PAPER CODE NO. EXAMINER:
PHYS490
DEPARTMENT:
Dr. M. Chartier
Physics
TEL. NO. 07970247384
MAY EXAMINATIONS 2013
Master of Mathematics: Year 4
Master of Physics: Year 4
ADVANCED NUCLEAR PHYSICS
TIME ALLOWED: 1 hour and a half
INSTRUCTIONS TO CANDIDATES
Answer all questions.
Question 1 and 2 each carry 50% of the total marks.
Answer either part (a) or part (b) of question 2.
In the event of a student answering both parts of an either/or question and not clearly crossing out
one answer, only the answer to part (a) of the question will be marked.
The marks allotted to each part of a question are indicated in square brackets.
All symbols have their usual meanings unless otherwise stated.
PAPER CODE PHYS490
Page 1 of 7
Continued
PAPER CODE NO. EXAMINER:
PHYS490
DEPARTMENT:
Dr. M. Chartier
Physics
TEL. NO. 07970247384
1. Answer all questions
[a]
Assuming the charge independence of the nuclear force, explain why there is no bound
state for the two-neutron or two-proton systems while a neutron and a proton can form a
[b]
bound state.
[4]
What information does this provide on the nucleon-nucleon force?
[1]
Energy is generated in the Universe by converting hydrogen into helium.
Briefly describe two nuclear processes by which this is achieved and state which is
favoured for low stellar temperatures.
[c]
[d]
[5]
Describe the () parameters used in the polar representation of a deformed quadrupole
nuclear shape.
[2]
Which values of  correspond to axially symmetric shapes?
[1]
Define what is meant by the term ‘triaxial nuclear shape’.
[1]
Define what is meant by the term K-isomer.
[2]
Such an isomeric state is observed in the nucleus
136
Sm (Z=62) based on a two-neutron
configuration. Use the attached Nilsson diagram (Figure 1) to derive the structure of this
isomeric state and determine its spin and parity Iπ. Assume ε2 ~ 0.2.
[e]
[4]
Write down an expression relating the energy E(I) of a rotational level in a deformed
even-even nucleus to its spin I, taking care to define your notations.
Given that rotational frequency  is defined as
[2]
, relate the rotational frequency to the
-ray energy (i) for a quadrupole electromagnetic transition and (ii) for a dipole
electromagnetic transition.
PAPER CODE PHYS490
[3]
Page 2 of 7
Continued
PAPER CODE NO. EXAMINER:
PHYS490
DEPARTMENT:
Dr. M. Chartier
Physics
TEL. NO. 07970247384
Figure 1: Nilsson diagram for neutrons, 50  N  82 (4 = 22/6).
PAPER CODE PHYS490
Page 3 of 7
Continued
PAPER CODE NO. EXAMINER:
PHYS490
DEPARTMENT:
Dr. M. Chartier
Physics
TEL. NO. 07970247384
2. Answer either [a] or [b]
[a]
i) Consider the nuclear reaction: 7Li(p,n)7Be.
What type of reaction is it?
[1]
Briefly discuss the main properties of such reactions and give two other examples.
[4]
ii) Given the following atomic mass excesses:
1
n
8071 keV
1
H
7289 keV
7
Li (Z=3)
14907 keV
7
Be (Z=4)
15769 keV
calculate the Q-value for the 7Li(p,n)7Be reaction and explain under what circumstances
the reaction will occur.
[3]
Give an expression for the threshold kinetic energy of the incident protons and compute
its value in keV.
[3]
iii) For this reaction derive an expression for the velocity of the centre-of-mass in the
laboratory frame.
[2]
At threshold, what is the neutron velocity in the laboratory?
[1]
Calculate the laboratory kinetic energy of the neutrons at threshold.
[3]
iv) Compute the values of TZ, ground-state isospin Tgs and all possible values of T for
the 7Li and 7Be nuclei.
[3]
What isospin states in 7Be can be populated with the above reaction?
Justify your answer.
PAPER CODE PHYS490
[5]
Page 4 of 7
Continued
PAPER CODE NO. EXAMINER:
PHYS490
DEPARTMENT:
[b]
Dr. M. Chartier
Physics
TEL. NO. 07970247384
i) Explain what is meant by the terms ‘backbending’ and ‘band termination’.
[5]
ii) Briefly describe the spectra shown in Figures 2a and 2b, below. Briefly discuss what
particular physical characteristics of 131Ce would result in such spectra.
[3]
Figure 2
iii) Using the data represented in Figure 2, determine the average rotational frequency and
then the number of revolutions performed by the 131Ce (Z=58) nucleus during this
decay.
[5]
iv) The rigid-body moment of inertia of a deformed (prolate) nucleus, of mass number
A, may be estimated as:
rigid
= (2/5) MR2 (1 + 0.36β)
where β denotes the usual quadrupole deformation parameter, and M and R are the mass and
radius of the nucleus, respectively.
PAPER CODE PHYS490
Page 5 of 7
Continued
PAPER CODE NO. EXAMINER:
PHYS490
DEPARTMENT:
Dr. M. Chartier
Physics
TEL. NO. 07970247384
Given β = 0.65, mN = 938.5 MeV/c2 (average nucleon mass), r0 = 1.2 fm (usual nuclear
radius parameter), and c = 197 MeV.fm, calculate the associated rigid-body moment of
inertia for the 131Ce nucleus.
[4]
v) The dynamic moment of inertia is expressed by:
(2)
=
dI/dω = ħ2 [d2E(I)/dI2]1
Use the data represented in Figure 2 to calculate the value of
(2)
for the 131Ce
nucleus.
[3]
vi) Compare and comment on the values obtained in questions 2 [b] iv) and 2 [b] v)
above.
[2]
vii) From the data presented in Figure 2 and the results obtained above, what can you
infer about the shape and structure of the 131Ce nucleus?
Justify your answer.
PAPER CODE PHYS490
[3]
Page 6 of 7
Continued
PAPER CODE NO. EXAMINER:
PHYS490
DEPARTMENT:
Dr. M. Chartier
Physics
TEL. NO. 07970247384
CONSTANTS
Speed of light in vacuum
c
=
3.00  108 ms-1
Permeability of vacuum
0
=
4  10-7 Hm-1
=
4  10-7 VsA-1m-1
=
8.85  10-12 Fm-1
=
8.85  10-12 AsV-1m-1
Permittivity of vacuum
0
Elementary charge
e
=
1.60  10-19 C
Planck constant
h
=
6.63  10-34 Js
Avogadro constant
NA
=
6.02  1023 mol-1
Boltzmann constant
k
=
1.38  10-23 JK-1
Gas constant
R
=
8.31 JK-1mol-1
Unified atomic mass constant
mu
=
1.66  10-27 kg
=
931.5 MeV/c2
=
9.11  10-31 kg
=
0.511 MeV/c2
=
1.67  10-27 kg
=
938.3 MeV/c2
Electron mass
Proton mass
me
mp
Gravitational constant
G
=
6.67  10-11 Nm2kg-2
Acceleration due to gravity
g
=
9.8 ms-2
Bohr magneton
B
=
9.27  10-24 JT-1
PAPER CODE PHYS490
Page 7 of 7
End