The University of Melbourne

Semester 2 Assessment 2009

School of Physics

640354 — Subatomic Physics

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Writing Time: 3 hours

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Instructions to Invigilators:

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Students may retain the examination paper

Instructions to Students:

Candidates should attempt EIGHT of the NINE questions

All questions have equal valueSome useful information, including a table of quarks and leptons isat the end of the paper

This paper is to be held by the Baillieu Library

Questions begin on page 2 page 1 of 5

1. Deuterons with an energy Ekin = 5 MeV are perpendicularly incident upon a tritium target,which has density ρ = 0.2 mg/cm2.

(a) How many neutrons per second pass through a detector of area A = 20 cm2 which isat a distance r = 3 m from the target and at an angle θ = 30o to the deuteron beamdirection, if the differential cross-section dσ/dΩ at this angle is 13 mb/sr (1 b = 100 fm2)and the deuteron current is id = 2µA?

(b) What is the distance of closest approach when the deuteron beam strikes the tritium atnormal incidence?

(the Deuteron or Heavy Hydrogen contains 1 neutron and 1 proton; the Tritium is also aHydrogen isotope and contains 1 proton and 2 neutrons )

2. An experiment similar to KamLAND detects νe neutrinos at a distance of 300 m from anuclear reactor. This experiment found that the flux of electron neutrinos is 95± 5% of thatexpected if there were no oscillations.

(a) Assuming a mixing angle of θ = π/4 and a neutrino beam energy of 3 MeV, estimatethe upper limit of ∆m2.(assume there are only two neutrino flavours νe and νµ)

(b) Find the ∆m2 range that the experiment would be able to detect for the above mixingangle.

3. Show that the set of 2 × 2 matrices(

1 α0 1

), where α is a complex number, form a group

under multiplication. Is this a SU(2) group?

Question 4 starts on page 3 page 2 of 5

4. In the shell model, the energy levels of the nucleons are ordered as in figure:

(a) Write down the shell-model configuration for 63Li and find its spin and parity.

(b) How do you interpret the difference in the total binding energy of 178 O and 17

9 F? Estimatethe radius of both nuclei.

(c) If the short distance repulsion between nucleons is generated by the exchange of an wmeson, of mass 782 MeV/c2, estimate the range of this repulsive interaction, and thusthe maximum density of nuclear matter.

5. The quark wave functions of the following mesons are:Vector mesons (spin 1)

K0 = ds

Pseudoscalar (spin 0)

η =1√6(uu + dd− 2ss)

(a) Find the meson masses and the 3rd component of the strong isospin.(b) Show that a meson which decay in π+π− pairs by the strong interaction must have

P=(-1)J where J is the spin of the meson. Both π± and π0 have JP = 0−.(c) The ρ0 and the f0 mesons decay by strong interactions to give π+π− pairs and have

spin-1 and spin-2 respectively. Which of the decay ρo → π0γ and f0 → π0γ is forbiddenin the electromagnetic interaction?

(d) Which of the particle, with lifetime listed in the table below, has the largest width?Why?

hadron B0 Ω nlifetime (s) 1.6 ×10−12 0.8 ×10−10 887

Question 6 starts on page 4 page 3 of 5

6. High-energy neutrino beams can be generated the pion and kaon decays :

π+ → µ+νµ

K+ → µ+νµ

(a) What fraction of the pions and kaons decay inside of a distance of 100 m? The beamenergy is 200 GeV.

(b) In the case of the Kaon decay, which is the direction direction of the outgoing muonwith respect to the direction of the Kaon?

(c) How large is the maximal neutrino energy in both cases?(mπ+=140 MeV/c2, mK+=494 MeV/c2, mµ=106 MeV/c2,τπ+ = 2.6−8 s, τK+ = 1.2−8 s)

7. For each of the following processes, say whether it is a strong, electromagnetic or weak process,or whether it is forbidden in the Standard Model, and explain the reasons for your answer.For each of the allowed processes explain your reasons and sketch the Feynman diagram ofthe decay.

(a) π0 → γγ

(b) n→ p e+νe

(c) Λ0 → K0π0

(d) ηc → e+e−

(e) B+ → µ+νµ

(f) Σ0 → Λ0e+e−

The quark content of the hadrons entering this question is

hadron n p Λ0 π0 π+ K0 Σ0 B+ D+ ηc

quark content udd uud uds uu + dd ud ds uds ub cd cc

Question 8 starts on page 5 page 4 of 5

8. Write a short (1-2 pages) account of ONE of the following topics

(a) The liquid drop model.

(b) The shell model.

(c) The Yukawa theory of nuclear interactions.

9. Write a short (1-2 pages) account of ONE of the following topics

(a) The strong interaction and the colour charge.

(b) The Klein-Gordon equation and the matter-antimatter.

(c) Discuss neutrino oscillation (you can assume only 2 family in the discussion).

Some useful numbers and formulae

1. 1 C = 6.24× 1018 electrons, NA = 6.02× 1023mol−1

2. mHc2 = 938.8 MeV; mnc2 = 939.7 MeV; mec2 = 0.511 MeV

3. α = e2

4πε0~c = 1137 ; ~c = 197 MeV fm; c = 3× 108 m s−1; A = 0.06 GeV3.

4. Mmes = mq + mq − 34

Amqmq

; Mmes = mq + mq + 14

Amqmq

.

5. P (νe → νµ) = sin2 2θ sin2(

1.27∆m2LE

)The elementary particles of the Standard Model

Leptons QuarksFlavour mass (MeV/c2) charge (e) Flavour mass (MeV/c2) charge (e) Isospin I3

e 0.51 -1 u 360 2/3 +1/2νe ≤ 2× 10−3 0 d 360 -1/3 -1/2µ 106 -1 c 1300 2/3 0νµ ≤ 0.2 0 s 483 -1/3 0τ 1780 -1 t 175000 2/3 0ντ ≤ 2 0 b 4300 -1/3 0

END OF EXAMINATION PAPER subject 640354

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