Study of Photon Emission with the Fission Event...

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

2Lawrence Livermore National Laboratory

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


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.


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


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


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)


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


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


Effect of including GDR and RIPL


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)


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


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


Effect on photons from varying gmin, tmax, and cS


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


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


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


Largest effects on photon observables due to variation of cS: sets rotational energy

§ Changing cS affects shape of Eg and Mg with TKE


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


Comparison to Data


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


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


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


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)


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

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Study of Photon Emission with the Fission Event...

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