Open problems for neutron emission in fission
N. Kornilov, CRP-PFNS, Vienna, 21-25 Oct. 2013
ENDF/B-7
235
U: AVERAGE ENERGY OF FISSION NEUTRONS
2.2
evaluation 1999 (Kornilov et al)
evaluation 2004 (ENDF/B-7)
average for Eth (exp I)
IPPE+RI; 1990-95 (exp I)
Johansson, 1977 (exp II)
evaluation 2002 (Hambsch et al)
<E>, MeV
2.1
2.0
Keff=1
????????
1.9
0
1
2
3
4
5
INCIDENT NEUTRON ENERGY, MeV
What was happened recently? (10-15years)
•
•
•
•
EXPERIMENT
2009. I.Guseva, et al, ISINN-16, 370,2009, EXFOR41516; (PNPI)
2010. N.Kornilov, F.-J. Hambsch, et al, NSE, 165(1), 2010; NSE 169, 2011;
(IRMM)
EVALUATION
Can predict macroscopic experiment (Mac-data)
2006. ENDF/B-7. “Theoretical” Madland-Nix (LANL) model with adjusted
parameters.
Cannot predict Mac-data
1999. N.V.Kornilov, A.B.Kagalenko, F.-J. Hambsch, Physics of Atomic Nuclei,
62(2), Semi-empirical “two Watt” model
2010. N.V.Kornilov, NS&E, 169, 2011,290, Semi-empirical “scale method”
2013. V.G. Pronyaev, GMA code for data evaluation. Covariance was included.
Available differential data for 235U
• Thermal point:
•
•
•
•
Starostov et al (1983), 3 spectra,
Lajtai et al (1985),
Yufeng et al (1989),
Kornilov et al (2010), 3 spectra,
• Vorobyev et al (2009);
Evaluation methods
•
Two Watt spectra
1. The PFN spectra may be described as a sum of two Watt distributions for light and heavy
fragments with equal contribution:
2
S( E, E 0 )  0.5  Wi ( E, E 0 , Tix ( E 0 ),  )
i1
(1)
where Tix are the temperature parameters for nucleus x and light and heavy fragments (i=1,2),
E0 is the incident neutron energy,  is the ratio of the total kinetic energy (TKE) at the
moment of the neutron emission to full acceleration value.
2. Temperature parameters for any fissile system were calculated with 252Cf data according to
the following formula:
*
Cf
Ex A
(2)
T =T
*
x
E Cf A
where E*=Er+Bn+E0-TKE, Er - energy release, Bn - binding neutron energy, E0 - incident neutron
energy, A - mass number of fissile nucleus. The ratio of the Tl/Th=1.248 does not depends on
fissile nucleus and incident energy.
3. There is the only free parameter  was fitted to the experimental data [9-11] for incident
neutron energy <6 MeV.
The experimental data for 232Th, 233U, 235U, 238U, 237Np and 239Pu (24 spectra) have been
described in the framework of this model inside the experimental errors.
x
l, h
Cf
l, h
Evaluation methods
•
Scale method
The 235U PFNS SU(E) at energy E was calculated with equations:
X  E / as
E Cf  X   E Cf 
S U ( E )  ai
,
S ( E )  E
as
Cf
Cf
Cf

where as is scaling factor and ai is a normalization parameter for i-th experiment.
These parameters were found by a non-linear least square method.
The agreement experimental points and evaluated function is shown in Table.
For each energy interval one may estimate the uncertainties with equation:
E1-E2, MeV
<0.3
0.3-0.5
0.5-0.7
0.7-1.0
1.0-1.5
1.5-2.0
2.0-2.5
2.5-3.0
3.0-4.0
4.0-5.0
5.0-6.0
6.0-7.0
7.0-8.0
8.0-9.0
9.0-10
10-11
<R>
0.999
1.020
1.011
0.997
0.987
0.990
1.006
1.010
1.009
1.003
1.004
1.006
0.988
0.960
0.974
0.959
δR
0.034
0.025
0.033
0.021
0.017
0.013
0.013
0.009
0.012
0.017
0.014
0.013
0.027
0.032
0.062
0.112
N points
19
11
11
16
27
21
20
12
23
28
25
21
20
16
11
11
Evaluation methods
•
Evaluation with GMA approach, (2013)
GMA approach to the evaluation of the standards
• GMA: generalized least-squares fit of experimental data
developed by Wolfgang Poenitz for standard neutron reaction
cross sections evaluation;
•
Non-model fit: no physical or mathematical model used in the fit;
•
Parameters of the fit are cross sections in the energy nodes (or
groups) and normalization constants.
Are microscopic data (Mic-data)
wrong?
Criteria!?
Only one conclusion we should made: are experimental data
measured in different laboratory, different time, and so on….
in agreement or not!!!!
So they are true OR not?
What we have for PFNS at thermal point?
All experimental data together
Ratio to “scale method” evaluation
1.4
1.0
1.0
0.8
0.8
0.6
0.6
0
2
4
6
E (MeV)
8
Kornilov et al, 2010
Starostov et al, 1983
Lajtai et al, 1985
Yufeng et al, 1989
1.2
R(E)
1.2
R(E)
1.4
Kornilov et al, 2010
Starostov et al, 1983
Lajtai et al, 1985
Yufeng et al, 1989
10
12
0.1
1
E (MeV)
10
All evaluations together
1.2
Scale method [15]
Kornilov, 1998 [1]
Pronyaev, 2013 [16]
ENDF/B-7, 2007
Obvious conclusion:
R(E), <E>=1.974 MeV
1.0
-ENDF/B-7 evaluation contradict
to Mic data!
-This conclusion dos not depend on
method used for evaluation!
0.8
0.6
0
2
4
6
E (MeV)
8
10
12
Mic-Mac problem
1.10
1.05
1.00
R=C/E
Average cross sections:
0.95
Open points - 252Cf ;
Mannhart.
0.90
Solid point - 235U;
Scale method
0.85
0.80
0
2
4
6
<E> (MeV)
8
10
12
Different microscopic experiments were applied
for measurement of PFNS
1. Total Fission Fragment integrated experiment. In this type of experiment all
fission fragment are integrated over TKE, masses, and emission angle relative
to neutron detector. We should avoid any possible selection which may destroy
PFNS shape (IRMM).
2. Differential Fission Fragment experiment. In this type of experiment PFNS
are measuring relative to fixed direction of FF . The total PFNS may be
calculated with integration of measured angular distributions over emission
angle (PNPI).
ENDF/B-7 and PNPI experiment
1.2
Scale method [15]
ENDF/B-7
Vorobyev, [4]
R(E), <E>=1.974 MeV
1.0
0.8
0.6
0
2
4
6
E (MeV)
8
10
12
ENDF/B-7 and PNPI experiment
3.5
3.0
R(E)=Cf/U
Normalization factor k
Kornilov et al, 2010
Starostov et al, 1983
scale method
power fit
Vorobyev et al, 2010
2.5
k=1.0195±0.0008 (Kornilov)
L~ 3m, FWHM~2 ns
2.0
k=0.9808±0.0016 (Starostov)
L~ 2.5-6m, FWHM~4ns
1.5
k=1 (Vorobyev)
L= 0.5m, FWHM~2ns
1.0
0
2
4
6
8
E (MeV)
10
12
14
Comparison of IRMM and PNPI experiments
Factor
IRMM, 2010
PNPI, 2009
Flight path, m
3
0.5
FWHM, ns/m
0.6
4
Shielding n-detector
Yes
Yes, but thickness is small
Scattering on chamber
Small, MC simulation
Big? It was not estimated
Possible distortion effect
It is not known
Due to angle integration
Comparison with previous Agreement inside uncertainties
results
Contradiction
Scattering on the FF detector materials
C.Budtz-Jorgensen, H-H. Knitter experiment
(NP A, 490, 1988)
L=500 mm
Chamber
Detector
20mmx10mm
130 mm
δ=0.5mm
μ=0.208
200 mm
μ=0.958
Cf-source
Model of PNPI experiment
Neutron detector
X
FF detector like “belt”
around axis OZ
θm
Z
φ
R
Мonte Carlo method.
R=14см, H=7.2см.
0<φ<2π
-cos(θm)< cos(θ)<cos(θm), cos(θm)=1, or 0.25
Neutron spectrum in CMS , S ( E )  E exp(
E
) , Т=0.65МeV.
T
CMS energy Ew=1.03 МeV.
So in LS we should have Watt spectrum with <E> =1.5T+Ew=2.005MeV.
θ
FF source
H
Integration over angles
1.4
1.4
R(E) ratio to analitical function
R(E) to Watt spectrum
1.2
1.0
no angle selection
0.8
angle selection
0.6
0
2
4
6
E (MeV)
8
10
12
1.2
1.0
d=0.001
0.8
d=0.01
d=0.1
0.6
0
2
4
6
E (MeV)
8
10
12
Differential experiment (conclusion)
• So, Differential Experiments (DE) may contain systematical
distortion effects!
• Results of these experiments after proper corrections should be
verified with total integral experiments and evaluations.
• ONLY these experiments (DE) gives us important information about
fission mechanism!
Madland-Nix model
•
•
•
•
•
Two FF or realistic distribution versus FF masses was included;
Triangle “temperature distribution” was assumed to simulate wide spread of
excitation energy according to TKE distribution, and multiple neutron
emission;
Optical model for absorption cross section;
Selection of the slope for Level Density parameter a=A/c;
Constant temperature assumption (Weisskopf type) for spectrum shape in
CMS.
Assumptions 3 and 4 are weekest points.
The motivation of the LD parameter reduction
Weisskopf’s assumption
S LD ( E )  E ( E )  (U ),
-1
N(E), 1/MeV
10
U  U 0  E,
-2
10
 (U )  exp(2 aU ) / U 1.25
Weisskopf
Level Density
-3
10
-4
10
SW ( E )  E ( E ) exp(E / T )
-5
10
0
2
4
6
E (MeV)
8
10
U 0  aT 2
Neutron spectra from (p,n) reactions
•
•
•
•
•
•
•
•
•
•
94Zr(p,n);
Ep=8, 11 MeV (Zhuravlev et all, IPPE)
109Ag(p,n); E =7, 8, 9,10 MeV (Lovchikova et all, IPPE)
p
113Cd(p,n); E =7, 8, 9,10 MeV (Lovchikova et all, IPPE)
p
124Sn(p,n); E =10.2, 11.2 MeV (Zhuravlev et all, IPPE)
p
165Ho(p,n),181Ta; E =11.2MeV (Zhuravlev et all, IPPE)
p
181Ta(p,n); E =6, 7, 8, 9, 10 MeV (Lovchikova et all, IPPE)
p
103Rh(p,n), 104-106,108,110Pd(p,n), 107,109Ag(p,n), E =18, 22, 25 MeV (Grimes et
p
al, LLNL)
51V(p,n), E =18, 22, 24, 26 MeV (Grimes et al, LLNL)
p
159Tb(p,n), 169Tm(p,n), E =25 MeV (Grimes et al, LLNL)
p
92-100Mo(p,n), E =25.6 MeV (Mordhorst et al, Un Hamburg)
p
Spectrum from (p,n) reaction
113Cd(p,n), Ep=10MeV
1.0E+03
G.N.LOVCHIKOVA,A.M.TRUFANOV, (48-CD-113(P,N)49-IN-113,,DE,,,EXP)
BCS, CS=2405, K&D
1.0E+02
BCS, W-E CS=2405, K&D
(n,p), mb/MeV
1.0E+01
1.0E+00
1.0E-01
1.0E-02
1.0E-03
0.0
2.0
4.0
6.0
En, MeV
8.0
10.0
12.0
Spectrum from 181Ta(p,n) reaction
10
10
S c (E), mb/MeV
10
10
10
3
2
1
0
-1
6 MeV
10
-2
8 MeV
11 MeV
10
10
-3
-4
0
1
2
3
4
E, MeV
5
6
7
Madland-Nix model (conclusion)
•
Madland-Nix model (LANL model) is semi-empirical model;
•
Parameters of this model were selected to describe macroscopic
•
The PFNS shape predicted with this model does not agree with microscopic
experimental data.
• So, “Mic-Mac problem” was not solved till now!!!!!
results.
Traditional assumption
•
•
Main assumptions for modeling of neutron emission in fission:
1. formation of compound and decay to Fission Fragment;
2. neutron emission from excited FF after total acceleration
Experimental data analysis:
Neutron energy distributions measured in Laboratory System LS are transformed
to CMS. These data are described by equation
with fitted
parameters λ,T. After this the data return back to LS with following conclusion
about reliability of main assumption. It seems this procedure may provide
misunderstanding.
Model result should be compared with experiment in LS
PFNS
ν(TKE)
ν(A)
ν(μ,E)
ν(μ)
Model for Prompt Fission Neutron Emission
N. Kornilov et al, ISINN-12, Dubna, 2004
N. Kornilov et al, NPA 786, 2007, 55-72
Neutron spectra for selected fission parameters are available now
Input data
•
•
•
•
1.
2.
3.
Y(A,TKE)
Level density. (Level density model should be applied to
extrapolate into FF mass range)
Absorption cross section (optical model)
Energy release and binding energies (G.Audi and
A.H.Wapstra)
Assumptions
Neutron emission from excited, moving FF (full acceleration)
Total excitation energy U= Uh +Ul = Er-TKE
Uh and Ul from equilibrium (correction is possible)
This model = LANL model (Weisskopf assumption)
Experimental and calculated data (PFNS)
235U(th)
252Cf(sf)
1
R(E), <E>=2.121MeV
R(E), <E>=1.974MeV
1.0
Scale method
Ignatyuk LD
W-E assumption
Ignatyuk LD, a=a*0.65
0
Ignatyuk LD
W-E
0.5
Ignatyul LD, a=a*0.75
Mannhart evaluation
0.0
0
2
4
6
E (MeV)
8
10
12
0
2
4
6
E (MeV)
8
10
12
Experimental and calculated data (ν(A))
235U(th)
252Cf(sf)
3.0
3.5
Nishio, 1998
Budtz-Jorgenson [27]
Vorobyev, 2004
2.5
3.0
Ignatyuk LD
W-E
Ignatyuk LD
W-E
Ignatyuk LD, a=a*0.65
2.5
2.0
Ignatyul LD, a=a*0.75
 (A)
 (A)
2.0
1.5
1.5
1.0
1.0
0.5
0.5
0.0
0.0
80
100
120
A
140
160
80
100
120
A
140
160
235U(th)
252Cf(sf)
6
8
PNPI, 2001
Nishio, 1998
Maslin, 1967
5
dTKE/dn=13.5 MeV
7
Ignatyul LD
Boldeman, 1971
Vorobyev, 2004
W-E
6
Ignatyul LD, a=a*0.75
dTKE/dn=19MeV
4
Ignatyuk LD
dTKE/dn=10 MeV
5
W-E
Ignatyuk LD, a=a*0.65
3
dTKE/dn=9.2MeV
 (TKE)
 (TKE)
Experimental and calculated data (ν(TKE))
2
4
3
2
1
1
0
120
140
160
180
TKE (MeV)
200
220
0
120
140
160
180
TKE (MeV)
200
220
240
ν(TKE)), S=(N-Z)/A?
• Experimental slope:
235U; 19 MeV/n, S=0.217
239Pu; 16 MeV/n, S=0.213
233U; 13 MeV/n, S=0.210
252Cf; 13 MeV/n, S=0.222
• Calculated result ~10 MeV/n
Slope estimation
Average <Bn> is ~6 MeV.
The ν~2.5 in this eq.
If <ε>~1.5 one may estimate the slope in eq.1, dU/dν~9 MeV.
So, we can explain what does mean value estimated with detail
calculation in the model.
Experimental and calculated data (ν(μ))
235U(th)
252Cf(sf)
1.0
1.0
0.8
Vorobyev, [4]
0.8
Ignatyuk LD, 0.2-8MeV
Ignatyuk LD, 0.56-5.9MeV
Ignatyul LD, a=a*0.65, 0.2-8MeV
Ignatyul LD, a=a*0.65, 0.56-5.9MeV
0.6
 n/sr
 n/sr
0.6
0.4
0.2
0.0
-1.0
Vorobyev, [4]
0.4
0.2
-0.5
0.0
, cosine to LF
0.5
1.0
0.0
-1.0
-0.5
0.0
, cosine to LF
0.5
1.0
What we can describe and it means what we
understand?
Experimental data
Absolute value and energy dependence <ν>
Yes
No
Yes, for any
isotopes
Macroscopic data
No
Microscopic PFNS (total)
No
Angular and LR effects
No
Dependence of ν(A)
235U?
No
CMS neutron energy e(A)
No
CMS spectra for selected A
No
Dependence ν(TKE) !!!!!
No
Conclusion 1
• Theoretical model can not describe simultaneously numerous
experimental data. So, this model is wrong in main assumption;
• ν(TKE) is the crucial point. May be if we will explain this huge slope
(~19 MeV/n instead of ~9 MeV/n) we will understand the mechanism of
neutrons emission in fission;
• It seems that some of fissions happened due to simultaneous emission
several particles (2 FFs and neutron(s)), providing continuous energy
distribution;
Conclusion 2
• Until detailed understanding of mechanism of neutron emission in
fission we have in hand only “semi-empirical models” for practical
application;
• Contradiction between microscopic and macroscopic data (Mic-Mac
problem) is still exist. May be this connected with energy-angular
selection. So, we should spend more effort to investigate the influence
of complicate nature of the neutron emission on macro-results.
• New experimental and theoretical efforts are extremely necessary to
clarify the problem, to suggest new model, and to formulate new
experiments for its investigation.
N.Corjan model.
• IV. CONCLUSIONS
• During the neck rupture neutrons are released (become unbound) due
to the non-adiabaticity of this process. They leave the fissioning system
during the next few 10E−21 sec after scisssion, i.e., during the
acceleration of the fission fragments. Even if the neutrons are released
predominantly in the inter fragment region, they do not move
perpendicular to the fission axis but instead they are focused (by the
fragments) along the fission axis. This feature is unexpected. The
resulting angular distribution of these neutrons with respect to the
fission axis resembles with the experimental data for all prompt
neutrons. This re-opens the 50 years old debate on the origin of the
fission neutrons. For a quantitative comparison the effects of
reabsorption of the unbound neutrons by the imaginary potential and
of the simultaneous separation of the fragments has to be included.
N.Corjan model.
T=40E-22 s
Request for future total PFNS experiment
• All fission fragments should be integrated over angle, masses, and TKE.
The efficiency of FF counting should be ~1 (as close as possible);
• Mass of fission chamber for fission counting should be reduced (as small as
possible);
• 235U spectrum should be measured relative to 252Cf;
• Cf-source should be placed in the same chamber, and provide similar count
rate;
• Time resolution <2ns (FWHM), and flight path ~3m;
• Shielding neutron detector to reduce counting of re-scattering neutrons
(room neutrons);
• The scattering on the FF counter material should be simulated taking into
account angular-energy selection effect.
The end
Total acceleration
Kornilov et al. Nucl Phys. A686, 187 (2001),
Phys. Atomic Nuclei, 64, 1372 (2001)
~40% fission events for 252Cf(sf) and 235U(th) are
accompanied by neutrons before total acceleration
Yscn(E), 1/MeV
0.1
0.01
Budtz-Jorgensen, 1988
Skarsvag, 1963
1E-3
0
2
4
6
E, MeV
8
10
0.0025
2D distribution TKE * A
0.0020
0.0015
0.0010
0.0005
TKE-100, MeV
80
100
120
140
160
40
60
80
100
1E-3
60
100
1E-4
80
40
1E-5
FF masses
Sharing of energy between fragments
235
235
U(th)
U(th)
4
2.5
th=tl, ILD, Uh*0.9
corrected as
Nishio, 1997
252
th=tl, ILD, Uh*0.9
Cf
2.0
(A), MeV
(A)
3
2
1
corrected as for Cf
Grudzevich
Nishio, 1997
1.5
1.0
0.5
0
0.0
80
100
120
A
140
160
80
100
120
A
140
160
Conclusion for future experimental efforts
• New experimental efforts are necessary to answer the
following very important questions:
• what is the nature of the “angular effect”, why the shape of the
prompt fission neutron spectrum may change so drastically,
• what is the physical reason responsible for the formation of a
more energetic spectrum in the integral experiments in
comparison with microscopic data, and
• what is happening inside nuclear reactors.