Nuclear Fission Cross Sections
Fission cross sections
Ludovic MATHIEU
Laboratoire de Physique des 2 infinis de Bordeaux
(LP2i Bordeaux)
A
cross section
is linked to the
probability of reaction
Neutron impinging on this area
(= cross section, aka XS)
will interact with the nucleus
In classical physic, the cross section equals
the
frontal area
of the nucleus:
~ 10
-24
cm²
Once the neutron interacts,
the nucleus can decay into
different channels:
fission
radiative capture
elastic scattering
(n,2n) reaction
and a lot more...
I) Cross Section introduction
≈ 10 fm
≈ 10
-12
cm
Cross sections are mandatory to calculate
reaction rates
(fission rate, capture rate...)
in nuclear reactors or physic experiment.
The unit of cross section is then: 1 barn = 10
-24
cm²
In
quantum physic
, it depends on the nuclei nuclear structures and neutron energy.
The XS can be larger or smaller than the nucleus area.
For low slow neutrons :
slow
neutrons
=> large wave functions
For epithermal neutrons,
IF
E
n
corresponds
exactly to an
excited state:
Very high XS
for a precise E
n
=>
resonance
High XS
because of
wave-functions
overlap
A cross section is a
complex
property depending on :
- isotope
- neutron energy
- reaction
I) Cross Section introduction
epithermal
neutrons
RRR
URR
Continuum
Thermal
part
I) Cross Section introduction
Fission cross section of
235
U, called
235
U(n,f),
is composed of several regimes:
- Thermal part
(no corresponding state)
- Resolved Resonance Range
(when the neutron energy
corresponds to an existing state)
- Unresolved Resonance Range
(too many states to be resolved)
- Continuum
A fissile nucleus can undergo fission when impinged by a thermal neutron
Comparison between
binding energy
and
fission barrier
:
- binding energy > fission barrier => fissile
- binding energy < fission barrier => fertile
Additional kinetic
energy => fission
becomes possible
Enough energy
to fission
Only sub-barrier
fission
(tunnel effect)
I) Cross Section introduction
235
U(n,f)
238
U(n,f)
Due to pairing effect, half of
nuclei are fissile, and half are
fertile:
- fissile:
233,235
U,
239,241
Pu
- fertile :
232
Th,
234,236,238
U,
240,242
Pu
.
II) Cross Section data
Cross sections are measured since the beginning of nuclear science.
as well for fission...
than for other reactions...
But all these
are not
experimental
data
The extensive experimental data are
compiled in databases
, but cannot be used “directly”.
A
simple average
is
not
the
true
cross section value.
The
more precise
the
experimental data,
the
closer
they are
from the
true value.
II) Cross Section data
However, measurements are not enough
...
Experimental data are investigated to check their consistency and looking for their bias.
Evaluators require
high quality and highly accurate experimental data
(including
uncertainties, covariances, experimental parameters...)
Theoretical calculations
with
models
are carried out to
re-create
the cross sections
Physical ingredients
and
models
depends on the
energy range
considered
(thermal range, resonance
range, continuum...)
Different
choices
are made by evaluators
=>
different evaluations
The
agreement
between evaluations
and with experimental
data
may vary
II) Cross Section data
Some experimental
data may be
difficult
to reproduce
(unknown phenomenon)
.
III) Measurement principles
The measurement of a neutron-induced reaction cross section requires :
1- Fission cross section are mainly measured for
actinides radioactive target
(uranium isotopes, plutonium isotopes, etc.)
. This has consequences :
- on the experimental setup
- on the administrative paper work and delays
1- a
sample
to be irradiated by neutrons
2- a way to
detect
the expected
reactions
3- a way to
produce neutrons
sample
?
detector
neutrons
III) Measurement principles
Fission process emits:
- two Fission Fragments with high energy (few 10 MeV each)
- several
-rays
(6-8 in average)
- several neutrons
(2-3 in average)
Easiest way:
- exactly two FF
- charged particle
(high detection efficiency)
- no background
Usual detector:
a fission chamber
G. de Izarra, Eur. Phys. J.
Conf. 225 (1):10003
Principle:
- FF create e-/hole pair in a gas
- charge drift thanks to an electric field
- signal collection
Properties:
-
possibly compact
-
high efficiency
-
radiation resistant (gas)
III) Measurement principles
Fission process emits:
- two Fission Fragments with high energy (few 10 MeV each)
- several
-rays
(6-8 in average)
- several neutrons
(2-3 in average)
Easiest way:
- exactly two FF
- charged particle
(high detection efficiency)
- no background
Other detectors:
Parallel Plate Avalanche
Counter:
-
provides FF positions
-
radiation resistant
Silicon detector:
-
easy to use
-
100% efficient
-
not radiation resistant
Solar cells
-
easy to use
-
radiation resistant
The detector used is
adapted to experiment
constraints.
and others...
III) Measurement principles
No isolated neutron exists in nature. They have to be
produced
with
nuclear reactions
:
7
Li(p,n), D(d,n), T(p,n), T(d,n),
7
Be(
,n),
238
U(
,n), ...
target
beam
neutrons
This production method:
-
is quite simple
-
produces quasi-monoenergetic neutrons
-
is applicable for E
n
> few 100 keV
E
n
depends on the angle => for a given angle, quasi-monoenergetic neutrons
Cross section are then measured
at specific neutron
energies
and
only at high energy
.
III) Measurement principles
A completely different technique can be used: Time of Flight (ToF)
neutron
source
thermalizer
irradiated
target
t
1
: high E
t
2
: medium E
t
3
: low E
t
4
: very low E
ToF technic enables the
different energies
to be
disentangled
The cross section can be measured for a lot of
different neutron energies
“simultaneously”
pulsation !
No isolated neutron exists in nature. They have to be
produced
with
nuclear reactions
:
7
Li(p,n), D(d,n), T(p,n), T(d,n),
7
Be(
,n),
238
U(
,n), ...
.
Conclusion
They are
mandatory
to calculate
reaction rates
Neutron induced cross sections are related to the ability of the nucleus to absorb the neutron
and decay in a given reaction channel
Cross section have been measured for several decades and a large amount of data have
already been gathered
Physical principles
Cross section data
1- sample to irradiate:
all “fission” samples are radioactive
Measurement principles
2- fission detector:
usually a ionisation chamber but a large diversity exists
3- neutron source:
. charge particle induced nuclear reaction
. the Time of Flight technique enables to obtain all energy at once
The
evaluation process
is crucial to obtain
usable cross section
from experimental data
This process need
high quality
and highly accurate
data
Merci de votre
attention
Nuclear fission cross sections play a crucial role in determining reaction rates in nuclear reactors and experiments. They represent the probability of nuclear interactions when neutrons collide with a nucleus, impacting fission and capture rates. These cross sections are influenced by factors such as isotope, neutron energy, and reaction type. Fissile and fertile nuclei exhibit different behaviors based on binding energy and fission barrier conditions, affecting their fission possibilities. The intricate properties of cross sections are vital for understanding nuclear reactions and reactor performance.
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Presentation Transcript
Fission cross sections Ludovic MATHIEU Laboratoire de Physique des 2 infinis de Bordeaux (LP2i Bordeaux) MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 1/23
I) Cross Section introduction Physical principles A cross section is linked to the probability of reaction Cross sections are mandatory to calculate reaction rates (fission rate, capture rate...) in nuclear reactors or physic experiment. Once the neutron interacts, the nucleus can decay into different channels: 10 fm 10-12cm Neutron impinging on this area (= cross section, aka XS) will interact with the nucleus In classical physic, the cross section equals the frontal area of the nucleus: ~ 10-24 cm The unit of cross section is then: 1 barn = 10-24 cm MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 2/23
I) Cross Section introduction Physical principles In quantum physic, it depends on the nuclei nuclear structures and neutron energy. The XS can be larger or smaller than the nucleus area. For low slow neutrons : For epithermal neutrons, IF En corresponds exactly to an excited state: slow neutrons => large wave functions epithermal neutrons Very high XS for a precise En => resonance High XS because of wave-functions overlap A cross section is a complex property depending on : - isotope - neutron energy - reaction MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 3/23
I) Cross Section introduction Example of Cross section Fission cross section of 235U, called 235U(n,f), is composed of several regimes: - Thermal part (no corresponding state) - Resolved Resonance Range (when the neutron energy corresponds to an existing state) - Unresolved Resonance Range (too many states to be resolved) - Continuum RRR Thermal part URR Continuum MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 4/23
I) Cross Section introduction Fissile and fertile nuclei A fissile nucleus can undergo fission when impinged by a thermal neutron Comparison between binding energy and fission barrier: - binding energy > fission barrier => fissile - binding energy < fission barrier => fertile Additional kinetic energy => fission becomes possible 235U(n,f) Enough energy to fission Due to pairing effect, half of nuclei are fissile, and half are fertile: - fissile: 233,235U, 239,241Pu - fertile : 232Th, 234,236,238U, 240,242Pu 238U(n,f) Only sub-barrier fission (tunnel effect) . MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 5/23
II) Cross Section data Existing data Cross sections are measured since the beginning of nuclear science. as well for fission... 243Am(n,f) 238U(n,f) 239Pu(n,f) 233U(n,f) 243Cm(n,f) 235U(n,f) 234U(n,f) But all these are not experimental data 56Fe(n, ) 235U(n, ) et (n,2n) 232Th(n,n) et (n, ) than for other reactions... 208Pb(n,n) MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 6/23
II) Cross Section data Experimental data The extensive experimental data are compiled in databases, but cannot be used directly . A simple average is not the true cross section value. The more precise the experimental data, the closer they are from the true value. However, measurements are not enough... MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 7/23
II) Cross Section data Evaluations Theoretical calculations with models are carried out to re-create the cross sections Physical ingredients and models depends on the energy range considered (thermal range, resonance range, continuum...) Some experimental data may be difficult to reproduce (unknown phenomenon) The agreement between evaluations and with experimental data may vary Different choices are made by evaluators => different evaluations Experimental data are investigated to check their consistency and looking for their bias. Evaluators require high quality and highly accurate experimental data(including uncertainties, covariances, experimental parameters...) . MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 8/23
III) Measurement principles Back to basic The measurement of a neutron-induced reaction cross section requires : 1- a sample to be irradiated by neutrons 2- a way to detect the expected reactions 3- a way to produce neutrons sample ? neutrons detector 1- Fission cross section are mainly measured for actinides radioactive target (uranium isotopes, plutonium isotopes, etc.). This has consequences : - on the experimental setup - on the administrative paper work and delays MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 9/23
III) Measurement principles 2- Fission detection Fission process emits: - two Fission Fragments with high energy (few 10 MeV each) - several -rays (6-8 in average) - several neutrons (2-3 in average) Easiest way: - exactly two FF - charged particle (high detection efficiency) - no background Usual detector: a fission chamber Principle: - FF create e-/hole pair in a gas - charge drift thanks to an electric field - signal collection Properties: - possibly compact - high efficiency - radiation resistant (gas) G. de Izarra, Eur. Phys. J. Conf. 225 (1):10003 MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 10/23
III) Measurement principles 2- Fission detection Fission process emits: - two Fission Fragments with high energy (few 10 MeV each) - several -rays (6-8 in average) - several neutrons (2-3 in average) Easiest way: - exactly two FF - charged particle (high detection efficiency) - no background Other detectors: Parallel Plate Avalanche Counter: - provides FF positions - radiation resistant Silicon detector: - easy to use - 100% efficient - not radiation resistant Solar cells - easy to use - radiation resistant and others... The detector used is adapted to experiment constraints. MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 11/23
III) Measurement principles 3- Neutron production No isolated neutron exists in nature. They have to be produced with nuclear reactions : 7Li(p,n), D(d,n), T(p,n), T(d,n), 7Be( ,n), 238U( ,n), ... target neutrons En depends on the angle => for a given angle, quasi-monoenergetic neutrons beam This production method: - is quite simple - produces quasi-monoenergetic neutrons - is applicable for En > few 100 keV Cross section are then measured at specific neutron energies and only at high energy. MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 12/23
III) Measurement principles 3- Neutron production No isolated neutron exists in nature. They have to be produced with nuclear reactions : 7Li(p,n), D(d,n), T(p,n), T(d,n), 7Be( ,n), 238U( ,n), ... A completely different technique can be used: Time of Flight (ToF) neutron source t1 : high E thermalizer irradiated target t2 : medium E t3 : low E t4 : very low E pulsation ! ToF technic enables the different energies to be disentangled The cross section can be measured for a lot of different neutron energies simultaneously . MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 13/23
Conclusion Physical principles Neutron induced cross sections are related to the ability of the nucleus to absorb the neutron and decay in a given reaction channel They are mandatory to calculate reaction rates Cross section data Cross section have been measured for several decades and a large amount of data have already been gathered The evaluation process is crucial to obtain usable cross section from experimental data This process need high quality and highly accurate data Measurement principles 1- sample to irradiate: all fission samples are radioactive 2- fission detector: usually a ionisation chamber but a large diversity exists 3- neutron source: . charge particle induced nuclear reaction . the Time of Flight technique enables to obtain all energy at once MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 14/23
Merci de votre attention MC1 Nuclear fission 5 Juillet 2023 Ludovic MATHIEU 15/23
