PH437 - Nuclear Physics
Spring 2008
Homework Set #5
Due: Before Spring Break
This homework set contains material on both properties of the nucleus and on models used to
explain the properties of the nucleus.
1.
Calculate the difference in binding energy of a nucleus of 12C and the sum of the three
4
He nuclei (α-particles). Assuming that 12C is composed of three α-particles in a
triangular structure, with three effective “α-bonds” between them, what would be the
binding energy per α-bond?
2.
Find the binding energy per nucleon for
a)
Helium 3
b)
Helium 4
c)
Using your results from part a) and b), to draw the nuclear binding well diagrams
for 3He and 4He.
d)
Using your nuclear well diagrams from part c), determine if the addition of a
neutron to 3He will make a more or less stable nuclei. Fully justify your answer!
3.
Use the liquid drop model to compute the total binding energy and B/A for 8Be, 12C, 56Fe,
and 208Pb. Compare your values with experimental values using a mass table.
4.
Use the shell model to calculate the spin and parity of the ground and first excited states
of the following nuclei:
a) 23Na
5.
b) 41Ca
c) 18O
d) 38Cl
Determine the Rutherford scattering cross sections for 150 keV protons scattered at 171
degrees off 197Au and 12C. Remember to apply electron shielding corrections if necessary.
6.
Assuming that the spin of a proton can be represented by a positive pion moving at a
speed of c in a circular orbit of radius 1.00 fm about a neutral core as shown in the
diagram below:
+
Neutral
Core
a)
Calculate the pion current
b)
Calculate the magnetic moment due to the pion current
c)
How does your value in part b) compare with the experimentally determined
magnetic moment for the proton of 2.79 μn.
7.
In a nuclear fission reactor, MeV neutrons are thermalized through multiple elastic
scattering events between the neutrons the nuclei that compose the moderator. Assuming
that the moderator nuclei are approximately at rest:
a)
show that if a neutron with incident energy, Eo, undergoes elastic scattering with a
moderator nuclei of nucleon number A, that the minimum energy scattering
energy of the neutron, E1, is given by the formula:
2
 A  1
E1  
 E
 A  1 o
Hint: Minimum energy for neutron means that maximum energy has been
transfered to the moderator nuclei so you can use your results from problem #1 of
Homework set #4 to simplify your work.
b)
Using the formula from part a) determine how many collisions are required the
kinetic energy of a neutron from 6 MeV to 1 eV if lead is used as the moderator
Use the most common isotope of the moderator material to perform the
calculation.
c)
Repeat part b) using a carbon moderator
d)
Based upon your results from part b) and c), would you want a high Z or low Z
material to shield neutrons.
8.
The following experimental data is similar to that obtained using the LC-400 Van de
Graaff accelerator by CDT Bull during the spring of 1996 for protons scattered off a
carbon foil as a function of proton beam energy.
Beam Energy (keV)
Counts
Beam Energy (keV)
Counts
255
237601
355
115096
265
213599
365
107074
275
198347
375
103147
285
184488
385
87232
295
168572
400
79313
305
162859
410
43635
315
152683
420
31718
325
142864
430
67415
335
128982
440
144886
345
122999
450
207407
Assuming that all data points were taken with the same experimental geometry and for
the same number of incident protons, determine all energy regions where the scattering
data indicates that the scattering between the proton and the carbon atom was Rutherford.
(Hint: Plot the data on the appropriate type of graph and check for the Rutherford
scattering energy dependence)