Investigation of the Prompt Neutron Emission in Low Energy Fission of 235 U

Investigation of the Prompt Neutron Emission in Low Energy Fission of 235U

Vorobyev A.S., Shcherbakov O.A., Petrov G.A.

Petersburg Nuclear Physics Institute.188300, Gatchina, Leningrad district, Russia

E-mail: [email protected]

2

Motivation

• Investigation of the prompt neutron emission mechanism.

• Scope of the experimental data available for end-to-end analysis is limited by 1 experiment for 235U (Skarsvag et.al.(1963)) and 3 experiments for 252Cf (Bowman et.al.(1962), Seregina et.al.(1985), Budtz-Jorgensen et.al.(1988)).

• To measure spectra of prompt fission neutrons from the 235U(nth,f) reaction at several angles relative to the light fragment direction to eliminate the absent of these data in literature.

• From previous works: the contribution of scission neutrons to the total yield of PFN ranges from 1% to 20%, so even existence of scission neutrons can hardly be considered as proven.

• The 235U is the most promising isotope for investigation as it was observed to provide the highest relative yield of supposed scission neutrons in previous experiments.

3

Methodology General features of the investigation of neutron emission mechanism:

• It is well established that the main source of prompt neutrons is accelerated fission fragments ~90%;

• The yield of neutrons with other emission mechanism is usually determined as difference between experimentally observable variables in the laboratory system and those calculated using known neutron spectra in the center-of-mass system;

• As the prompt neutron energy spectra in the center-of-mass system of light and heavy fragments the Maxwellian or Weisskopf spectra are usually used. The parameters of these spectra are adjusted so as to show the best correlation with available experimental data.

• The model of two fragments with average mass and kinetic energy is used frequently for calculation of neutron spectra in the laboratory system instead of real mass and kinetic energy distributions. Such substitution has a minor influence (3%) on the total neutron energy distribution.

3

4

D.G. Madland, IAEA Report INDC(NDS) – 251, Vienna, 1991, p. 201

Methodology

5

Main features of calculation

• The neutron spectra in the c.m.s of the fission fragments, nc.m.(Ec.m), are obtained using experimental data , nlab (En , lab), for 00, 180 and 360 angles relative to the fission direction

free of any parameters derived from other experiments; no dependence on spectrum shape;

• Using equations (two fragments approximation):

nlab (En , lab) = (En / Ec.m.) 1/2 φ(Ec.m. , c.m. ) nc.m.(Ec.m) ,

Ec.m. = En + Ef - 2 cos( lab ) (En Ef ) 1/2,

Ef = TKE [ 1/mf – 1/A ],

(Ec.m. ) 1/2 cos(cm ) = (En) 1/2 cos( lab ) – (Ef ) 1/2;

• Since the fragments have the angular momenta normal to the fragment direction the angular distribution of prompt neutrons in the center-of-mass system of fission fragment may be given by:

φ(Ec.m. , c.m. ) = 1 + A2 Ec.m. (3 cos2( c.m. ) - 1) / 2 ,

where A2 = (1 - φ(1,900) / φ(1,00) ) 0.

5

Methodology

6

1

2

2

3

4

5

6

7

8

8

3

4

5

6

7

1

Schematic view of the experimental set-up

Reaction Chamber:235U target (Ø15mm) – 280 μg/сm2

UF4 onto 70 μg/сm2 Ti backing;start MWPD (68 x 92 mm2)

located within 7 mm range from the 235U target;

stop MWPD (72 x 38 mm2) located at a distance of 140 mm from the chamber axis.

Neutron detectors: stilbene crystals (50 x 50 mm2

and 40 x 60 mm2 mounted onthe Hamamatsu - R6091)neutron registration threshold –

150 200 keV;double-discrimination method –

pulse shape and time-of-flight criteria

time-of-flight distance from 235U target – ~ 50 cm

7

Raw experimental data: counts rate of fission fragments from different fragment detectors

Number of registered fission events as a function of MWPDs pulse timing delay from both ends of Arc N1

-1200 -800 -400 0 400 800 1200

1000

2000

3000

4000

5000

6000

7000

8

765432

1

Co

un

ts

T11

- T12

, channel

8

Raw experimental data: fission fragments time-of-flight

(a) fission fragments time-of-flight spectrum detected by second MWPD of Arc N1 (wasn’t shaded by start MWPD)

(b) number of fragments as a function of TOF difference for fragments registered by two opposite detectors of Arc N1 and N2

1600 1800 2000 2200 2400

100

200

300

400

500

(a)

Co

un

ts

T11

- T22

, channel

Co

un

ts

Fragment TOF channel-300 -200 -100 0 100 200 300

200

400

600

800(b)

9

Raw experimental data: neutron - - quanta separation method

100 200 300 400 500

50

100

150

200

250

300Neutrons

- quanta

Total Integral [arb. units]

Part

ial In

teg

ral [a

rb. u

nit

s]

Both integrals were measured for pulse of neutron detector in a time window of 300 nsec, while the partial integral window – with a delay ~30 nsec.

10

Raw experimental data:total prompt neutron time-of flight spectrum

1000 1500 2000 2500 3000 35001

10

100

1000

10000

(b)

(a)

Background

Co

un

ts

Neutron TOF Channel

850 875 900 925 950

500

1000

1500

2000

2500

3000

3500

Co

un

ts

Neutron TOF Channel

initial prompt neutron TOF spectrum corrected for the pulse-height dependence of timing jitter of the start MWPD corrected for the dependence on the integral of neutron detector pulse corrected for the fragment flight time from the target to start MWPD

Measurement of the Total Prompt Neutron Spectrum of 235U(nth, f) Relative to 252Cf(sf)

(neutron detector efficiency determination)

252Cf target placed into the experimental set-up in place of 235U

12

)sin(),(

)sin(),(

)()(

)()()(

exp

exp

exp

exp

nCf

nU

nStdCf

nCf

nUn

StdCfnU

EN

EN

ENEN

ENENEN

)( nStdCf EN

1)1( 2

1

222

0Tc

lEEn 20 288.72 TlE

where is the angle between the neutron direction and the direction of motion of the light fragments, of T is the flight time in nanoseconds, c is the velocity of light, l is the flight path between source and the detector;

is linear interpolation of the 252Cf prompt neutron spectrum evaluation (C.W.REICH, W MANNHART, T ENGLAD – ENDF-B/VII).

Analysisfirst approximation

13

• For 11 fixed angles between the neutron and light fragment direction (from 00 to 1800 in 180 interval) the prompt neutron spectra were obtained independently for two neutron detectors as weighted averages of 4 measurement cycles;

• Each measurement cycle was analyzed separately

• The errors of 235U spectra for fixed angle neutron emission relative to the light fragment direction are the RMS deviation from weighted means. These errors include the possible instability of electronic (uncertainties of neutron threshold determination …), the statistical and energy determination uncertainties as well as for total prompt neutron spectrum uncertainties due to the fact that in the measurements we have the experimental histogram distributions instead of continuous distributions.

• Result is a weighted average of two neutron spectra obtained by individual detectors.

• The errors of 252Cf spectra measurements were obtained as in the case with 235U .

Analysisdegree of reliability – experimental errors determination

14

Total prompt neutron spectrafirst approximation

There is a good agreement between spectra obtained by two individual neutron detectors

0.1 1 10

0.6

0.8

1.0

1.2

Maslov ENDF/B-VIINeutron detector ND1Neutron detector ND2Average

Rat

io to

Max

wel

lian

<E

n> =

1.9

71 M

eV

Neutron energy, En [MeV]

15

Total prompt neutron spectra first approximation

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.6

0.8

1.0

1.2

Maslov ENDF/B-VIINeutron detector ND1Neutron detector ND2Average

Rat

io to

Max

wel

lian

<E

n> =

1.9

71 M

eV


There is a good agreement between spectra obtained by two individual neutron detectors

16

)(

)()()()()(

)(

)()()()(

exp

exp

exp

exp

nCf

nUn

StdCfnn

Eresn

Ares

nCf

nUn

StdCfnnU

EN

ENENEIEfEf

EN

ENENEFEN

)(

)()(

),(

),(

)(exp

exp

)sin(exp

)sin(exp

0)sin(),(

exp

0)sin(),(

exp

nCf

nUn

nCf

nU

n

dnECfN

dnEUN

EN

ENEI

EN

EN

EI

Analysissecond approximation – experimental resolution was taken into account

)(

)(

)(

1

)(

1

0)sin(

' '

''):',():',(),(

0)sin(

' '

''):',():',(),(

0)sin(),(

exp

0)sin(),(

exp

nStdCf

nU

nEAresfnE

Eresf

d

E

dEdEnEECffnE

ACffnE

StdCfN

d

E

dEdEnEEUfnE

AUfnEUN

dnECfN

dnEUN

EN

EN

17

0 2 4 6 8 10 12 14 16 18

0.10

0.15

0.20

0.25

Neutron detector ND1 Neutron detector ND2F

WH

M /

En

[MeV

]


Analysissecond approximation: neutron energy resolution

Resolution function is supposed to be Gaussian in every energy point.

18

235U 252Cf

Analysissecond approximation: neutron energy resolution correction

Ratio of corrected to non-corrected neutron energy spectra.

0 2 4 6 8 10 12 14

0.4

0.5

0.6

0.7

0.8

0.9

1.0

720

540

360

1800

1620

1440

1260

1080

180

900

00

Energy Resolution Correction (235U)

Rat

io

Neutron energy, En [MeV]0 2 4 6 8 10 12 14

0.4

0.5

0.6

0.7

0.8

0.9

1.0

720

540

360

1800

1620

1440

1260

1080

180

900

00

Energy Resolution Correction (252Cf)

Rat

io


19

Analysissecond approximation: angular resolution function

18 36 54 72 90 108 126 144 162 1800

1

2

3

4

5

6

Angular resolution function

160.10

125.50

171.10

143.2107.8072.20

8.90

54.5036.80900

19.90

A

rbitr

ary

uni

ts

[degree]

calculated using the real dimensions of fragment and neutron detectors

20

235U 252Cf

Analysissecond approximation: angular resolution correction

Ratio of corrected to non-corrected neutron energy spectra.

0 2 4 6 8 10 12 14 16 18

0.8

0.9

1.0

10801260

1440

16201800

900

720

540

360

180

00

Angle Resolution Correction (252Cf)

Rat

io


0 2 4 6 8 10 12 14 16 18

0.8

0.9

1.0

1080

1260

1440

16201800

900

720

540

360

180

00

Angle Resolution Correction (235U)

Rat

io


21

Analysissecond approximation: total resolution corrections

0 2 4 6 8 10 12 14

0.98

1.00

1.02

1.04

1.06 angular resolution - fres

A(E

n)

energy resolution - fres

E(E

n)

due to summing over angle - I (En)

total correction - F(En)

R

atio


22

Analysisdegree of reliability – experimental and systematic errors

0 2 4 6 8 10 12 14

0.01

0.1

1

due to background uncertainty

252

Cf measurements

235

U measurements

total experimental uncertainty of 235

U(nth,f) measurements

Rel

ativ

e e

rro

r


23

Results: total prompt neutron spectrum of 235U(ntn,f) comparison to literature data

0,1 1 10

0,7

0,8

0,9

1,0

1,1

ENDF/B-VII Maslov calc.(2010) Kornilov fit Yufeng (1989) Johansson (1977) Starostov, Nefedov data (1984) Average present dataR

atio

to M

axw

ellia

n <

En>

= 1

.971

MeV


0 2 4 6 8 10 12 14

0,7

0,8

0,9

1,0

1,1

ENDF/B-VII Maslov calc.(2010) Kornilov fit Yufeng (1989) Johansson (1977) Starostov, Nefedov data (1984) Average present data

Rat

io to

Max

we

llia

n <

En>

= 1

.97

1 M

eV


Present experiment : < > = 2.44 ± 0.05 ENDF/B-VII: < > = 2.421

The obtained PFNS agrees with literature experimental data in full energy range

24

Method 1 – summation over angles;

Method 2 – calculated in a framework of neutron emission from accelerated fragments using the c.m.s. spectra for light and heavy fragments obtained from experimental spectra measured at small angles relative to fragment direction in the lab. system.

Results: total prompt neutron spectrum of 235U(ntn,f) comparison to evaluation

0,1 1 10

0,7

0,8

0,9

1,0

1,1

T = 0.965 Ef=0.595

<En> = 2.041 ± 0.023

Maslov calc.(2010) ENDF/B-VII Present data (method1) Present data (method2) Watt fit of present data

Rat

io to

Max

wel

lian

<E

n> =

1.9

71 M

eV


0 2 4 6 8 10 12 14

0,7

0,8

0,9

1,0

1,1

T = 0.964 Ef=0.595

<En> = 2.041 ± 0.023

Maslov calc.(2010) ENDF/B-VII Present data (method1) Present data (method2) Watt fit of present data

Rat

io to

Max

wel

lian

<E

n> =

1.9

71 M

eV


25

0.1 1 10

0.9

1.0

1.1

1.2

Maslov calc. (2010)

error of 252Cf standard method 1 method 2

Rat

io to

EN

DF

/B-V

II


0 2 4 6 8 10 12 14

0.9

1.0

1.1

1.2

Maslov calc. (2010)

error of 252Cf standard method 1 method 2

Rat

io to

EN

DF

/B-V

II


Results: total prompt neutron spectrum of 235U(ntn,f)

Conclusion:

• Our PFNS agrees with differential experimental data in full energy range.• Results of two different measurements are in a good agreement. • The average of two measurements is in a good agreement ENDF/B-VII.

Angle and Energy distributions of the Prompt Fission Neutrons of 235U(n, f)

27

Analysis of the dataApplied corrections for **:

• time uncertainties in TOF measurements;

• neutron detector background (a double-discrimination method, true coincidence subtracted and the linear approximation of the remain part of background);

• fission fragment detector efficiency;

• complementary fission fragment contribution;

• angular and neutron energy resolution;

• neutron detector efficiency determined as the ratio of the measured total neutron spectrum of 252Cf to the reference standard spectrum;

• normalization to the average fission neutron multiplicity of 235U recommended by ENDF/B-VII;

** - Measurements of angular and energy distributions of prompt neutrons from thermal neutron-induced fission A.S. Vorobyev, O.A. Shcherbakov, Yu.S. Pleva, A.M. Gagarski, G.V. Val’ski, G.A. Petrov, V.I. Petrova, T.A. Zavarukhina, NIM A598 (2009) 795

27

28

Analysis of the data Calculation procedure

• At the first step, the neutron energy spectra in c.m.s are calculated on the assumption that neutrons registered at fixed angles relative to light fragment direction were emitted solely by the light and heavy fragments, respectively;

• At the second step, the neutron contribution to the complementary fragment is subtracted and the energy spectra for these angles in the laboratory system are obtained;

• Further, using these energy spectra in the laboratory system, the neutron energy spectra for light and heavy fragments are obtained in the center-of-mass system;

• Finally, the spectra obtained in the center-of-mass system are used for calculation of neutron angular and energy distributions in the laboratory system.

28

29

Results U-235:yield of prompt neutrons as a function of angle relative to the direction of light fission fragment in the lab. system

0 18 36 54 72 90 108 126 144 162 180

0,2

0,4

0,6

0,8

235U

Skarsvag data (1963) Our data (2010) calculated with A

2= 0.04

n(

) [n

eutr

on

/ fi

ssio

n /

sr]

[degree]0 18 36 54 72 90 108 126 144 162 180

0,9

1,0

1,1

235U

calculated with A2 = 0.04

calculated with A2 = 0

error "corridor" due to uncertainty of neutron c.m.s spectra

n(

) exp

/ n

() ca

lc

[degree]

30

Results U-235:angular distribution of the average prompt neutron emission

energy in the lab. system

0 18 36 54 72 90 108 126 144 162 180

1,4

1,6

1,8

2,0

2,2

2,4

2,6

2,8

Skarsvag data (1963) Our data (2009) Calculation

235U

Ave

rag

e n

eutr

on

en

erg

y, <

En(

)> [

MeV

]

[degree]0 18 36 54 72 90 108 126 144 162 180

0,95

1,00

1,05

Ra

tio

Ratio of the experimental average neutron energy to calculated one

calculated with A2 = 0.04


235U

[degree]

31

Results U-235: total prompt neutron spectra in the laboratory system

2 4 6 8 10

0,2

0,4

0,6

0,8 Our data (2010) calculated with A

2 = 0.04


235U

<n(E

n )

> [

neu

tro

n /

fiss

ion

/ M

eV ]


2 4 6 8 101E-3

0,01

0,1

Our data (2010) calculated with A

2 = 0.04


235U

<n(E

n )

> [

neu

tro

n /

fiss

ion

/ M

eV ]


32

Conclusion• The angular and energy distributions of the prompt fission neutrons of

235U(nth,f) have been measured in neutron energy range 0.2 – 12 MeV.• Total prompt fission neutron spectrum of 235U is in a good agreement with

ENDF/B-VII.• Comparison of experimentally obtained angular and energy distributions of

prompt neutron for 235U and calculated ones on the base of neutron evaporation from accelerated fragments enables:

to estimate the contribution of “scission” neutrons as not to exceed 5% of total neutron yield in an assumption of isotropic evaporation in the laboratory system;

• to conclude that the angular anisotropy of the neutron emission in the fragment center-of–mass system, which is alike to 1 + 0.06 Ec.m. cos2( c.m.), should be included into any calculation of prompt neutron properties in the nuclear fission

• Now we are doing the same analysis of the measured angle-energy distributions of 233U(nth,f).

• In future we are planning to carry out the same experiment for 239Pu(nth,f).

33

Thank you very much for your attention

Documents

Investigation of the Prompt Neutron Emission in Low Energy Fission of 235 U