LANL FIESTA: Fission School & Workshop SEPTEMBER 8–12 ...t2.lanl.gov/fiesta2014/presentations/Moller.pdf · LANL FIESTA: Fission School & Workshop SEPTEMBER 8–12, 2014, E LDORADO

LANL FIESTA: Fission School & WorkshopSEPTEMBER 8–12, 2014, ELDORADO HOTEL,

SANTA FE, NM, USA

Fission Barriers and Fission-Fragment Yieldsin the Region 170 < A ≤ 330

Peter MollerTeoretical Divison, Los Alamos National Laboratory

Collaborators on this and other projects:W. D. Myers, J. Randrup(LBL), H. Sagawa (Aizu), S. Yoshida(Hosei), T. Ichikawa(YITP), A. J. Sierk(LANL), A. Iwamoto (JAEA),S. Aberg (Lund), R. Bengtsson (Lund), S. Gupta (IIT, Ropar),and many experimental groups (e. g. K.-L. Kratz (Mainz), H.Schatz (MSU), A. Andreyev (York), K. Nishio (JAEA) . . . ).

More details about fission (PRC 79 064304, PRC 84 034613,PRC 88 064606), other projects (beta-decay,masses), associ-ated ASCII data files, interactive access to data (type in Z, Aand get specific data, contour maps) and figures are at

http://t2.lanl.gov/nis/molleretal/

Potential Energy of Deformation

We use the macroscopic-microscopic method introduced by

Swiatecki and Strutinsky:Epot(shape) = Ema r(shape) +Emi r(shape) (1)

The macroscopic term is calculated in a liquid-drop type

model (for a specific deformed shape).

The microscopic correction is determined in the following

steps

1. A shape is prescribed

2. A single-particle potential with this shape is generated.

A spin-orbit term is included.

3. The Schrodinger equation is solved for this deformed

potential and single-particle levels and wave-functions

are obtained

4. The shell correction is calculated by use of Strutinsky’s

method.

5. The pairing correction is calculated in the BCS or

Lipkin-Nogami method.

Shape Parameterizations

For small distortions we use multipole expansions, for

example the � parameterization:

r(�; �) = R0(1 + 1Xl=1 lXm=�l�lmY ml )

For large deformations near the outer saddle in the actinide

region or beyond we use the three-quadratic-surface

parameterization:

�(z)2 =8>>>>>>><>>>>>>>:

a12 � a12 12 (z � l1)2 ; l1 � 1 � z � z1a22 � a22 22 (z � l2)2 ; z2 � z � l2 + 2a32 � a32 32 (z � l3)2 ; z1 � z � z2

36 72Kr36

Scale 0.20 (MeV)

0.00 0.10 0.20 0.30 0.40 0

20

40

60

3

4

4

5

5

5A

xial

Asy

mm

etry

γ

Spheroidal Deformation ε2

Discrepancy (Exp. − Calc.)

Calculated

Experimental

σth = 0.559 MeV

FRDM (2012)

0 20 40 60 80 100 120 140 160 Neutron Number N

− 10

0

10

0

10

0

10

Mic

rosc

opic

Ene

rgy

(MeV

)

E(def?)? E(def?)?

In fission, what are the shapes and related energiesinvolved in the transition from a single ground-stateshape to two separated fission fragments?

234U

234U : Asymmetric valley at Q2 = 76

εf1 = − 0.1000 εf2 = 0.2500 MH/ML = 135.7/98.3

234U : Symmetric valley at Q2 = 76

εf1 = 0.1500 εf2 = 0.1000 MH/ML = 119.3/114.7

136I 98Y

117Pd 117Pd

From: Nucl. Phys A469 (1987) 1

0.75 1.00 1.25 1.50 1.750.50

0.75

1.00

Distance between Mass Centers r (Units of R0)

Fra

gmen

t Elo

ngat

ion

σ (U

nits

of R

0)

Family of shapes considered

From: Journ. Phys. G: Nucl. Part. Phys. 20 (1994) 1681

0.75 1.00 1.25 1.50 1.75 2.000.50

0.75

1.00

1.25

Distance between Mass Centers r (Units of R0)

Fra

gmen

t Elo

ngat

ion

σ (U

nits

of R

0)

− 4 − 2 0 2 4 6

Potential energy for 258Fm

E (MeV)

Q2

45 Q2 ~ Elongation (fission direction)

15 εf1

~ Left fragment deformation

εf1

εf2

15 εf2

~ Right fragment deformation

15

⊗

⊗

⊗

⊗d ~ Neck

d

35 αg ~ (M1-M2)/(M1+M2) Mass asymmetry

Five Essential Fission Shape Coordinates

M1 M2

⇒ 5 315 625 grid points − 306 300 unphysical points⇒ 5 009 325 physical grid points

Graphics by P

eter Möller

Fission Barrier and Associated Shapes for 232Th

Separating ridge Symmetric mode Asymmetric mode

0 2 4 6 8 10 Nuclear Deformation (Q2 / b)(1/2)

− 5

0

5

10

Fis

sion

-Bar

rier

Hei

ght (

MeV

)

Experimental

Calculated (FRLDM (2002))

rms = 1.00 MeV

Discrepancy (Exp. − Calc.)

0 20 40 60 80 100 120 140 160 Neutron Number N

− 10

0

10/0

10

20

30

40

50/0

10

20

30

40

50 F

issi

on B

arrie

r H

eigt

(M

eV)

Calculated Fission-Barrier Height

1 2 3 4 5 6 7 8 Bf(Z,N) (MeV)

130 140 150 160 170 180 190 200 210 220 230 Neutron Number N

80

90

100

110

120

130

Pro

ton

Num

ber

Z

Calculated Fission-Barrier Height

1 2 3 4 5 6 7 8

Bf(Z,N) (MeV)

SF Observed (t1/2<30d)

140 150 160 170 180 Neutron Number N

90

100

110

120

Pro

ton

Num

ber

Z

JR: NPF 2010

Brownian shape mo.on

Nuclear deforma5on energy: Edef(i,j,k,l,m)

Q2

45 Q2 ~ Elongation (fission direction)

35 !g ~ (M1-M2)/(M1+M2) Mass asymmetry

15 "f1

~ Left fragment deformation

"f1

"f2

15 "f2

~ Right fragment deformation

15#

#

#

#

d ~ Neck

d

Five Essential Fission Shape Coordinates

M1 M2

$ 5 315 625 grid points % 306 300 unphysical points

$ 5 009 325 physical grid points

Bias poten5al: Vbias(i) = V0 (Q0/Q2)2

Scission: Cri5cal neck radius c0 ≈ 2.5 fm

Level density parameter: aA = A/(8 MeV)

Temperature T: E*‐ Edef = aAT2

Metropolis walk:

P. Möller et al, Nature 409 (2001) 785

i

j

k

l

m

=> V(χ) = Edef + Vbias

Change shape: χ －> χ’ ? V(χ’) < V(χ): move with P = 1

V(χ’) > V(χ): move with P = exp(‐ΔV/T)

χ

N. Metropolis et al, J Chem Phys 26 (1953) 1087

a b

c d

Exp. 233U(n,f) Calc. (6.54 MeV) 234U

30 40 50 60

0

5

10

15

20

25

Exp. 239Pu(n,f) Calc. (6.84 MeV) 240Pu

0

5

10

15

20

25

Yie

ld Y

(Zf)

(%)

Exp. 235U(n,f) Calc. (6.54 MeV) 236U

Exp. 234U(γ,f) Calc. (11.0 MeV) 234U

30 40 50 60 Fragment Charge Number Zf

205At120 E* = 17.41 (MeV)

20 30 40 50 60 70 Fragment Charge Number Zf

0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

206At121 E* = 18.63 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

204Rn118 E* = 14.10 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

205Rn119 E* = 15.20 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

206Rn120 E* = 16.20 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

207Rn121 E* = 17.14 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

208Rn122 E* = 17.93 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

209Rn123 E* = 18.75 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

206Fr119 E* = 13.98 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

207Fr120 E* = 14.85 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

208Fr121 E* = 15.71 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

209Fr122 E* = 16.60 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

210Fr123 E* = 17.40 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

211Fr124 E* = 18.02 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

212Fr125 E* = 18.72 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

217Fr130 E* = 14.74 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

218Fr131 E* = 14.40 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

209Ra121 E* = 14.54 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

210Ra122 E* = 15.26 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

211Ra123 E* = 16.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

212Ra124 E* = 16.40 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

213Ra125 E* = 17.11 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

214Ra126 E* = 16.94 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

215Ra127 E* = 15.93 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

216Ra128 E* = 15.01 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

217Ra129 E* = 13.80 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

218Ra130 E* = 13.25 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

219Ra131 E* = 12.81 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

212Ac123 E* = 14.65 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

213Ac124 E* = 14.99 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

214Ac125 E* = 15.52 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

215Ac126 E* = 15.36 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

216Ac127 E* = 14.19 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

217Ac128 E* = 13.08 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

218Ac129 E* = 12.40 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

219Ac130 E* = 12.03 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

220Ac131 E* = 11.71 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

221Ac132 E* = 11.34 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

222Ac133 E* = 11.13 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

223Ac134 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

224Ac135 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

225Ac136 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

226Ac137 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

217Th127 E* = 13.02 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

218Th128 E* = 11.99 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

219Th129 E* = 11.17 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

220Th130 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

221Th131 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

222Th132 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

223Th133 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

224Th134 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

225Th135 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

226Th136 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

227Th137 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

228Th138 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

229Th139 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

224Pa133 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

225Pa134 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

226Pa135 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

227Pa136 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

228Pa137 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

229Pa138 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

230Pa139 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

231Pa140 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

232Pa141 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

230U138 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

231U139 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

232U140 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

233U141 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

234U142 E* = 11.00 (MeV)


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

172W E* = 28.05 (MeV)

50 60 70 80 90 100 110 120 130 140 150 Fragment Mass Number Af

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

173W E* = 29.14 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

174W E* = 29.86 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

175W E* = 30.88 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

176W E* = 31.60 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

177W E* = 32.75 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

178W E* = 33.56 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

179W E* = 34.62 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

180W E* = 35.32 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

181W E* = 36.21 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

182W E* = 36.42 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

183W E* = 36.92 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

184W E* = 36.70 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

185W E* = 37.13 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

186W E* = 37.37 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

187W E* = 38.18 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

188W E* = 38.74 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

189W E* = 38.24 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

190W E* = 38.29 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

191W E* = 38.47 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

192W E* = 38.98 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

193W E* = 39.22 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

194W E* = 39.91 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

195W E* = 40.78 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

196W E* = 41.51 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

175Hg E* = 11.77 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

176Hg E* = 11.62 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

177Hg E* = 11.41 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

178Hg E* = 11.32 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

179Hg E* = 11.68 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

180Hg E* = 11.81 (MeV)


0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Yie

ld Y

(Af)

(%)

4 8 12 16 20 24 28 32

Fission-Barrier Height (MeV)

90 100 110 120 130 140 150Neutron Number N

70

80

90

Pro

ton

Num

ber

Z

ε2=-0.130 ε4= 0.010 ε6= 0.010

T1/2= 1.74 (s) Folded-Yukawa potential λn=34.88 MeV

λp=32.50 MeV a= 0.80 fm

∆n=0.99 MeV ∆p=0.51 MeV

(L-N) Ti Hg+e+ 81 180 180 80

B f

QEC

0 5 10 15 Excitation Energy (MeV)

0.0

2.5

5.0

Gam

ow-T

elle

r S

tren

gth

Asymmetric Symmetric0.2 0.4 0.6 0.8

Fission-Yield Valley-to-Peak Ratio

90 100 110 120 130 140 150Neutron Number N

70

80

90

Pro

ton

Num

ber

Z

10 15 20 25 30 35 40 45

Fission-Fragment Mass Division (MH-ML)

90 100 110 120 130 140 150Neutron Number N

70

80

90

Pro

ton

Num

ber

Z

Contrasting Fission Potential-Energy Surfaces Hg↔U

Ichikawa et al., PRC 86 024610 (2012)

180Hg 236U

0

2

4

6

8

1012

14

Quadrupole Moment q2

−0.3−0.2−0.1

0.0

0.1

0.2

0.3

MassAsymmetryα g

−50

510

1520

PotentialEnergy(MeV)

180Hg

sample text sample text sample text sample text

0

2

4

6

8

Quadrupole Moment q2

−0.3−0.2−0.1

0.0

0.1

0.2

0.3

MassAsymmetryα g

05

10

PotentialEnergy(MeV)

236U

c

<Eex(a)> = 7.86 (n,f), E*=6.84 234U


0

5

10

15

20

Cha

rge

Yie

ld Y

(Zf)

(%)

b

<Eex(a)> = 11.60

(γ,f), E*=11 234U

0

5

10

15

20

Cha

rge

Yie

ld Y

(Zf)

(%)

a

<Eex(a)> = 11.32 (n,f), E*=6.54 240Pu

0

5

10

15

20

Cha

rge

Yie

ld Y

(Zf)

(%)

(nth,f): Eex = Etot − U(gs) = 6.54 MeV Eex = Etot − U(10) = 9.73 MeV

Eex

240Pu

0 2 4 6 8 10 Nuclear Deformation (Q2 / b)(1/2)

− 5

0

5

10

Ene

rgy

(MeV

)

234U

(nth,f): Eex = Etot − U(gs) = 6.84 MeV

Eex = Etot − U(10) = 6.22 MeV

(γ,f): Eex = Etot − U(gs) = 11 MeV

Eex = Etot − U(10) = 11.4 MeV

Eex

− 5

0

5

10

c

<Eex(a)> = 7.86 (n,f), E*=6.84 234U


0

5

10

15

20

Cha

rge

Yie

ld Y

(Zf)

(%)

b

<Eex(a)> = 11.60

(γ,f), E*=11 234U

0

5

10

15

20

Cha

rge

Yie

ld Y

(Zf)

(%)

a

<Eex(a)> = 11.32 (n,f), E*=6.54 240Pu

0

5

10

15

20

Cha

rge

Yie

ld Y

(Zf)

(%)

exp. th.,no odd

(n,f), E*=6.54

236U


0

5

10

15

20

25 C

harg

e Y

ield

Y(Z

f) (%

)

READ(LU,’(2f10.3)’) r,rw

idiv =(N+1)/2if(N+1 .eq. 2*idiv) r = r + (rw-1 +0.01)*2*1.0

E(I,J,K,L,N) = r

exp. th.,odd

∆ = 1.0 (n,f), E*=6.54

236U


0

5

10

15

20

25 C

harg

e Y

ield

Y(Z

f) (%

)

82

92

124 120

104 106

108

110

86

114

128

Hexadecapole Deformation ε4 0.00 0.00 0.00 0.08 0.08

272110 λp = 34.80, ap = 0.80 fm

− 0.4 − 0.2 0.0 0.2 0.4− 8

− 6

− 4

− 2

0

2

Spheroidal Deformation ε2

Sin

gle-

Pro

ton

Ene

rgy

(MeV

)

I-2 I-1Elongation Index

I I+1 I+2

36

37

38

39

40

Fra

gmen

t Cha

rge

Z

Next Track-Point Candidates

exp. th.,1p1qp

∆ = 1.0 (n,f), E*=6.54

236U


0

5

10

15

20

25 C

harg

e Y

ield

Y(Z

f) (%

)

exp. th.,odd

∆ = 1.0 (n,f), E*=6.54

236U


0

5

10

15

20

25 C

harg

e Y

ield

Y(Z

f) (%

)

exp. th.,1p1qp

∆ = 1.0 (n,f), E*=6.84

234U


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

exp. th.,odd

∆ = 1.0 (n,f), E*=6.84

234U

0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

exp. th., no odd

(n,f), E*=6.84

234U

0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

∆ = 1.0

exp. th.,1p2qp

(γ,f), E*=11

234U


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

∆ = 1.0

exp. th.,odd

(γ,f), E*=11

234U

0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

exp. th., no odd

(γ,f), E*=11

234U

0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

exp. th.,1p1qp

∆ = 1.0 (n,f), E*=6.54

236U


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

exp. th.,odd

∆ = 1.0 (n,f), E*=6.54

236U

0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

exp. th.,no odd

∆ = 1.0 (n,f), E*=6.54

236U

0

5

10

15

20

25 C

harg

e Y

ield

Y(Z

f) (%

)

exp. th.,1p1qp

∆ = 1.0 (n,f), E*=6.54

240Pu


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

exp. th.,odd

∆ = 1.0 (n,f), E*=6.54

240Pu

0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

exp. th.,no odd

(n,f), E*=6.54

240Pu

0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

a b

c d

Exp. 233U(n,f) Calc. (6.54 MeV) 234U

30 40 50 60

0

5

10

15

20

25

Exp. 239Pu(n,f) Calc. (6.84 MeV) 240Pu

0

5

10

15

20

25

Yie

ld Y

(Zf)

(%)

Exp. 235U(n,f) Calc. (6.54 MeV) 236U

Exp. 234U(γ,f) Calc. (11.0 MeV) 234U


exp. th.,1p1qp

∆ = 1.0 (n,f), E*=6.84

234U


0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

exp. th.,1p1qp

∆ = 1.0 (n,f), E*=6.54

240Pu

0

5

10

15

20

25

Cha

rge

Yie

ld Y

(Zf)

(%)

exp. th.,1p1qp

∆ = 1.0 (n,f), E*=6.54

236U

∆ = 1.0

exp. th.,1p2qp

(γ,f), E*=11

234U


Documents

LANL FIESTA: Fission School & Workshop SEPTEMBER 8–12 ...t2.lanl.gov/fiesta2014/presentations/Moller.pdf · LANL FIESTA: Fission School & Workshop SEPTEMBER 8–12, 2014, E LDORADO