NE 301 - Introduction to Nuclear ScienceSpring 2012

Classroom Session 5:

•Isotopes and Decay Diagrams•Nuclear Reactions

• Energy of nuclear reactions• Neutron Cross Sections• Activation Calculations

•Radioactive Decay and Growth

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ReminderLoad TurningPoint Reset slides Load List

Page 98-Shultis

-, + produce three products:

Cannot say energy of Neutrinos by Fermi (1933)We only can say maximum energy of

Binary Nuclear ReactionsBinary = 2 reactants (many times 2 products too)

Most important type of nuclear reactionMost elements produced by binary rxns. in starsNomenclature:

4

x X Y y Light nuclide usually projectile

Heavy nuclide usually target

Heavy Product

Light Product

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For Binary Reactions: x +X Y + yx is a projectile with KE (Ex). X is a target stationary nucleus EX=0

simplification

y Cosy

0, RealyE

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y Cosy

0, RealyE

A 5.5 MeV particle is incident on Li causing 7Li(,n)10B. What is the KE of neutron scattered 30o?

A 5.5 MeV particle is incident on Li causing 7Li(,n)10B. What is the KE of neutron scattered 30o?

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0, RealyE

y Cosy

1. 0 MeV2. 0.31 MeV3. 1.31 MeV4. 2.31 MeV5. 3.31 MeV6. 5.5 MeV

7Li(alpha,n)10B

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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…

Solution exists only if 0, RealyE

Potential “” Factors Q<0 Heavy projectiles (mY-mx<0) Large scattering angles Cos <0Big enough Ex can guarantee Physical meaning: Threshold

Energy

0, RealyE

Argument of root >0

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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:

ONLY FOR Q<0 i.e. endothermic rxns.

E xth 1

mxmX

Q

What is the kinematic threshold for: 7Li(,n)10B ?

11 0.4 M

eV

1.4 MeV

2.4 MeV

3.4 MeV

4.4 MeV

17%

0%

83%

0%0%

1. 0.4 MeV2. 1.4 MeV3. 2.4 MeV4. 3.4 MeV5. 4.4 MeV

E xth 1

mxmX

Q

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7 10Li ( ,n) B(4.002603 7.016004 -1.008665 -10.012937) 931.494 -2.790 MeV

4.0026031 - 1 (-2.790) 4.382 MeV7.016004

th xx

X

Q

mE Q

m

What is the kinematic threshold for: 13C(d,t)12C

13 -1

.5 MeV

0 MeV

1.5 MeV

3 MeV

9.6 MeV

0% 0% 0%0%0%

Exth 1

mxmX

Q

1. -1.5 MeV2. 0 MeV3. 1.5 MeV4. 3 MeV5. 9.6 MeV

Remember: Kinematic Threshold only for Endothermic Reactions

Balance. Then:(13.003355+2.014102-12-3.016049)*931.494Q=1.31154 MeV

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Remember: Kinematic Threshold only for Endothermic Reactions

Exothermic = Kinematic Threshold is 0 MeV

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Coulomb Barrier Threshold (fig. 3.9)ONLY when the incident nuclide is chargedAll nuclides are positive Projectile needs

energy to overcome electrostatic repulsion1/3 1/31.2 [MeV]C x X

xx X

Z ZEA A

Engineering Equation. MeV units already worked out (don’t worry)

NOT for incident NEUTRONS nor ’s

Binding Energy

Coulombic Threshold

What is the coulomb barrier threshold for: 7Li(,n)10B ?

16 1 M

eV

2 MeV

3 MeV

4 MeV

5 MeV

0% 0% 0%0%0%

1. 1 MeV2. 2 MeV3. 3 MeV4. 4 MeV5. 5 MeV

1/3 1/31.2 [MeV]C x Xx

x X

Z ZE

A A

Clicker Answer

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1.2 3 2

73 43 2.057 MeV

What is the coulomb barrier threshold for: 14N(n,)11B ?

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0 MeV

1 MeV

2 MeV

3 MeV

Q M

eV

0% 0% 0%0%0%

1. 0 MeV2. 1 MeV3. 2 MeV4. 3 MeV5. 0.98 x Q MeV

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Overall Threshold EnergyNeutral Incident particle=No Coulomb Barrier.Q>0 = No Kinetic ThresholdCharged particles and Q<0 = both thresholds apply, and:

Do NOT add – Use BIGGEST of the two

min

max , th C thx x xE E E

What would be the minimum KE of Products? – think about it!

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Min. Kinetic Energy of the products is:

min

thxQ E

Energy produced in the reaction Minimum required

energy of the incident particle

What is the threshold for the 7Li(,n)10B nuclear reaction?

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0 MeV

2.06 MeV

4.4 MeV

6.46 MeV

0% 0%0%0%4.4 MeV, 2.06 MeVth Cx xE E

1. 0 MeV2. 2.06 MeV3. 4.4 MeV4. 6.46 MeV

Remember: Threshold is minimum energy the incident particle has to have

What is the threshold of 14C(p,n)14N ?And Minimum KE of the Products ?

22 3.1 M

eV and 3....

2.1 MeV and 2....

3.1 MeV and 2....

2.1 MeV and 3....

0 MeV an

d 6 Me...

0% 0% 0%0%0%

1th xx

X

mE Q

m

E xC 1.2 ZxZX

Ax1/ 3 AX

1/ 3

1. 3.1 MeV and 3.74 MeV

2. 2.1 MeV and 2.74 MeV

3. 3.1 MeV and 2.74 MeV

4. 2.1 MeV and 3.74 MeV

5. 0 MeV and 6 MeV

14C(p,n)14N

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Q 14.003242 1.007825 1.008665 14.003074 931.494 0.626 MeV

Exth 0

ExC 1.2 6 1

143 13 2.11 MeV

Min. KE Prod 2.11 0.626 2.736 MeV

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Neutron Scattering First Type:

Scattering reactions

Elastic scattering (Q=0)

Inelastic scattering (Q<0)

*

X nn X

X n

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N Scattering Kinematics

Solving for the scattering angle:

E ' 1(A 1)2 E coss E(A2 1 cos2s) A(A 1)Q

2

1cos ( 1) ( 1)2s

E E QAA AE E EE

E incident energyE' final energy

x y n

X Y

m m m

m m M

*n X X n

Simplifies to:

It is still a binary rxn. So eq. still applies, but

atomic mass numbernmAM

What is the energy of a 5MeV neutron after it is elastically scattered 30o by a 10B atom?

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1.9 MeV

2.9 MeV

3.9 MeV

4.9 MeV

5.9 MeV

0% 0% 0%0%0%

E ' 1(A 1)2 E coss E(A2 1 cos2s) A(A 1)Q

2

1. 1.9 MeV2. 2.9 MeV3. 3.9 MeV4. 4.9 MeV5. 5.9 MeV

Hint: for elastic collisions only “+” matters

Notice it is an elastic collision:Q=0

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Accelerator in Columbia (8.4 MeV d)

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56

56

56

56 3

56

Fe + d +

Fe + d + p

Fe + d + n

Fe + d + He

Fe + d +

How many of these could happen?