NE 301 - Introduction to Nuclear Science
Spring 2012
Classroom Session 5:
•Isotopes
and Decay Diagrams
•Nuclear Reactions
•
•
•
Energy of nuclear reactions
Neutron Cross Sections
Activation Calculations
•Radioactive
Decay and Growth
Reminder
Load TurningPoint


Reset slides
Load List
2
-, + produce three products:
Cannot say energy of 
Neutrinos by Fermi (1933)
We only can say maximum energy of 
Page 98-Shultis
Binary Nuclear Reactions
Binary = 2 reactants (many times 2 products too)
Most important type of nuclear reaction
Most elements produced by binary rxns.
in stars
Nomenclature:
x X Y  y
Light nuclide usually
projectile
Heavy nuclide
usually target
Heavy
Product
Light
Product
4
For Binary Reactions:
x +X  Y + y
x is a projectile with KE (Ex). X is a target
stationary nucleus EX=0
simplification
E y  0, R eal
 y  Cos  y
5
A 5.5 MeV  particle is incident on Li causing
7Li(,n)10B. What is the KE of neutron scattered 30o?
E y  0, R eal
 y  Cos  y
6
A 5.5 MeV  particle is incident on Li causing
7Li(,n)10B. What is the KE of neutron scattered 30o?
1.
2.
3.
4.
5.
6.
0 MeV
0.31 MeV
1.31 MeV
2.31 MeV
3.31 MeV
5.5 MeV
E y  0, R eal
 y  Cos  y
7
7Li(alpha,n)10B
FIRST BALANCE THE EQUATION!!!
Endothermic Rxn
Neutron Energy = 1.31MeV
What would be the neutron energy if incident alpha
particle is 1MeV instead?
Can’t happen…
8
Solution exists only if
Potential “” Factors



Q<0
Heavy projectiles (mY-mx<0)
Large scattering angles Cos <0
Big enough Ex can guarantee

E y  0, R eal
Argument of
root >0
E y  0, R eal
Physical meaning: Threshold Energy
Kinematic Threshold (only if Q<0)
Arises from conservation of:


Energy
Linear momentum
(Details are in the textbook)
In most nuclear reactions (mi’s>Q), the
kinematic threshold simplifies to:
E
th
x

m x 
  1 
Q
 m X 
ONLY FOR Q<0

i.e. endothermic rxns.
10
What is the kinematic threshold for:
7Li(,n)10B ?
1.
2.
3.
4.
5.
0.4
1.4
2.4
3.4
4.4
MeV
MeV
MeV
MeV
MeV
83%
17%
eV
M
4.
4
M
eV
0%
3.
4
M
eV
0%
2.
4
eV
M
1.
4
M

m x 
  1 
Q
 m X 
0.
4
E
th
x
eV
0%
11
7
Li (  ,n) B
10
Q  (4.002603  7.016004 - 1.008665 - 10.012937 )  931 .494  -2.790 M eV
E
th
x

mx 
4.002603 

  1 
 Q  - 1 
 (-2.790)  4.382 M eV
mX 
7.016004 


12

What is the kinematic threshold for:
13C(d,t)12C
0%
M
eV
0%
eV
0%
9.
6
-1
.5
Remember: Kinematic Threshold only for
Endothermic Reactions
0%
3M
0%
eV

m x 
  1 
Q
 m X 
M
E
th
x
1.
5
5.
eV
4.
0M
3.
eV
2.
-1.5 MeV
0 MeV
1.5 MeV
3 MeV
9.6 MeV
M
1.
13
Remember: Kinematic Threshold only for
Endothermic Reactions
Balance. Then:
(13.003355+2.014102-12-3.016049)*931.494
Q=1.31154 MeV
Exothermic = Kinematic Threshold is 0 MeV
14
Coulomb Barrier Threshold (fig. 3.9)
Coulombic
Threshold
ONLY when the incident
nuclide is charged
All nuclides are positive

Binding
Energy
Projectile needs energy
to overcome electrostatic
repulsion
E
C
x
Z xZ X
 1.2
A
1/ 3
x
 A
1/ 3
X
[M eV ]
NOT for incident NEUTRONS nor ’s
Engineering Equation. MeV units already worked out (don’t worry)
15
What is the coulomb barrier
threshold for: 7Li(,n)10B ?
5.
E
C
x
Z xZ X
 1.2
A
1/ 3
x
 A
1/ 3
X
[M eV ]
1M
eV
0%
0%
0%
0%
0%
5M
eV
4.
4M
eV
3.
MeV
MeV
MeV
MeV
MeV
3M
eV
2.
1
2
3
4
5
2M
eV
1.
16
Clicker Answer
1.2
3 2
3
7
3
2.057 MeV
4
17
What is the coulomb barrier
threshold for: 14N(n,)11B ?
0%
Q
M
eV
0%
eV
0%
3M
0%
eV
0%
2M
5.
eV
4.
1M
3.
eV
2.
0 MeV
1 MeV
2 MeV
3 MeV
0.98 x Q MeV
0M
1.
18
Overall Threshold Energy
Neutral Incident particle=No Coulomb
Barrier.
Q>0 = No Kinetic Threshold
Charged particles and Q<0 = both
thresholds apply, and:
E 
th
x
m in
 m ax  E , E
C
x
th
x

Do NOT add – Use BIGGEST of the two
19
What would be the minimum KE of
Products? – think about it!
Min. Kinetic Energy of the products is:
Q  E
Energy produced in
the reaction
th
x

m in
Minimum required
energy of the incident
particle
20
What is the threshold for the
7Li(,n)10B nuclear reaction?
E x  2.06 M eV
C
0%
eV
0%
M
0M
eV
Remember: Threshold is minimum energy the
incident particle has to have
0%
6.
46
0%
eV
th
M
E x  4.4 M eV ,
4.
4
4.
eV
3.
M
2.
0 MeV
2.06 MeV
4.4 MeV
6.46 MeV
2.
06
1.
21
What is the threshold of 14C(p,n)14N ?
And Minimum KE of the Products ?
0%
0%
0%
0%
an
d
6
M
e.
..
3.
...
0M
eV
2.
1
M
eV
an
d
2.
...
an
d
3.
1
M
eV
an
d

mx 
  1 
Q
mX 

2.
...
1/3
 AX
eV
th
x
1/3
Ax
0%
M
E
 1 .2
ZxZX
3.
...
E
C
x
2.
1
5.
an
d
4.
MeV
MeV
MeV
MeV
eV
3.
3.74
2.74
2.74
3.74
MeV
M
2.
3.1 MeV and
2.1 MeV and
3.1 MeV and
2.1 MeV and
0 MeV and 6
3.
1
1.
22
14C(p,n)14N
Q
14.003242 1.007825
1.008665 14.003074
Eth
x
0
ECx
1.2
Min. KE Prod
6 1
3
14
3
931.494
0.626 MeV
2.11 MeV
1
2.11 0.626
2.736 MeV
23
Neutron Scattering

First Type:
 Scattering reactions
 X  n  Elastic scattering (Q=0)

n X  
 *
 X  n   Inelastic scattering (Q<0)
24
N Scattering Kinematics
n X  X n
*
It is still a binary rxn. So eq. still applies, but
mx  m y  mn
m X  mY  M
E in cid en t en erg y
E ' fin al en erg y
Simplifies to:
E '
1
( A  1)
2

E cos  s 
E ( A  1  cos  s )  A ( A  1)Q
2
2
A
mn

atom ic m ass num ber
M
Solving for the scattering angle:
1
cos  s   ( A  1)
2
E
E
 ( A  1)
QA 



E
EE  
2
E
25
What is the energy of a 5MeV neutron after
it is elastically scattered 30o by a 10B atom?
E '
1
( A  1)
2
 E cos 
s

2
5.
9
M
E ( A  1  cos  s )  A ( A  1)Q
2
0%
eV
0%
M
0%
eV
0%
4.
9
1.
9
M
eV
0%
eV
Hint: for elastic collisions
only “+” matters
M
5.
3.
9
4.
eV
3.
MeV
MeV
MeV
MeV
MeV
M
2.
1.9
2.9
3.9
4.9
5.9
2.
9
1.
2

26
Notice it is an elastic collision:
Q=0
27
Accelerator in Columbia (8.4 MeV d)
56
Fe + d 
+ 
56
Fe + d 
+ p
56
Fe + d 
+ n
56
Fe + d 
+
3
56
Fe + d 
+ 
He
How many of these could happen?
28