Protons experience the Coulomb barrier, which confines them near the nucleus even at low binding energy. Neutrons, being uncharged, have no Coulomb barrier and can extend much further.

  7. (a) The naive shell model predicts a $1/2^-$ ground state ($0p_{1/2}$ orbit), but the observed ground state is $1/2^+$ ($1s_{1/2}$ orbit) — positive parity instead of negative.

  8. (b) The tensor force (from one-pion exchange) and three-nucleon forces shift single-particle energies as a function of which orbits are occupied, modifying shell gaps far from stability.

  9. (c) The island of inversion is where deformed intruder configurations (neutrons promoted across the $N = 20$ gap) gain enough correlation energy from deformation to become the ground state.

  10. (b) Neutrons are promoted from the $sd$ shell ($0d_{3/2}$) across the $N = 20$ gap into the $fp$ shell ($0f_{7/2}$, $1p_{3/2}$).

  11. (c) A Borromean system is bound as a whole, but no pair of its constituents forms a bound subsystem. Named after the Borromean rings.

  12. (c) $^{6}$He $= ^{4}$He $+ n + n$; neither $^{5}$He nor the dineutron is bound.

  13. (b) Ground-state proton radioactivity was first identified in $^{151}$Lu by Hofmann et al. at GSI in 1981.

  14. (c) The elevated $E(2^+_1) = 2.043$ MeV in $^{54}$Ca (and $E(2^+_1) = 2.563$ MeV in $^{52}$Ca for $N = 32$) indicates a robust shell closure, consistent with three-nucleon force predictions.

  15. (b) The rapid neutron capture process (r-process) synthesizes heavy elements along a path through neutron-rich nuclei, many of which are experimentally unstudied.

  16. (b) Rare isotope production rates scale approximately linearly with beam intensity. Higher beam power means higher production rates, enabling the study of the rarest isotopes.

  17. (a) By the Heisenberg uncertainty principle, a spatially extended halo ($\Delta x$ large) implies a narrow momentum distribution ($\Delta p$ small). The narrow FWHM of 45 MeV/$c$ corresponds to a halo extending ~9 fm from the core.

  18. (c) $N = 32$ was confirmed as a new magic number by the high $E(2^+_1)$ in $^{52}$Ca measured at ISOLDE.

  19. (b) Three-nucleon forces raise the $\nu 0d_{3/2}$ orbit in oxygen, creating a large gap at $N = 16$ (between $\nu 1s_{1/2}$ and $\nu 0d_{3/2}$). The $N = 20$ gap effectively collapses for oxygen, making $^{24}$O the last bound oxygen isotope and $^{28}$O unbound.

  20. (b) In $^{45}$Fe, the one-proton separation energy $S_p$ is positive (or only barely negative), meaning one-proton emission to $^{44}$Mn is energetically forbidden or strongly suppressed. However, the two-proton separation energy $S_{2p}$ is significantly negative, making simultaneous two-proton emission to $^{43}$Cr the favored decay channel.