Eventby’EventFission!Modeling! - T-2 : LANLt2.lanl.gov/fiesta2014/presentations/Vogt.pdf · Photon observables are studied for 252Cf(sf) and 235U(n,f) up to now"! ... Photon observables

Ramona Vogt (LLNL), Jørgen Randrup (LBNL), & Jerome Verbeke (LLNL)

Event-‐by-‐Event Fission Modeling

This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344"LLNL-PRES-659318"

2 Lawrence Livermore National Laboratory

Outline !!

§  A flexible modeling tool is needed for fast simulation of fission events for applications "

§  Our code FREYA has been developed to address this need for spontaneous and neutron-induced fission"

§  Neutron observables and correlations have been studied in detail for all isotopes"

§  Photon observables are studied for 252Cf(sf) and 235U(n,f) up to now"§  In this talk we:"

•  Introduce FREYA!•  Present neutron and photon results, compare to data"•  Present new results on neutron correlations"•  Describe integration of FREYA into transport codes"


Event-by-event modeling is efficient framework for incorporating fluctuations and correlations!

Goal(s): Fast generation of (large) samples of complete fission events""

Complete fission event: Full kinematic information on all final particles

Two product nuclei: ZH , AH , PH and ZL , AL , PL ν neutrons: pn , n = 1,…,ν Nγ photons: pm , m = 1,…,Nγ

Advantage of having samples of complete events: Straightforward to extract any observable, including fluctuations and correlations, and to take account of cuts & acceptances

Advantage of fast event generation: Can be incorporated into transport codes


How do complete event treatments differ from traditional fission models?!

•  In ‘average’ models, fission is a black box, " neutron and gamma energies sampled from" same average distribution, regardless of " multiplicity and energy carried away by each" emitted particle; fluctuations and correlations " cannot be addressed""•  FREYA generates complete fission events: " energy & momentum of neutrons, photons," and products in each individual fission event; " correlations are automatically included"

Fission model in frequently used"simulation code MCNP:"

•  Traditionally, neutron multiplicity" sampled between nearest values" to get correct average value"•  All neutrons sampled from same" spectral shape, independent of" multiplicity"

0

0.2

0.4

0.6

0.8

1

P(i)

10-610-510-410-310-210-1100

f ni (E) (

1/M

eV)

1 2 3 4 5 6Neutron multiplicity i

0

0.2

0.4

0.6

0.8

P(i)

0 5 10 15 20Outgoing neutron energy (MeV)

10-610-510-410-310-210-1

f ni (E) (

1/M

eV)

0.5 MeV14 MeV

239Pu(n,f)

235U(n,f) 235U(n,f)

239Pu(n,f)

Blue: 0.5 MeV"Red: 14 MeV"

previous!


We are developing FREYA (Fission Reaction Event Yield Algorithm) for correlation studies and spectral evaluations !

§  FREYA developed in collaboration with J. Randrup (LBNL) "§  Phys. Rev. C 80 (2009) 024601, 044611; 84 (2011) 044621; 85 (2012) 024608;

Phys. Rev. C 89 (2014) 044601User Manual LLNL-TM-654899. "§  Submitted to Comp. Phys. Comm. with J. Verbeke"§  Available with LLNL fission library in Geant4, TRIPOLI, and, soon, MCNP6 "


Fragment mass and charge distribution!

[W. Younes et al: PRC 64 (2001) 054613]

P (Af ) =m=+2!

m=−2

N|m| Gm(Af )

Gm(Af ) = (2πσ2|m|)

− 1

2 e−(Af−Af−D|m|)/2σ2

|m|

m=+2!

m=−2

N|m| = 1Mass!number!

N1,2(En) =N 0

1,2

e(En−E)/E + 1

E ≈ 10 MeV

E ≈ 1 MeV

Dependence on En:

P(Af) is sampled either from the measured mass distribution"or from five-gaussian fits to data: "

PAf(Zf ) ∼ e−(Zf−Zf )/2σ2

Z

Zf =Z0

A0

Af

Charge!number!

[W. Reisdorf et al: NPA 177 (1971) 337]"

σZ = 0.38 − 0.50

252Cf 240Pu

No quantitative models for P(Af) exists yet, so …"

60 80 100 120 140 160 180Fragment Mass A

10-4

10-3

10-2

10-1

100

101

Frag

men

t Yie

ld (%

)Thermal14 MeV

En = 14 MeV:

1st: 44%"

2nd: 35%"

3rd: 21%" 0 5 10 15 20Incident neutron energy (MeV)

0.0

0.2

0.4

0.6

0.8

1.0

Fiss

ion

prob

abilit

y

1st chance2nd chance3rd chance4th chance


Fission fragment kinetic energies!

80 90 100 110 120 130 140 150 160Fragment mass number Af

50

60

70

80

90

100

110

120

Frag

men

t kin

etic

ene

rgy

(MeV

)

Tsuchiya (2000)Nishio (1995)

120 130 140 150 160 170Heavy fragment mass number AH

130

140

150

160

170

180

190

Tota

l Fra

gmen

t Kin

etic

Ene

rgy

(MeV

)

TsuchiyaNishioWagemans

239Pu(n,f)

Average TKE versus heavy"fragment mass number AH!

Average fragment kinetic energy "versus fragment mass number Af!

239Pu(n,f)

TKE = TKEdata - dTKE(En)"

we adjust TKE to exp data:"

with an adjustable shift"to reproduce the mean"neutron multiplicity <ν>(En)"

H: heavy L: light

No models for TKE(Af) exists yet, so …"


Fragment excitation energies!

σ 2(Ef*) = 2Ef*T

=> Ef* = afT2

T = [E*/(aL+aH)]1/2 Common temperature:

Thermal fluctuations:

Ef* = Ef* + δEf*

Fragment momenta then follow from energy & momentum conservation:

Mean thermal excitation:

Fragment excitation:

H: heavy Q value: L: light QLH = M(240Pu*) – ML - MH

E* = QLH - TKE = EL* + EH*

TKE = TKE - δEL* - δEH*

Excitation is shared: EL* : EH* = aL : aH Thermal equilibrium:

=> δEf*

pL + pH = 0

*)

*) aA(E*) from Kawano et al, J. Nucl. Sci. Tech. 43 (2006) 1

Small adjustment: EL* -> x EL* (x>1) - dist?


Angular momentum at scission: Rigid rotation plus fluctuations!

I+ = (IH+IL)I/IR

I- = IHIL/(IH+IL)

Si = (Ii/I)S0 + δSi Rigid rotation:

Wriggling:

Bending:

The dinuclear rotational modes (+ & -) have thermal fluctuations governed by an adjustable “spin temperature” TS = cS Tsc, where Tsc is the scission temperature

I = IL + IH + IR; IR = µR2; R = RL – RH; µ = mNALAH/(AL + AH)


Fluctuations Contribute to Fragment Rotational Energy!

Fluctuating angular momentum components of fragments, δSL

k = (IL/I+)s+k + s-

k; δSHk = (IH/I+)s+

k - s-k;

Total angular momenta of fragment i are then Si’ = Si + δSi with orbital angular momentum L’ = L – δSL – δSH; contribution to dinuclear rotation modes δErot = S+

2/2I+ + S-2/2I-, as well as rigid rotation part Erot,

is not available for statistical excitation Mean statistical excitation is reduced correspondingly and shared between fragments:

H: heavy L: light

E* = QLH - TKE - Erot - δErot = EL* + EH*

SL

SH

P(s±) ~ exp(-s±2/2I±TS)

Scission induces statistical agitation of dinuclear rotation modes – wriggling (s+) and bending (s-) s± = (s±

x,s±y,0):

TS: related to scission temperature by TS = cSTsc (used cS = 0,0.1,1)

Photon observables are very sensitive to fragment spin while neutrons are not


Neutron evaporation from fragments!

M∗

i = Mgs

i+ εi

M∗

f = Mgs

f + εf

M∗

i = M∗

f + mn + ϵ

ϵ + εf = M∗

i − Mgs

f − mn = Q∗

n

Qn ≡ Q∗

n(εi =0) = Mgs

i − Mgs

f − mn = −Sn

Q∗

n= εi + Qn = εi − Sn

ϵ + εf = Q∗

n=

!

εmax

f

ϵmax

Tmax

f =

!

εmax

f /af =

!

Q∗

n/af

Neutron energy spectrum: d3N

d3pd3p ∼

√ϵ e

−ϵ/Tmax

f√

ϵ dϵ dΩ = e−ϵ/Tmax

f ϵ dϵ dΩ

d3p ∼

√ϵ dϵ dΩ

A−1

A

εi fε

S

Q

n

n*

εn

εn

P( )

Lorentz boost both ejectile and daughter motion from emitter frame to laboratory frame

(non-relativistic)


Neutron evaporation from rotating fragments

ω x r

ω = S/I vn = v0 + ω x r

Usual thermal emission from the moving surface element, v0 , subsequently boosted with the local rotational velocity ω x r .

Conserves energy as well as linear & angular momentum.

S’ = S – r x pn


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 remaining excitation energy is disposed of by sequential photon emission …

(ultra-relativistic) d3pγ ∼ ϵ

2dϵ dΩd3Nγ

d3pγ

d3pγ ∼ c e

−ϵ/Tiϵ2dϵ dΩ

E∗

f = E∗

i − ϵγ

… first by statistical photon cascade 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


External parameters in FREYA which can be adjusted to data!

§  In addition to isotope-specific inputs such as Y(A) and TKE(AH), there are also intrinsic parameters such as nuclear masses (Audi and Wapstra for experimentally-measured masses, supplemented by masses calculated by Moller, Nix, Myers and Swiatecki), barrier heights, pairing energies and shell corrections"

§  There are also external parameters that can be adjusted, either universally or per isotope"•  Shift in total kinetic energy, dTKE, adjusted to give the evaluated average neutron

multiplicity"•  Asymptotic level density parameter, e0, ai ~ (A/e0)[1+ (δWi/Ui)(1 – exp(-γUi))] where

Ui = E*i – Δi, γ = 0.05, and the pairing energy, Δi, and shell correction, δWi, are

tabulated (if δWi ~ 0 or Ui is large so that 1 – exp(-γUi) ~ 0, ai ~ A/e0)"•  Excitation energy balance between light and heavy fragment, x"•  Width of thermal fluctuation, σ 2(Ef*) = 2cEf*T, c is adjustable (default = 1) •  Multiplier of scission temperature, cS, that determines level of nuclear spin •  Energy where neutron emission ceases and photon emission takes over, Sn + Qmin

•  Default values: e0 ~ 10/MeV, c = 1, cS = 1, Qmin = 0.01 MeV •  Specific to 252Cf(sf): x = 1.3, dTKE = 0.5 MeV


Neutron observables: ν(A) and multiplicity distribution, P(ν)!

Mean neutron multiplicity as a function of fragment mass; agrees with sawtooth shape of data""ν(A) calculation shows dispersion in Z for a given mass (FREYA ‘error bars’)"

80 100 120 140 160Mass number A

0

1

2

3

4

i(A)

ShangyaoVorobievZakharovaFREYA

252Cf(sf)

0 1 2 3 4 5 6 7 8 9Neutron multiplicity i

0

0.1

0.2

0.3

0.4

P(i)

VorobievFREYAPoisson

252Cf(sf)

Neutron multiplicity distribution, different from Poisson due to removal of neutron separation "energy, Sn, as well as neutron kinetic energy, En"


Two-neutron angular correlations reflect emitter source!

0 30 60 90 120 150 180Relative angle φ

12 (degrees)

0

1

2

3

4

Corr

ela

tion y

ield

En > 1.5 MeV

En > 1.0 MeV

En > 0.5 MeV

ν=2 (1.0 MeV)

239Pu(n

th,f)

0 30 60 90 120 150 180Relative angle φ

12 (degrees)

0

1

2

3

4

5

6

Corr

ela

tion y

ield

ν=2

(1,1)

(2,0)

(0,2)

239Pu(n

th,f)

Correlations of neutrons with energies above"a specified threshold energy""Yield forward and backward is more symmetric"for higher-energy neutrons"

Correlations between neutrons when exactly"2 neutrons with En > 1 MeV are emitted:""One from each fragment (blue) back to back;"both from single fragment emitted in same "direction, tighter correlation when both from "light fragment (green) than from heavy (red);"open circles show sum of all possibilities"

φ12

n1

n2


Sensitivity of correlations to input parameters!

1.001.251.501.752.002.252.502.753.00

n-n

corre

latio

n

(a)

cS = 1, Qmin = 0.01 MeVcS = 0.1Qmin = 1 MeV

(b)

cS = 1, x = 1.3x = 1x = 1.6x = 0.75

0 30 60 90 120 150θnn (degrees)

1.001.251.501.752.002.252.502.75

n-n

corre

latio

n

(c)

cS = 1, e0 = 10/MeVe0 = 8/MeVe0 = 12/MeV

0 30 60 90 120 150 180θnn (degrees)

(d)

cS = 1, c = 1.0c = 1.2c = 0.8

Changing Qmin, cS, e0 and c does not have a strong effect on the shape of the n-n correlations""Only changing x strongly modifies the correlation shape: x < 1.3 default reduces the correlation"at θnn = 0° while leaving that at 180° unchanged; x > 1.3 (giving more excitation to light fragment)"produces a significantly stronger correlation at θnn = 0°""Correlation shape is relatively robust with respect to model parameters"


Effect of changing input parameters on other observables!

80 100 120 140 160Fragment mass A

0

1

2

3

4

ν(A)

ShangyaoVorobievZakharovax = 1.3x = 1x = 1.6x = 0.75

252Cf(sf)

0 1 2 3 4 5 6 7 8 9Neutron multiplicity ν

0

0.1

0.2

0.3

0.4

P(ν)

VorobievFREYAPoissonc = 1.2c = 0.8

252Cf(sf)

(Left) changing x reduces agreement with ν(A) in the range of highest yield, 100 < A < 140;"x = 1.3 gives best agreement in this range, x = 0.75 gives too much energy to the heavy "fragment, x = 1 does somewhat better for A < 100 but is bad everywhere else, x = 1.6 is far off""(Right) changing the width of the thermal distributions reduces the agreement of FREYA with "the Vorobiev P(ν) data, increasing c makes P(ν) too broad, decreasing c makes it too narrow"


Default version of FREYA gives rather good agreement with angular correlation data!

0 20 40 60 80 100 120 140 160 180θnn (degrees)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

n-n

corre

latio

n (a

rb. u

nits

)

FREYA 252Cf(sf)Pringle and BrooksGagarski et al

20 40 60 80 100 120 140 160 180θnn (degrees)

0

1

2

3

4

5

n-n

corre

latio

n (a

rb. u

nits

)

En = 0.425 MeVEn = 0.550 MeVEn = 0.800 MeVEn = 1.200 MeVEn = 1.600 MeVFREYA

0

2

4

6

0

2

4

6

n-n

angu

lar c

orre

latio

n (a

rb. u

nits

)

0 20 40 60 80 100 120 140 160 180θnn (degrees)

0

2

4

6 FREYA235U data

En > 1.00 MeV

En > 1.75 MeV

En > 2.50 MeV

Gagarski et al 252Cf(sf), 2008"

Franklyn et al, 1978"

1975"

•  All experiments took measurements at different"angles, discriminating between photons and "neutrons by timing, Gagarski et al used time of"flight, others used pulse shape discrimination"•  Newer data seems to show higher back-to-back"correlation, more consistent with FREYA, than"older data"•  Higher Qmin might bring data and calculations"closer together at lower energies and θnn > 120°"where calculation and data are most discrepant"


Correlation between neutron and light fragment!

0 20 40 60 80 100 120 140 160 180θnL (degrees)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

neut

ron

- lig

ht fr

agm

ent c

orre

latio

n (a

rb. u

nits

)

Bowman FREYA En > 0.5 MeVGagarski

0 20 40 60 80 100 120 140 160 180θnL (degrees)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

neut

ron

- lig

ht fr

agm

ent c

orre

latio

n (a

rb. u

nits

)

neutrons from light fragmentneutrons from heavy fragmentall neutrons

Neutron emission can also be correlated with individual fragments""(Left) Angle of neutrons emitted by either the light or heavy fragment or both fragments"with respect to the direction of the light fragment: neutrons from light fragment emitted "preferentially toward θnL = 0°; neutrons from heavy fragment are typically moving opposite the "light fragment in the lab frame, θnL = 180°; correlation becomes more tightly peaked for "higher neutron kinetic energies, here En > 0.5 MeV""(Right) FREYA result is compared to data, light fragment is determined and correlation is made"with all measured neutrons, as in black curve at left; good agreement is seen "


Other possible neutron correlation observables!

Neutron-induced fission endows compound nucleus"with small initial angular momentum S0, giving the"fragments non-vanishing angular momentum along"S0 in addition to that acquired from fluctuations;"fragment angular momentum modified by each "neutron emission"angle between initial angular momentum of compound"nucleus and fragment after evaporation is the"dealignment angle ∆θ (Si’·S0 = Si’S0 cos Δθ)"

Angular distribution of neutrons evaporated from"rotating nucleus acquires oblate shape –"rotational boost enhances emission in plane"perpendicular to angular momentum of emitter"centrifugal effect quantified by 2nd Legendre "moment" 〈P2(cos θ)〉 = 〈P2(p·S/|p||S|)〉"0 for isotropic emission; + for prolate (polar);"- for oblate (equatorial) – small effect overall"

-1.0 -0.5 0.0 0.5 1.0cos(∆θ)

0.5

1.0

1.5

2.0

2.5

3.0

Dealig

nm

ent dis

trib

utio

n P

de

alig

n(c

os

∆θ)

cS = 0.0

cS = 0.1

cS = 1.0

239Pu(n

th,f)

-1.0 -0.5 0.0 0.5 1.0cos θ

n

0.90

0.92

0.94

0.96

0.98

1.00

1.02

1.04

1.06

1.08

1.10

An

gu

lar

dis

trib

utio

n

dν/d

cos

θn

cS = 0.0

cS = 0.1

cS = 1.0

252Cf(sf)


Photon Results: 235U(n,f), Pleasonton et al.

Employing same values of cS as for 252Cf(sf), we see similar results: multiplicity relatively good"with cS = 0.1 but rather good agreement with energy for cS = 1, increasing Qmin hardens gamma spectra"We are looking into ways to improve Eγ/Nγ in FREYA!

80 90 100 110 120 130 140 150Fragment mass A

-1

0

1

2

3

4

5

6

7

8

Aver

age

tota

l pho

ton

ener

gy E

γ (M

eV)

Pleasonton 235U(nth,f)cS = 0.1cS = 1

80 90 100 110 120 130 140 150Fragment mass A

-1

0

1

2

3

4

5

6

7

8

9

Aver

age

phot

on m

ultip

licity

Nγ

cS = 0.1cS = 1

Pleasonton 235U(nth,f)

140 150 160 170 180 190 200Total fragment kinetic energy (MeV)

2

3

4

5

6

7

8

9

Aver

age

tota

l pho

ton

ener

gy E

γ (M

eV)

Pleasonton 235U(nth,f)cS = 0.1cS = 1

0.60.81.01.2

E γ/N

γ (M

eV)

468

1012

Nγ

120 125 130 135 140 145 150 155 160Heavy fragment mass AH

456789

E γ (M

eV) Pleasonton cS = 0.1 cS = 1


Photon Results: 252Cf(sf), Nardi et al. and Niefenecker et al.

Calculated Eγ dependence on TKE is almost"flat for Cf, very different from behavior of ν(TKE)"Which decreases linearly with TKE"Nifenecker data decrease linearly,"Nardi data decrease and flatten for TKE > 190 MeV"

150 160 170 180 190 200 210 220Total fragment kinetic energy (MeV)

5

6

7

8

9

10

11

Aver

age

tota

l pho

ton

ener

gy E

γ (M

eV) cS = 0.1

cS = 1

Nifenecker 252Cf(sf)Nardi 252Cf(sf)

84 88 92 96 100 104 108 112 116 120 124Light fragment mass AL

5

6

7

8

9

10

Aver

age

tota

l pho

ton

ener

gy E

γ (M

eV) cS = 0.1

cS = 1

Nifenecker 252Cf(sf)Nardi 252Cf(sf)

(Top) Eγ(A) shows sawtooth-like shape similar to Nardi"data with smaller, less sharp tooth at A ~ 135"(Bottom) Eγ(AL) + Eγ(AH) vs AL independent of AL for AL<112 "

80 90 100 110 120 130 140 150 160Fragment mass A

1

2

3

4

5

6

7

Aver

age

tota

l pho

ton

ener

gy E

γ (M

eV) cS = 0.1

cS = 1

Nardi 252Cf(sf)


Summary!

§  Event-by-event treatment shows significant correlations between neutrons that are dependent on the fissioning nucleus"

§  FREYA agrees rather well with most neutron observables for several spontaneously fissioning isotopes and for neutron-induced fission"

§  Comparison with n-n correlation data very promising"§  Photon data do not present a very clear picture – clearly more

experiments with modern detectors needed to verify older data"§  Incorporation of FREYA into MCNP6, FREYA1.0 with neutrons,

released as open source in July 2013, is in progress"§  FREYA1.0 is available from

http://nuclear.llnl.gov//simulation/main2.html!

Documents

Eventby’EventFission!Modeling! - T-2 : LANLt2.lanl.gov/fiesta2014/presentations/Vogt.pdf · Photon observables are studied for 252Cf(sf) and 235U(n,f) up to now"! ... Photon observables