RamonaVogt(LLNL&UCDavis)andJørgen Randrup (LBNL)
StudyofPhotonEmissionwiththeFissionEventGeneratorFREYA
This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344and the Office of Defense Nuclear Nonproliferation Research and Development
LLNL-PRES-730117
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Outline§ Introduction to FREYA
§ Photon observables in FREYA, using 252Cf(sf) as an example• Effects of including GDR and RIPL-3 lines• Effects of changing key photon parameters
§ Comparison to current data on photon observables
§ Summary
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FREYA (Fission Reaction Event Yield Algorithm) developed at LLNL & LBNL
§ FREYA developed in collaboration with J. Randrup (LBNL); neutron-transport code integration by J. Verbeke (LLNL) for MCNP6, TRIPOLI4.9, Geant4
§ FREYA journal publications: Phys. Rev. C 80 (2009) 024601, 044611; 84 (2011) 044621; 85(2012) 024608; 87 (2013) 044602; 89 (2014) 044601; 90 (2014) 064623; other papers in collaboration with experimentalists: Phys. Rev. C 89 (2014) 034615; Phys. Rev. C 93 (2016) 014606, PRC submitted
§ FREYA1.0 published in Comp. Phys. Comm. 191 (2015) 178.§ Isotopes currently included: spontaneous fission of 252Cf, 244Cm, 238,240,242Pu, 238U and neutron-
induced fission of 233,235,238U(n,f), 239,241Pu(n,f) for En ≤ 20 MeV§ FREYA2.0 recently released and available – still some parameter tuning needed – updated
manual, new version announcement submitted to Comp. Phys. Comm.
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Event-by-event modeling is efficient framework for incorporating fluctuations and correlations
Goal(s): Fast generation of (large) samples of complete fission eventsEvent generators (FREYA) aid in detector development and data analysis
Complete fission event: Full kinematic information on all final particlesTwo product nuclei: ZH , AH , PH and ZL , AL , PLn neutrons: pn , n = 1,…,nNg photons: pm , m = 1,…,Ng
Advantage of having samples of complete events:Energy, linear and angular momentum conserved in FREYAStraightforward to extract any observable,including fluctuations and correlations,and to take account of detector cuts & acceptances
Advantage of fast event generation:Can be incorporated into transport codes
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Models like FREYA require fragment yields and kinetic energies as input, neutron and photon observables are output
60 80 100 120 140 160 180Product mass number Ap
10-4
10-3
10-2
10-1
100
101
Fiss
ion
Prod
uct Y
ield
Y(A
p) (%
)
nth +239Pu
120 130 140 150 160Heavy fragment mass number AH
150
160
170
180
190
200
Tota
l kin
etic
ene
rgy
TKE
(MeV
)
Tsuchiya Nishio Wagemans
0 5 10 15 20Incident neutron energy En (MeV)
2
3
4
5
6
7
8
9
Aver
age
neut
ron
mul
tiplic
ity ν
241Pu241Am245Cm249Cf237Np227Th235U
80 100 120 140 160Mass number A
0
1
2
3
4ν(
A),
Eγ/1
.75
(MeV
)
ShengyaoVorobievZakharovaNardi γ
(a) 252Cf(sf)
Input data
Input data
Input data for fits
Model result
• Data for modeling other than a few isotopes and neutron energies above thermal are sparse• Photon measurements like the one shown at lower right not repeated since early ‘70s
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How FREYA works, the short version§ For a given Z, A and energy (En = 0 for spontaneous fission), FREYA selects mass and
charge of fragment from either data or a model (5 gaussian) parameterization§ Second fragment mass and charge obtained assuming binary fission, mass and
charge conservation§ From fragment identities, fission Q value is obtained§ TKE(AH) sampled from distribution; TXE obtained by energy conservation§ ‘Spin temperature’ sets level of rotational energy, remaining TXE given to intrinsic
excitation energy§ Intrinsic excitation divided between fragments, based on level densities, then thermal
fluctuations introduced to obtain final excitation energy sharing§ Thermal fluctuations remove energy from TKE to maintain energy conservation,
equivalent to width of TKE distribution§ Spin fluctuations (conserving angular momentum), introduced for wriggling and
bending modes§ Pre-equilibrium emission and n-th chance fission included for En ≤ 20 MeV§ After scission, fragments are de-excited first by emitting neutrons (Weisskopf-Ewing
spectra) until the remaining energy is less than the neutron separation energy § Photon emission follows until fragment no longer excited (see next slide)
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Photon emission follows neutron emission
ABCDE&ABCDE&ABCDE&&
E*&
J&
Sn&
E*max&
Eyrast&
Discrete&γ&
Sta5s5cal&γ&
Sta5s5cal&&neutron&
Ini5al&&fragment&
After neutron evaporation has ceased, E* < Sn , the remainingexcitation energy is disposed of by sequential photon emission …
… first by statistical photon cascades down to the yrast line …
Each photon is Lorentz boosted from the emitter to the laboratory frame
… then by stretched E2 photons along the yrast line …Sf = Si − 2
IA = 0.5 ×2
5AmNR
2
A
ϵγ = S2
i /2IA − S2
f/2IA
(ultrarelativistic)d3pγ ∼ ϵ
2dϵ dΩ
E∗
f = E∗
i − ϵγ
<=
!
Tmax
0
dN
dEP (T )dT =
2E
T 2max
!
Tmax
0
exp(−E/T )dT
T
d3N
d3pγd3
pγ ∼
"
Γ2GDR
ϵ2
(ϵ2− ϵ
GDR2)2− Γ2
GDRϵ2
#
ϵ2e−ϵ/Ti
ϵGDR =$
31.2A−1/3 + 20.6A−1/6%
MeV
ΓGDR = 5 MeV
1
!
Tmax
0
dN
dEP (T )dT =
2E
T 2max
!
Tmax
0
exp(−E/T )dT
T
d3N
d3pγd3
pγ ∼
"
Γ2GDR
ϵ2
(ϵ2− ϵ
GDR2)2− Γ2
GDRϵ2
#
ϵ2e−ϵ/Ti
ϵGDR =$
31.2A−1/3 + 20.6A−1/6%
MeV
ΓGDR = 5 MeV
1
!
Tmax
0
dN
dEP (T )dT =
2E
T 2max
!
Tmax
0
exp(−E/T )dT
T
d3N
d3pγd3
pγ ∼
"
Γ2GDR
ϵ2
(ϵ2− ϵ
GDR2)2− Γ2
GDRϵ2
#
ϵ2e−ϵ/Ti
ϵGDR =$
31.2A−1/3 + 20.6A−1/6%
MeV
ΓGDR = 5 MeV
1
… whenever possible, the RIPL decay tables are used instead…
Sf = Si - 1
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FREYA relies on some external parameters, adjusted to data§ Shift in total kinetic energy, dTKE, adjusted to give the evaluated average neutron
multiplicity§ Asymptotic level density parameter, e0, ai ~ (A/e0)[1+ (dWi/Ui)(1 – exp(-gUi))] where Ui =
E*i – Di, g = 0.05, and the pairing energy, Di, and shell correction, dWi, are tabulated (if
dWi ~ 0 or Ui is large so that 1 – exp(-gUi) ~ 0, ai ~ A/e0)§ Excitation energy balance between light and heavy fragment, x, influences neutron
multiplicity as a function of mass, n(A), and neutron-neutron angular correlations § Width of thermal fluctuation, s2(Ef*) = 2cEf*T, influences width of neutron multiplicity
distribution P(n)§ Multiplier of scission temperature, cS, determines level of nuclear spin and affects
photon multiplicity and energy§ Energy where neutron emission ceases and photon emission takes over, Sn + Qmin, Sn
is neutron separation energy, Qmin is fixed to be 0.01 MeV§ Minimum energy of detected photon, gmin (detector dependent)§ Maximum lifetime of discrete photon transition lines in RIPL-3 table, tmax (detector
dependent, if lifetime is long, cascade gets stuck and photon is not detected) § dTKE is energy dependent, e0 is assumed to be universal; x, c and cS so far assumed
to be independent of energy – not enough data to know for sure§ cS, gmin and tmax affect photon observables, no influence on neutron observables
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Effect of including GDR and RIPL
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How do the GDR form factor and RIPL tables change photon results?§ First version of FREYA did not include form factor or low energy
transitions, included in FREYA 2.0.2§ Photon spectrum is harder at high energies (right), low energy
transitions visible at low energy part of spectrum (left)
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Photon energy and multiplicity as a function of fragment mass and TKE § Note that the energy and multiplicity with A uses parameters fixed
with GDR and RIPL included and TKE§ Initial spin (rotational energy) is independent of form factor, RIPL
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Photon multiplicity distribution with and without form factors and RIPL lines
§ Note that the multiplicity is higher without the form factors: with same spin, without the form factor the multiplicity is higher along the yrast line; same is true with form factor and without RIPL
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Effect on photons from varying gmin, tmax, and cS
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Changing gmin modifies photon multiplicity, little effect on total photon energy§ Changing gmin cuts out lowest part of spectrum, changes
multiplicity by ~20% for 0.05 < gmin < 0.20 MeV
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Changing tmax has small effect on photon observables
§ Increasing tmax increases the photon multiplicity and energy by a few percent (shown relative to the “asymptotic” value at tmax = 5 µs)
§ Relative changes in energy are smaller than those in multiplicity
§ Relative results are also shown for different values of gmin and cS
Increasing gmin has large effect on Mgbecause RIPL lines are relatively lowenergy
Changing cS by a factorof 10 has a much smallereffect on Mg/Mg(5 µs)than changing gmin by 4
Note that while relativechanges are small, absolute changes can be large
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Largest effects on photon observables due to variation of cS: sets rotational energy
§ While change in both Eg and Mg is large Eg/Mg changes less
cS = 0.2 reducesrotational energyalmost away;cS = 2.0 gives large rotationalenergy, twice scission temperature
Eg/Mg inverts effect, small cS gives largest ratio butoverall effect is not large
N.B. Changing cS also affectsneutron observables, not justphoton results since it tilts the balance betweenrotational and intrinisicexcitation energy
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Largest effects on photon observables due to variation of cS: sets rotational energy
§ Changing cS affects shape of Eg and Mg with TKE
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Largest effects on photon observables due to variation of cS: sets rotational energy§ When cS is small, almost all photons emitted are statistical,
continuum photons; low spin, angular momentum changes little§ For large cS, the emission is dominated by rotational energy,
multiplicity can change by as much as a factor of two
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Comparison to Data
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Comparison with 252Cf(sf) photon data (from 70s)
(Left) Total photon energyas a function of AH and Acompared to Nardi andNifenecker data; agreementis relatively reasonable
(Top right) Total photonenergy as a function oftotal kinetic energy, comparedto Nardi and Nifeneckerdata; FREYA result is ratherflat compared to data
(Bottom right) Photonmultiplicity compared to datafrom Pleasonton and Johanssonas a function of A; data areinconsistent, FREYA is flatterthan both
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Comparison with 235U(nth,f) photon data (from 70s)
(Left) Photon energy (top)and multiplicity comparedto data from Pleasonton(black) and Albinsson(blue) as a function of A;agreement relatively goodgiven large uncertainties
(Top right) Energy perphoton as a function of Acompared to Pleasontondata; agreement is good
(Bottom right) Photonenergy as a function oftotal kinetic energycompared to Pleasontondata; rather good agreement
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Dependence of 239Pu photon multiplicity and energy with excitation energy
5
6
7
8
9
Eγ
(MeV
)
1
1.1
1.2
Eγ/
Nγ
(MeV
)
0 5 10 15 20
En (MeV)
5
6
7
8
9
Nγ
0 5 10 15 20
En (MeV)
2
3
4
5
νcS = 1.2
cS = 0.2
cS = 0.87
[best fit from 252
Cf]
• Results show variation in Eg, Mg, Eg/Mg and average neutron multiplicity as afunction of incident neutron energy for three different values of cS
• Red lines show result with almost no rotational energy; black is ‘best fit’ to Cf data; blue shows cS = 1.2, if cS = 2 used instead, Mg and Eg would increase significantly
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Dependence of 233U photon multiplicity and energy with excitation energy
5
6
7
8
9
Eγ
(MeV
)
0.9
1
1.1
1.2
Eγ/
Nγ
(MeV
)
0 5 10 15 20
En (MeV)
5
6
7
8
Nγ
0 5 10 15 20
En (MeV)
2
3
4
5
ν
cS = 0.87 [best fit
252Cf(sf)]
cS = 0.2
cS = 1.2
• Energy dependence is not linear, shape with En reflects multi-chance fission• Change in neutron multiplicity with cS is significant, any attempt to tune cS
to data like this could not be done without also maintaining agreement with n(En)
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Summary§ FREYA 2.0.2 has a number of improvements that particularly affect
photon observables§ Low energy part of photon spectrum is most affected by
implementation of RIPL-3 lines§ We are working on making physics-based fits to data to fix
parameters – ongoing process as more and better data are accumulated and included
§ FREYA can be downloaded from https://nuclear.llnl.gov/simulation/main.html