Self-Assessment Quiz — Chapter 30
Test your understanding of the core concepts before moving on. Try to answer each question before checking the solutions at the end.
Q1. (Multiple Choice) A tandem Van de Graaff accelerator with terminal voltage $V$ accelerates an ion that enters as a singly negative ion and is stripped to charge state $q = Ze$ at the terminal. The final kinetic energy is:
(a) $ZeV$ (b) $(1 + Z)eV$ (c) $2ZeV$ (d) $Z^2 eV$
Q2. (True/False) The cyclotron frequency of a non-relativistic charged particle in a uniform magnetic field depends on the particle's speed.
Q3. (Multiple Choice) The non-relativistic maximum kinetic energy of a particle in a cyclotron is:
(a) $T = qBR$ (b) $T = q^2 B^2 R^2 / (2m)$ (c) $T = qBR^2 / (2m)$ (d) $T = q^2 B R^2 / m$
Q4. (Short Answer) Why does the classical cyclotron fail for relativistic particles? How does the isochronous cyclotron solve this problem?
Q5. (Multiple Choice) The magnetic rigidity $B\rho$ of a charged particle is equal to:
(a) $mv/q$ (non-relativistic) (b) $p/q$ (exact, all regimes) (c) $2T/qB$ (d) $qB/m$
Q6. (True/False) In a synchrotron, both the magnetic field and the RF frequency must change during acceleration.
Q7. (Multiple Choice) FRIB's primary accelerator is a:
(a) Coupled superconducting cyclotron (b) Synchrotron (c) Superconducting linear accelerator (linac) (d) Tandem Van de Graaff
Q8. (Short Answer) Name the three stages of a modern heavy-ion linac, in order of increasing beam energy: (1) _, (2) _, (3) ____.
Q9. (Multiple Choice) In the ISOL method for radioactive beam production, the primary beam strikes:
(a) A thin target; products continue forward at beam velocity (b) A thick target; products stop, diffuse out, and are re-ionized (c) A gas target; products are stopped in helium gas (d) A liquid target; products are extracted chemically
Q10. (True/False) The ISOL method can efficiently produce beams of all elements, regardless of their chemical properties.
Q11. (Multiple Choice) Which radioactive beam production method is best suited for studying nuclei with half-lives of 10 microseconds?
(a) ISOL (the diffusion time is too long for fragmentation) (b) Projectile fragmentation (production to experiment in microseconds) (c) Either method works equally well (d) Neither method — 10 microseconds is too short for any technique
Q12. (Short Answer) In projectile fragmentation, the fragment separator selects isotopes using two physical quantities measured in two stages. What are they?
Q13. (Multiple Choice) Gamma-ray tracking arrays like GRETINA achieve Doppler correction for fast beams by:
(a) Using very thick germanium crystals to stop all gamma rays in one interaction (b) Determining the 3D position of each gamma-ray interaction to reconstruct the photon direction (c) Placing detectors only at 90 degrees where the Doppler shift is zero (d) Slowing the beam to $\beta < 0.01$ before the target
Q14. (True/False) A Penning trap uses a combination of magnetic and electrostatic fields to confine charged ions.
Q15. (Multiple Choice) The mass resolving power of a Penning trap is typically:
(a) $m/\Delta m \sim 10^2$–$10^3$ (b) $m/\Delta m \sim 10^4$–$10^5$ (c) $m/\Delta m \sim 10^7$–$10^9$ (d) $m/\Delta m \sim 10^{12}$
Q16. (Short Answer) What three ground-state nuclear properties can laser spectroscopy measure simultaneously?
Q17. (Multiple Choice) An active target like the AT-TPC differs from a conventional solid target in that:
(a) It uses a liquid target for higher density (b) It uses a gas that serves simultaneously as target and detection medium (c) It uses a spinning solid target to distribute beam heating (d) It uses a cryogenic solid hydrogen target
Q18. (True/False) In the particle identification method for fragmentation experiments, the atomic number $Z$ is determined from the energy loss $\Delta E$ in a detector, while the mass-to-charge ratio $A/Z$ is determined from magnetic rigidity and time of flight.
Q19. (Short Answer) What is a Program Advisory Committee (PAC), and what role does it play in the lifecycle of a nuclear physics experiment?
Q20. (Multiple Choice) Which of the following is NOT a major radioactive beam facility?
(a) FRIB (Michigan State University, USA) (b) CERN-ISOLDE (Geneva, Switzerland) (c) SLAC (Stanford, USA) (d) RIKEN-RIBF (Saitama, Japan)
Solutions
Q1. (b) — The negative ion gains energy $eV$ approaching the terminal, is stripped to charge $+Ze$, then gains energy $ZeV$ leaving. Total: $(1 + Z)eV$.
Q2. False — The non-relativistic cyclotron frequency $\omega_c = qB/m$ depends only on $q/m$ and $B$, not on speed. This is the fundamental property that makes the cyclotron work.
Q3. (b) — $T = q^2 B^2 R^2 / (2m)$, derived from setting the Lorentz force equal to the centripetal force at the extraction radius.
Q4. As the particle becomes relativistic, $\gamma$ increases and the revolution frequency $\omega = qB/(\gamma m)$ decreases, falling out of synchronism with the fixed RF. The isochronous cyclotron compensates by making $B$ increase with radius as $B(r) = \gamma(r) B_0$, keeping the revolution frequency constant.
Q5. (b) — $B\rho = p/q$ is the exact relativistic definition. Option (a) is the non-relativistic approximation.
Q6. True — The field ramps to maintain a constant orbit radius as momentum increases, and the RF frequency tracks the changing revolution frequency.
Q7. (c) — FRIB uses a superconducting linear accelerator (folded linac) with 324 superconducting cavities.
Q8. (1) Radio-Frequency Quadrupole (RFQ), (2) Drift Tube Linac (DTL), (3) Superconducting linac.
Q9. (b) — ISOL uses a thick target; the products stop inside, diffuse out of the heated target material, are ionized, mass-separated, and optionally post-accelerated.
Q10. False — The ISOL method depends on the diffusion and effusion of products from the target. Refractory elements (e.g., Zr, Nb, Mo) diffuse slowly from most target materials, making ISOL inefficient for these species.
Q11. (b) — Projectile fragmentation delivers isotopes in microseconds (the flight time through the separator). The ISOL diffusion time (milliseconds to seconds) is far too long for 10-$\mu$s species.
Q12. First stage: magnetic rigidity $B\rho = p/q$, which selects on $A/Z$ (since fragments have similar velocities). Second stage: after a wedge degrader that introduces $Z$-dependent energy loss, a second $B\rho$ selection separates isotopes with different $Z$.
Q13. (b) — Tracking arrays determine the 3D coordinates of each gamma-ray interaction point to $\sim 2$ mm, then reconstruct the photon emission direction from the Compton scattering kinematics, enabling event-by-event Doppler correction.
Q14. True — A strong axial magnetic field provides radial confinement; a weak electrostatic quadrupole field provides axial confinement.
Q15. (c) — Penning traps routinely achieve $\delta m / m \sim 10^{-8}$ to $10^{-9}$, corresponding to resolving powers of $10^7$–$10^9$.
Q16. Nuclear charge radius (from isotope shifts), nuclear spin (from the hyperfine structure pattern), and nuclear electromagnetic moments — magnetic dipole moment $\mu$ and electric quadrupole moment $Q_s$ (from hyperfine splitting constants).
Q17. (b) — An active target uses a gas (e.g., deuterium, helium) that serves simultaneously as the reaction target and as the detection medium: charged reaction products ionize the gas, and the resulting electron tracks are recorded.
Q18. True — $Z$ from $\Delta E \propto Z^2/\beta^2$ (Bethe-Bloch), and $A/Z$ from $B\rho / (\beta\gamma) = (A/Z)(m_u c / e)$, with $\beta$ measured by TOF.
Q19. A PAC is a committee of external experts that reviews experimental proposals submitted to a facility. It evaluates proposals on scientific merit, technical feasibility, and efficient use of facility resources, and recommends which proposals should receive beam time. PAC approval is required before an experiment can be scheduled.
Q20. (c) — SLAC is the Stanford Linear Accelerator Center, used for particle physics (electron-positron collisions, photon science). It is not a radioactive beam facility. FRIB, ISOLDE, and RIKEN-RIBF are all major radioactive beam facilities.