Investigation of the prompt neutron emission in low energy fission of 235 U( n th , f )

Investigation of the prompt neutron emission in low energy fission of 235U(nth, f)

Vorobyev A.S., Shcherbakov O.A., Gagarski A.M., Val’ski G.V., Petrov G.A.

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

E-mail: [email protected]

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1

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5

6

7

8

8

3

4

5

6

71

Schematic view of the experimental set-up

• TOF measurement technique used for fission fragments (140 mm) and prompt neutrons registration (~50 cm)

• 235U target (99,9%, Ø15mm) - 280 μg/сm2 UF4 onto 70 μg/сm2 Ti backing at centre of reaction chamber at the low operating gas pressure (4-6 Torr)

• Two neutron stilbene detectors (50 x 50 mm2 and 40 x 60 mm2 mounted on the Hamamatsu - R6091) in a cylindrical shielding (30 mm thick layer of lead and 40 mm polyethylene), neutron registration threshold ~200 keV

235U

Stop MWPDs

Start MWPD

3

Electronic set-up

START

PH 1

PS 1

PH 2

PS 2

PF 3

PF 1

PF 2

STOP ND1

STOP ND2

STOP1 FF1

STOP2 FF1

STOP2 FF2

STOP1 FF2

GATE

Stop MWPDs Arc N1, T11 2 CFD

Stop MWPDs Arc N1, T12 2 CFD

Stop MWPDs Arc N2, T22

2 CFD

Stop MWPDs Arc N2, T21

2 CFD

ND 2 2 CFD

2 Delay

Delay

ND 1 2 CFD

2 Delay

Delay

Start MWPD 2 CFD

AND

AND

AND

AND

PC

TDC

QDC

QDC

QDC

Input

Clear

Timer

Counter

CAMAC

TFA

TFA

TFA

TFA

TFA

TFA

TFA

TFA

TFA

4

Analysis of the data

Applied correction for:

• Time uncertainties in TOF measurement:– Pulse-height dependent time walk in neutron and fission fragment channels– Different fission fragments TOF to start MWPD

• Neutron detector background :– a double-discrimination method (TOF and pulse shape with gamma suppression factor ~200)– true coincidence subtracted and the linear approximation of the remain part of background

• Fission fragment detector efficiency

• Complementary fission fragment contribution and neutron recoil correction

• Angular and neutron energy resolution (timing resolution : 1.0 - 1.2 ns)

• Neutron detector efficiency determined as the ratio of the measured total neutron spectrum of 252Cf(sf) to the reference standard spectrum 4

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

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]

-1200 -800 -400 0 400 800 1200

1000

2000

3000

4000

5000

6000

7000

8

765432

1

Co

un

ts

T11

- T12

, channel

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

Analysis of the data: Measurement of the total prompt neutron spectrum of 235U(nth, f) relative

to 252Cf(sf) (neutron detector efficiency determination)

5

)(

)()()()()(

)sin(),(

)sin(),(

)()()(exp

exp)(

0

exp

0

exp

)(

)(

nCf

nU

EF

nnnE

resnA

res

nCf

nU

nnE

resnA

res EN

ENEIEBWEfEf

dEN

dEN

EBWEfEf

n

nEStd

CfN

nE

UN

)(

)()(

),(

),(

)(exp

exp

)sin(exp

)sin(exp

0)sin(),(

exp

0)sin(),(

exp

nCf

nUn

nCf

nU

n

dnECfN

dnEUN

EN

ENEI

EN

EN

EI

- the angle between the neutron direction and the direction of motion of the light fragmentsNexp(E, ) – measured prompt neutron spectrum for fixed angle fres

A and fresE – angular and energy resolution corrections

BW – bin-width correctionI - correction due to summing over angle which was found by means of the following equation:

)( nStdCf EN - linear interpolation of the 252Cf prompt neutron spectrum evaluation

(C.W.REICH, W MANNHART, T ENGLAD – ENDF-B/VII).

Analysis of the data: Correction applied for ratio of neutron spectra 235U(nth, f) to 252Cf(sf)

6

The angular and energy resolution correction are a minor influence on the total prompt neutron spectrum as well as correction due to summing over angle .

2 4 6 8 10 12 14 16

0,98

1,00

1,02

1,04

1,06

1,08

1,10

1,12

1,14

angular resolution - fres

A(En)

energy resolution - fres

E(En)

due to summing over angle - I (En)

bin-width correction BW(En)

total correction - F(En)

Cor

rect

ion

fact

or

Neutron energy, En [MeV]

0 2 4 6 8 10 12 14 16

0,01

0,1

1

252

Cf measurement

235

U measurement due to background uncertainty total uncertainty

Re

lativ

e e

rro

r [ %

/10

0]


7

All these data are the TOF measurements of the absolute ratio 235U(En)/ 252Cf(En). Therefore presented PFNSs were obtained as the product of measured ratios, which were multiplied by 3.759/2.421, and the Mannhart’s evaluated spectrum of 252Cf.

Present experiment <tot> = 2.44 ± 0.05

Result: PFNS of 235U(nth, f) Comparison with literature data

0,1 1 100,4

0,5

0,6

0,7

0,8

0,9

1,0

1,1

1,2

Starostov et.al. 198340871011, 40871012, 40872007

Lajtai 1985 (30704003) HambschKornilov Present data ENDF/B-VII Maslov_2010R

atio

to M

axw

elli

an <

En>

= 1

.971

Me

V


1 2 3 4 5 6 7 8 9 10 11 120,4

0,5

0,6

0,7

0,8

0,9

1,0

1,1

1,2

Starostov et.al. 198340871011, 40871012, 40872007

Lajtai 1985 (30704003) HambschKornilov Present data ENDF/B-VII Maslov_2010

Rat

io to

Max

we

llian

<E

n> =

1.9

71 M

eV


8

Result: PFNS of 233U(nth, f) Comparison with literature data

0,1 1 100,5

0,6

0,7

0,8

0,9

1,0

1,1

1,2

Lajtai_30704002 Bojcov_40873002 Nefedov_40871013 Starostov_40872008 Maslov ENDF/B-VII ResultU3

Rat

io to

Max

wel

lian

<E

n> =

2.0

1 M

eV


1 2 3 4 5 6 7 8 9 10 11 120,5

0,6

0,7

0,8

0,9

1,0

1,1

1,2

Lajtai_30704002 Bojcov_40873002 Nefedov_40871013 Starostov_40872008 Maslov ENDF/B-VII ResultU3

Ra

tio to

Ma

xwe

llian

<E

n> =

2.0

1 M

eV


All these data are the TOF measurements of the absolute ratio 233U(En)/ 252Cf(En). Therefore presented PFNSs were obtained as the product of measured ratios, which were multiplied by 3.759/2.4894, and the Mannhart’s evaluated spectrum of 252Cf.

Present experiment <tot> = 2.54 ± 0.06

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

0,05

0,10

0,15

0,20

Yie

ld,[n

eutr

on/(

str*

MeV

)]Y

ield

,[neu

tron

/(st

r*M

eV)]

Neutron energy in the lab. system, [MeV]

Yie

ld,[n

eutr

on/(

str*

MeV

)]

= 180 = 0

0

= 360

= 540

0,03

0,06

0,09

0,12 = 180

0

= 1620

= 1440

2 4 6 8 10 12

= 1260

2 4 6 8 10 12

= 900

2 4 6 8 10 12

0,02

0,04

0,06 = 720

2 4 6 8 10 12

= 1080

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10

General features of the investigation of neutron emission mechanism:

• The contribution of “scission” neutrons 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 fit of available experimental data.

• In our analysis the angular and energy spectra of the prompt fission neutrons emitted by accelerated fragments are calculated using experimental data for 00, 180 and 360 angles relative to the fission direction. Thus the calculated spectra are free of any parameters concerning the prompt neutron spectra in c.m.s.

• As a first step, the model of two fragments with average mass and kinetic energy is used for calculation of neutron spectra in the laboratory system instead of real mass and kinetic energy distributions.

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Main features of our calculation

• Used equations (two fragments approximation): The neutron spectra in the laboratory system:

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

The neutron energy and spectra in the c.m.s of the fission fragments: Ec.m. = En + Ef - 2 cos( lab ) (En Ef ) 1/2

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

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

• Two fragments approximation gives a very good result, since, it was shown for 252Cf(sf)** , it has a minor influence on the total neutron energy spectrum.

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

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Analysis of the data Calculation procedure

• At the first step, the neutron energy spectra in c.m.s are calculated under the assumption that neutrons registered at fixed angles relative to the 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;

12

1 2 3 4 5 6 7 8 9 10 11 120,00

0,05

0,10

0,15

0,20

0,25

0,30

= 00

Light fragment

252Cf

present data neutron yield from heavy fragment

Yie

ld, [

neut

ron/

(str

*MeV

)]

Neutron energy in lab. system, [MeV]1 2 3 4 5 6 7 8 9 10 11 12

0,05

0,10

0,15

0,20 present data neutron yield from light fragment

252Cf

Heavy fragment

= 00

Yie

ld, [

neut

ron/

(str

*MeV

)]

Neutron energy in lab. system, [MeV]

13

Analysis of the data Calculation procedure• 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.

13

1 2 3 4 5 6 70,00

0,02

0,04

0,06

0,08

252Cf

Heavy fragment

180

360

00

Fit

Yie

ld, [

neut

ron/

(str

*MeV

)]

Neutron energy in c.m.s, [MeV]

1 2 3 4 5 6 7 8 9 10 11 12 131E-6

1E-5

1E-4

1E-3

0,01

252Cf

Heavy fragment

180

360

00

Fit

Yie

ld, [

neut

ron/

(str

*MeV

)]


1 2 3 4 5 6 7

0,02

0,04

0,06

0,08

0,10Light fragment

252Cf

Data: L18_BModel: MaksChi^2 = 1.5644E-6P1 2.01313 ±0.02936P2 0.08747 ±0.11261P3 0.43539 ±0.17916P4 0.94645 ±0.07304

180

360

00

Fit

Yie

ld, [

neut

ron/

(str

*MeV

)]

Neutron energy in c.m.s, [MeV]1 2 3 4 5 6 7 8 9 10 11 12 13

1E-5

1E-4

1E-3

0,01

0,1

Light fragment

252Cf

Data: L18_BModel: MaksChi^2 = 1.5644E-6P1 2.01313 ±0.02936P2 0.08747 ±0.11261P3 0.43539 ±0.17916P4 0.94645 ±0.07304

180

360

00

Fit

Yie

ld, [

neut

ron

/(st

r*M

eV

)]


<L> = 2.04 ± 0.02<H> = 1.69 ± 0.03

14

Results:yield of prompt neutrons as a function of angle relative to the direction of light

fission fragment in the lab. system

• Introduction of anisotropy with A2 = 0.04 into the calculation improves agreement with obtained experimental data. At that, there is some surplus of measured yield over calculated at angles near 900.

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]

15

Results:angular distribution of the average prompt neutron emission energy

• Under the assumption that the “additional” neutrons are emitted isotropically in the laboratory system, their yield is deduced as about 3% of the total neutron yield for 235U(nth, f).

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]

16

2 4 6 8 10

0,2

0,4

0,6

0,8 Our data (2010) calculated with A

2 = 0.04


235U

<n

(En )

> [

neu

tro

n /

fiss

ion

/ M

eV ]


0.1 1 10

0.85

0.90

0.95

1.00

ncalc

(En, A

2 = 0.04)

Ratio = ----------------------- n

calc(E

n, A

2 = 0)

Ra

tio


Method 1 – summation over angles;

Method 2 – calculated in a framework of neutron emission from accelerated fragments (two fragment approximation, A2=0.04) using experimental spectra measured at small angles relative to fragment direction.

Result: PFNS of 235U(nth, f) Comparison with calculation

0,1 1 10

0,8

0,9

1,0

1,1

Method 1 Method 2

error of 252Cf standard

Rat

io to

EN

DF

/B-V

II


17

The 252Cf(sf) total prompt neutron spectrum calculated from measured prompt neutron spectra at small angles relative to FF direction agree with Mannhart’s evaluation exclude low energy region.

The difference between these two spectra obtained by us coincide with obtained by U. Brosa and H.-H. Knitter (p0 = 1.1±0.3%; TSCN = 0.20±0.03MeV).

Result: PFNS of 252Cf(sf)Comparison with calculation

1 2 3 4 5 6 7 8 9 10 11 120.8

0.9

1.0

1.1

1.2

1.3

Calculation

error of 252

Cf standard

Ra

tio to

Ma

nn

ha

rt

Neutron energy, [MeV]0 1 2 3 4 5

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

ps(E

SCN) = p

0/ T

SCN

2 * ESCN

* exp(-ESCN

/TSCN

)

TSCN

= 0.27 +- 0.03 MeV p

0 = 1.7 +- 0.3 %

Difference Fit

Diff

eren

ce b

etw

een

Man

nhar

t's e

valu

atio

nan

d C

alcu

latio

n, [n

eutr

on/M

eV]

Neutron energy, [MeV]

18

Targetprompt (Neutron / fission)

CalculatedExperiment ENDF/B-VII

A2 = 0 A2 = 0.04

252Cf(sf) 3.86 3.73 3.77 ± 0.02 3.7590

235U(nth, f) 2.56 2.45 2.44 ± 0.05 2.421

233U(nth, f) 2.60 2.48 2.54 ± 0.06 2.4894

• Both experimental and calculated prompt neutron spectra have been compared in 0.2-12 MeV energy range.

• The calculation performed using experimental data obtained for small angles relative to the fission fragment direction reproduces the total prompt neutron spectra both the shape and the average multiplicity .

• Also, the calculated energy spectra for fixed angles agree rather well with experimentally obtained ones.

• There is a minor distinction which is that the calculation (A2 = 0) gives overestimated value of fission neutron yield as compared with experimental data.

Result:Comparison with calculation

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Results (correlation with FFs):

120 140 160 180 200

1

2

3

4

Nishio Maslin Present data

tot

Present data L

Present data H

Num

ber

of n

eutr

ons,

tot(T

KE

)

Pre-neutron fragment TKE [MeV]

• The transformation of neutron spectra in the laboratory system (at small angles relative to fragments direction) to the center-of-mass system was performed for each fragment fixed mass and energy.

• A good agreement is observed between average number of prompt neutrons obtained by this experiment and other authors.

average prompt neutron multiplicity vs TKE

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Results (correlation with FFs):average prompt neutron multiplicity vs fragment mass

80 100 120 140 1600.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Nishio (small-angle geometry) Maslin (large liquid detector) Maslin tot

Mueler (2E-2V - method) Present work Present work tot

Nu

mb

er o

f n

eutr

on

s, (

m)

Pre-neutron fragment mass, m [a.m.u.]

• The total number of prompt neutrons calculated from measured data at small angle is practically coincident with obtained from direct measurement of Maslin et.al. (large Gd-loaded liquid scintillation counter with efficiency about 85% - 4-geometry). Probably, this means that a fraction of neutrons originating from sources other than accelerated fragments is small.

80 100 120 140 1600,0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

Maslin (large liquid detector) Maslin tot

Present work (235

U)

Present work tot(235U)

Present work (233

U)

Present work tot(233

U)

Nu

mb

er o

f n

eutr

on

s, (

m)

Pre-neutron fragment mass, m [a.m.u.]

21

Conclusion

• Results of two our measurements (“efficiency” measurement and calculation performed using data obtained by us in previous experiment) are in a good agreement.

• The average of two measurements is in a good agreement with ENDF/B-VII in 0.5- 12 MeV energy range.

• Comparison of experimentally obtained angular and energy distributions of prompt neutron and calculated one on the base of neutron evaporation from fully 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 (two fission fragment approximation); 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.• To obtain certain estimation of the emission mechanism other than emission from

accelerated fragments now we are doing more careful analysis of the obtained angle-energy distributions to determine the dependence of main characteristics of “scission” neutrons on fragment mass and kinetic energy.

22

Thank you very much for your attention

Documents

Investigation of the prompt neutron emission in low energy fission of 235 U( n th , f )