Keele University Physics Exam - Nuclear and Particle Physics, 2009, Exams of Nuclear Physics

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KEELE UNIVERSITY

DEGREE EXAMINATIONS, 2009

Level 2 (PRINCIPAL COURSE)

Tuesday 26th May 2009, 9:30 - 11:

PHYSICS

PHY-

Nuclear and particle physics

Candidates should attempt to answer FOUR questions.

Tables of physical and mathematical data may be obtained from the invigilator.

1. (a) Describe the charge numbers, strangeness S, charm C, and relative mass of the 6 quarks. [20]

(b) Deduce the quark structure of the following mesons, none of which contain a top quark: i. K+; S = 1, C = 0, mass=495 MeV/c^2 , [10] ii. D+; S = 0, C = 1, mass=1866 MeV/c^2 , [10] iii. F +; S = 1, C = 1, mass=1971 MeV/c^2 , [10] iv. B+; S = 0, C = 0, mass=5271 MeV/c^2. [10]

(c) The K+^ can be produced via the strong interaction:

π+^ + n → Λo^ + K+

i. Discuss the conservation of baryon number B, strangeness and charm in this reaction and state the values of these quantities for all particles in- volved. [20] ii. Assuming no top or bottom quarks are involved deduce, with explanation, the quark structure of the Λo. [20]

2. (a) Explain which feature of the strong nuclear force results in stable light nuclei tending to have equal atomic Z, and neutron N , numbers, so N ≈ Z. [10]

(b) Explain why N > Z for large stable nuclei. [10]

(c) Describe the spin dependence of the nuclear force and therefore explain why stable 2 H exists but not 2 He or a nucleus of two neutrons. [25]

(d) Explain why an α particle has spin zero. [5]

(e) The ground states of the 2 H and the 6 Li nuclei have the same spin quantum number, 1. Explain this with reference to parts (c) and (d). [10]

(f) The lowest energy shell model state is 1s 1 / 2 and the next is 1p 3 / 2. Draw simple shell model diagrams for i. 3 H [20] ii. 7 Li [20] and deduce the spin-parity for the ground state in each case.

3. (a) Describe the contributions to the total angular momentum quantum number of a nucleon within a nucleus and discuss the values this can take. [20]

(b) Explain how the ground state spin quantum numbers result from the angular momentum of individual nucleons for i. nuclei with even atomic and neutron numbers and [10] ii. nuclei with an odd mass number. [15]

(c) Describe why a collective rotational model rather than a shell model is needed to describe the energies of the lowest 2+^ states in even-even nuclei in the mass number A region 150 < A < 190 and A > 230. [15]

(d) The rotational energy for a state of spin quantum number I is given by

EI =

I(I + 1)¯h^2 2 I

for moment of inertia I. Use the 76.5 keV energy of the lowest 2+^ state in the even-even nucleus 174 Yb to calculate the moment of inertia for this nucleus.[15]

(e) State and explain the multipolarity of the γ ray arising from the de-excitation of the state of part (d) and whether it is electric or magnetic. [25]

4. (a) Show that α decay produces an α particle with a kinetic energy Tα such that

Tα =

Q

1 + (^) mmDα

where Q is the total energy release of the decay and mα and mD are the masses of the α particle and daughter nucleus respectively. [20]

(b) Using the information below, calculate the energy of α particles emitted in the α decay of 224 Ra to the ground state of the daughter nucleus. [25] u (1u=931.5 MeV/c^2 ) (^4) He 4. (^220) Rn 220. (^224) Ra 224.

(c) i. Approximately 95% of 224 Ra α decays populate the 220 Rn ground state and approximately 5% populate the first excited state, with small fractional percentages populating higher energy states. Explain this. [25] ii. Describe other factors which could potentially affect which states in the daughter are most likely to be populated. [30]

5. (a) For the following reactions, replace the question mark with the appropriate nucleus or particle: i. 12 C(^4 He,^3 He)? [5] ii. 7 Li(p,?)^4 He [5] iii. 208 Pb(?,^23 Na)^208 Pb [5] iv. ?(α,αn)^8 Be [5]

(b) Using the information below, calculate the Q value for the 12 C(^12 C,^11 C)^13 C reaction. [20] u (1u=931.5 MeV/c^2 ) (^11) C 11. (^12) C 12. (^13) C 13.

(c) In the laboratory frame, where a projectile of mass ma and kinetic energy Ta is incident on a stationary target nucleus, the ejectile kinetic energy Tb at angle θb may be determined from

√ Tb =

F ±

√ F 2 + (mY + mb)[mY Q + (mY − ma)Ta] mY + mb

where F = cos θb

√ mambTa mb and mY are the masses of the ejectile and residual nucleus respectively and Q is the reaction Q value. For the reaction of part (b): i. Define and calculate the threshold energy. [40] ii. Determine the range of projectile energies for which there are two possible ejectile energies. [20]

6. (a) State what is meant by neutron induced fission, explaining the two stages by which it occurs. [15]

(b) A plot of number of fragments versus mass number, for thermal neutron in- duced fission on 235 U shows a broad peak around mass number 138. Assume that on average each fission produces one more neutron. Describe and explain another broad peak in the plot. [15]

(c) Show that the ratio of the two fission fragment kinetic energies is approximately inversely proportional to the ratio of their masses, stating any approximations made. [25]

(d) Using the information below, calculate the Q value for the fission reaction

(^235) U + n → (^138) Xe + (^96) Sr + 2n [15]

u (1u=931.5 MeV/c^2 ) n 1. (^96) Sr 95. (^138) Xe 137. (^235) U 235.

(e) Estimate the kinetic energy of; i. the 96 Sr nucleus, [20] ii. the 138 Xe nucleus. [10]