RFSS: Lecture 7 Fission • Readings: Modern Nuclear Chemistry, Chapter 11; Nuclear and Radiochemistry, Chapter 3 • General Overview of Fission • Energetics • The Probability.
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Transcript RFSS: Lecture 7 Fission • Readings: Modern Nuclear Chemistry, Chapter 11; Nuclear and Radiochemistry, Chapter 3 • General Overview of Fission • Energetics • The Probability.
RFSS: Lecture 7 Fission
• Readings: Modern Nuclear Chemistry,
Chapter 11; Nuclear and Radiochemistry,
Chapter 3
• General Overview of Fission
• Energetics
• The Probability of Fission
• Fission Product Distributions
Total Kinetic Energy Release
Fission Product Mass Distributions
Fission Product Charge Distributions
• Fission in Reactors
Delayed neutron
• Proton induced fission
7-1
Nuclear Fission
• Fission discovered by Otto Hahn and Fritz
Strassman, Lisa Meitner in 1938
Demonstrated neutron irradiation of
uranium resulted in products like Ba
and La
Chemical separation of fission
products
• For induced fission, odd N
Addition of neutron to form even N
Pairing energy
• In 1940 G. N. Flerov reported that 238U
undergoes fission spontaneously
half life of round 1016 y
Several other spontaneous fission
isotopes found
Z > 90
Partial fission half lives from
nanoseconds to 2E17 years
7-2
•
Fission
Can occur when enough energy is supplied by bombarding particle for Coulomb
barrier to be surmounted
Fast neutron
Proton
• Spontaneous fission occurs by tunneling through barrier
• Thermal neutron induces fission from pairing of unpaired neutron, energy gain
Nuclides with odd number of neutrons fissioned by thermal neutrons with large
cross sections
follows1/v law at low energies, sharp resonances at high energies
7-3
Energetics
Calculations
• Why does 235U undergo neutron
induced fission for thermal
energies?
Where does energy come
from?
• Generalized energy equation
AZ + n A+1Z + Q
• For 235U
Q=(40.914+8.071)-42.441
Q=6.544 MeV
• For 238U
Q=(47.304+8.071)-50.569
Q=4.806 MeV
• For 233U
Q=(36.913+8.071)-38.141
Q=6.843 MeV
• Fission requires around 5-6 MeV
7-4
Fission Process
• Usually asymmetric mass split
MH/ML1.4 for uranium and
plutonium
due to shell effects, magic numbers
Heavy fragment peak near
A=132, Z=50, N=82
Symmetric fission is suppressed by
at least two orders of magnitude
relative to asymmetric fission
• Occurs in nuclear reactions
Competes with evaporation of
nucleons in region of high atomic
numbers
• Location of heavy peak in fission
remains constant for 233,235U and 239Pu
position of light peak increases
• 2 peak areas for U and Pu thermal
neutron induced fission
• Influence of neutron energy observed
235U
fission yield
7-5
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Fission yield distribution varies with
fissile isotope
Heavier isotopes begin to demonstrate
symmetric fission
Both fission products at Z=50 for
Fm
As mass of fissioning system increases
Location of heavy peak in fission
remains constant
position of light peak increases
Fission Process
7-6
Fission products
• Primary fission products
always on neutron-excess
side of stability
high-Z elements that
undergo fission have
much larger neutronproton ratios than
stable nuclides in
fission product region
primary product
decays by series
of
successive processes
to its stable isobar
• Yields can be determined
Independent yield:
specific for a nuclide
Cumulative yield:
yield of an isobar
Beta decay to
valley of
stability
Data for
independent and
cumulative yields
can be found or
calculated
Comparison of cumulative and
independent yields for A=141
http://www-nds.iaea.org/sgnucdat/c2.htm
7-7
Fission Process
•
•
•
•
•
Nucleus absorbs energy
Excites and deforms
Configuration “transition state” or “saddle point”
Nuclear Coulomb energy decreases during deformation
Nuclear surface energy increases
Saddle point key condition
rate of change of Coulomb energy is equal to rate of change of nuclear surface energy
Induces instability that drives break up of nucleus
If nucleus deforms beyond this point it is committed to fission
Neck between fragments disappears
Nucleus divides into two fragments at “scission point.”
two highly charged, deformed fragments in contact
Large Coulomb repulsion accelerates fragments to 90% final kinetic energy within 10 -20 s
7-8
Fission Process: Delayed Neutrons
•
•
Fission fragments are neutron rich
More neutron rich, more energetic
decay
In some cases available energy high
enough for leaving residual nucleus
in such a highly excited state
Around 5 MeV
neutron emission occurs
Particles form more spherical shapes
Converting potential energy to
emission of “prompt” neutrons
Gamma emission after neutrons
Then decay
Occasionally one of these
decays populates a high lying
excited state of a daughter that
is unstable with respect to
neutron emission
“delayed” neutrons
0.75 % of total neutrons from
fission
137-139I and 87-90Br as examples
7-9
Delayed Neutron Decay Chains
• For reactors
Emission of several neutrons per
fission crucial for maintaining chain
reaction
“Delayed neutron” emissions
important in control of nuclear
reactors
7-10
Delayed Neutrons in Reactors
• Control of fission
0.1 msec for neutron from fission to react
Need to have tight control
0.1 % increase per generation
* 1.001^100, 10 % increase in 10 msec
• Delayed neutrons useful in control
Longer than 0.1 msec
0.75 % of neutrons delayed from 235U
0.26 % for 233U and 0.21 % for 239Pu
• Fission product poisons influence reactors
135Xe capture cross section 3E6 barns
7-11
Nuclear reactors and Fission
• Probable neutron energy from fission is
0.7 MeV
Average energy 2 MeV
Fast reactors
High Z reflector
Thermal reactors need to slow
neutrons
Water, D2O, graphite
* Low Z and low cross section
• Power proportional to number of available
neutrons
Should be kept constant under
changing conditions
Control elements and burnable
poisons
k=1 (multiplication factor)
Ratio of fissions from one
generation to next
* k>1 at startup
7-12
Fission Process and Damage
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•
•
•
Neutron spatial distribution is along direction of motion of fragments
Energy release in fission is primarily in form of kinetic energies
Energy is “mass-energy” released in fission due to increased stability of fission
fragments
Recoil length about 10 microns, diameter of 6 nm
About size of UO2 crystal
95 % of energy into stopping power
Remainder into lattice defects
* Radiation induced creep
High local temperature from fission
3300 K in 10 nm diameter
7-13
Fission Energetics
• Any nucleus of A> 100 into two nuclei of
approximately equal size is exoergic.
Why fission at A>230
• Separation of a heavy nucleus into two positively
charged fragments is hindered by Coulomb
barrier
Treat fission as barrier penetration
Barrier height is difference between
following
* Coulomb energy between two fragments
when they are just touching
* energy released in fission process
• Near uranium both these quantities have values
close to 200 MeV
7-14
Energetics
•
Generalized Coulomb barrier equation
Compare with Q value for fission
Z1Z 2e 2
Z1Z 2
Vc
0.96 1/ 3
MeV
1/ 3
R1 R2
A1 A2
•
•
•
Z1Z 21.44
Vc
1.8( A11/ 3 A21/ 3 )
Determination of total kinetic energy
Equation deviates at heavy actinides (Md, Fm)
Consider fission of 238U
Assume symmetric
238U119Pd + 119Pd + Q
Z=46, A=119
* Vc=462*1.440/(1.8(1191/3)2)=175 MeV
* Q=47.3087-(2*-71.6203) = 190.54 MeV
asymmetric fission
238U91Br + 147La + Q
Z=35, A=91
Z=57, A=147
* Vc=(35)(57)*1.44/(1.8*(911/3+1471/3))=164 MeV
* Q=47.3087-(-61.5083+-66.8484) = 175.66 MeV
Realistic case needs to consider shell effects
Fission would favor symmetric distribution without shell
7-15
Energetics
•
200Hg
give 165 MeV for Coulomb energy
between fragments and 139 MeV for energy
release
Lower fission barriers for U when
compared to Hg
• Coulomb barrier height increases more slowly
with increasing nuclear size compared to fission
decay energy
• Spontaneous fission is observed only among
very heaviest elements
• Half lives generally decrease rapidly with
increasing Z
7-16
Half lives generally decrease rapidly with increasing Z
7-17
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Some isomeric states in heavy
nuclei decay by spontaneous
fission with very short half lives
Nano- to microseconds
De-excite by fission process
rather than photon
emission
Fissioning isomers are states in
these second potential wells
Also called shape isomers
Exists because nuclear
shape different from that
of ground state
Proton distribution results
in nucleus unstable to
fission
Around 30 fission isomers are
known
from U to Bk
Can be induced by neutrons,
protons, deuterons, and a
particles
Can also result from decay
Fission Isomers
7-18
Fission Isomers: Doublehumped fission barrier
• At lower mass numbers,
second barrier is ratedetermining, whereas at
larger A, inner barrier is
rate determining
• Symmetric shapes are most
stable at two potential
minima and first saddle, but
some asymmetry lowers
second saddle
7-19
Proton induced fission
• Energetics impact fragment
distribution
• excitation energy of fissioning
system increases
Influence of ground
state shell structure of
fragments would
decrease
Fission mass
distributions shows
increase in symmetric
fission
7-20
Topic Review
• Mechanisms of fission
What occurs in the nucleus during fission
• Understand the types of fission
Particle induced
Spontaneous
• Energetics of fission
Q value and coulomb barrier
• The Probability of Fission
Cumulative and specific yields
• Fission Product Distributions
Total Kinetic Energy Release
Fission Product Mass Distributions
7-21
Questions
• Compare energy values for the symmetric and asymmetric
fission of 242Am.
• What is the difference between prompt and delayed
neutrons in fission.
• What is the difference between induced and spontaneous
fission.
• What influences fission product distribution?
• Compare the Coulomb barrier and Q values for the fission
of Pb, Th, Pu, and Cm.
• Describe what occurs in the nucleus during fission.
• Compare the energy from the addition of a neutron to 242Am
and 241Am. Which isotope is likely to fission from an
additional neutron.
• Provide calculations showing why 239Pu can be fissioned by
thermal neutrons but not 240Pu
7-22
Pop Quiz
• Compare the Q value and Coulomb energy (Vc)
from the thermal neutron induced fission of
239Pu resulting in 138Ba and 102Sr. Is this
energetically favored?
Z1Z 21.44
Vc
1.8( A11/ 3 A21/ 3 )
• Provide comments on blog
• Bring to class or submit via e-mail
7-23
Questions
• Respond to PDF Quiz 7
Submit quiz when complete
• Comment on the blog
http://rfssunlv.blogspot.com
7-24