Anisotropic neutron evaporation from spinning fission fragments

Kazimierz 2008

2008 Kaz 01

E. Chernysheva, Frank Lab Dubna

O. Dorvaux, In2P3 Strasbourg

F.-J. Hambsch, IRMM Geel

F.Hanappe, ULB Bruxelles

J. Itkis, Flerov Lab Dubna

Y. Kopatch, Frank Lab Dubna

M. Mutterer, TU Darmstadt

L. Stuttgé, In2P3 Strasbourg

H.-J. Wollersheim, GSI Darmstadt

F. Gönnenwein, Univ. Tübingen

for the collaboration

Kinematical anisotropy of neutrons in lab system

Assume neutrons are evaporated from fully accelerated fission fragments but with the emission in their own cms being isotropic

θcmθlab

Centre of mass system of LF

Laboratory

system

velocity n velocitiesn velocities

of LF fragment

In the transformation from the cms to the lab system the neutrons are thrown into the forward hemisphere. In the lab the angular distribution of neutrons is no longer isotropic as shown here for LF moving to the leftLikewise the energy distribution of neutrons is transformed

fission axisLF HF

Experimental Result for 252Cf(sf)

Density of neutrons in velocity space:

ρ(V)d³V = ρ(V,θlab) V² dV dω

for FF masses

<ML> ~ 120 and <MH> ~ 132 H.R.Bowman et al. 1963

2008 Kaz 2

adiabatic

132 15610884

Mass

4

8

12

Fission Fragments carry large angular momenta

J.O.Rasmussen et al 1969

M.Zielinska-Pfabé, K. Dietrich 1974

Bending Model:

Coulomb + nuclear forces bring about a potential pocket

which aligns deformed fragments on the fission axis.

Angular vibrations are excited as zero point oscillations or

non-adiabatically at neck rupture or thermally.

235U(n,f) 238U(γ,f)

J.L.Durell 1997 D.DeFrenne 1984

<I p

rim>

/ ħ

<I p

rim>

/ ħ

Mass

12

8

4

80 120 160

Large angular momenta

Note:

Angular momenta are perpendicular to fission axis

● ●

Non-deformed (spherical) fragments acquire very large

angular momenta via single particle excitations

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Neutron evaporation from rotating nuclei

Neutrons evaporated from a rotating nucleus will preferentially be emitted in the equatorial plane of spin

z

x

I

fission axis

n

n

cms n anisotropy ~ (1 + A sin² θ)

θ

Averaging over all possible orientations of spin ┴ fission axis, a

forward – backward preference along fission axis results in cmsAveraged over spin

cms n anisotropy ~ (1 + b cos² θcm)

For fixed spin

spin

where θ is polar angle relative to spin

where θcm is polar angle relative to fi-axis

Calculated anisotropy in cms of fragment

Isotropic evaporation for l = 0 neutrons.Anisotropic evaporation for l > 0.

Note that the yield of neutrons is rapidly decreasing for l increasing

From V. Bunakov, I. Guseva et al. 2004

2008 Kaz 4

non-zero n-anisotropy in cms observed from fit to n-spectrum

Ratio of n spectra with/without anisotropy

where cms anisotropy ~ ( 1 + b cos² θcm)

b = 0

n-spectrum from evaporation theory

J. Terrell 1959: “it is probably not possible to prove anything about anisotropy from the fission neutron spectrum alone”

235U(n,f) En = thermal

without cms anisotropy

From F.-J. Hambsch et al. 2003

2008 Kaz 5

ISSUE

Scission Neutrons and/or cms Anisotropy

The cms anisotropy will reinforce the kinematical anisotropy in the labHowever, the effect is very small, prohibitively small for experiments

From V. Bunakov , I.Guseva et al 2005

235U(n,f)

Isotropy in cms

No scission n

- - - - 15% scission n

50% from LF

35% from HF

235U(n,f)

Angular distribution of neutrons in lab as a function of angle θlab relative to LF. The intensities with both LF and HF contributing at 0° : 90° : 180° are 9 : 1 : 4

From K. Skarsvag et al 19632008 Kaz 6

z

x

I

fission axis

n

n

θ

spin

Concept of “CORA” experiment

How to disentangle in the lab the contributions of kinematical and cms anisotropy?

Analyse triple coincidences between 1 fission fragment and 2 fission neutrons

z

x

yI

O●●

●●

Assume - for the sake of argument - extreme cms anisotropy: all n in a plane spin

Project fission axis and

all n events on a plane

perpendicular to fi axis.All neutron events will

be aligned on a single

line, e.g. the x-axis.

as observed in the

projection plane

Extreme cms ANISOTROPY Perfect ISOTROPY

triple coincidences

Assume - for the sake of argument - orientation of fragment spin is fixed

x

y

●O

● ●● ●●●x

y

O●

●

●

●

●

●●

Φ1Φ2

all n-events on a line n-events distributed isotropically in plane

Due to kinematical focussing

density of events is enhanced

near origin O

Plane of projectionPlane of

projection

Fission axis

2008 Kaz 7

Setup of “CORA” experiment

252Cf(sf) fission source

CODIS back-to-back

Ionisation Chamber

with 5-sector cathode

DEMON

neutron detectors

Up to 100 units

●

Fission axis

x

yO

Projection plane for evaluation

Only fission events in cone ± 15° are considered

VIEW FROM TOP

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252Cf spont. fission source

2008 Kaz 9

Layout of experiment CORA II (June 2008)

Fragment detector CODIS

In green: modular neutron detectors DEMON

Predictions from Theory

0 10 20 30 40 50 60 70 80 900

2

4

6

8

10

12

14

16

heavy fragment, <Ii>=8.2 h

light fragment, <Ii>=7.5 h

A*sin2()

W(

)/W

(0o)-

1, %

, deg.

0 30 60 90 120 150 180 210 240 270 300 330 360

0,98

0,99

1,00

1,01

1,02

1,03

n-n

co

un

t ra

te, a

rb.u

.

, deg.

wn() = 1 + 0.9 x sin2(

n-anisotropy in FF cm system

A sin² θcm

heavy fragment

light fragment

Distribution of ΔΦ

with ΔΦ the difference in Φ-angle

for 2 neutrons from same fi event

relative to fragment spin

I. Guseva 2007

2008 Kaz 10

MC simulation for isotropic neutron distribution

0 30 60 90 120 150 180 210 240 270 300 330 3600

200

400

600

800

1000

Efficiency

Cou

nts

n [o]

Due to the modular pattern of the neutron detectors of DEMON the counting efficiency can not be expected to be perfectly flat

Neutron counting efficiency versus detection angle Φ

Difference ΔΦ = Φ2 – Φ1 in Φ- angle for two neutrons detected per fission

Contrary to the Φ-distribution the ΔΦ- distribution is rather smooth

2008 Kaz 11

0 30 60 90 120 150 180 210 240 270 300 330 3600

250

500

750

1000

1250

1500

1750

Co

un

ts

Summary

● WELL KNOWN: fission neutrons being emitted from moving fragments exhibit a kinematical anisotropy in lab

● ISSUE: are neutrons evaporated isotropically or anisotropically in their own cms system ?

● SUGGESTION: cms anisotropy may be attributed to large angular momenta of fission fragments

● PROBLEM: how to disentangle in experiment kinematical and cms anisotropy ?

● CORA: is a project to directly observe the cms anisotropy based on triple correlation data (fragment, n, n)

● EVALUATION: particular scheme of evaluation allows to have model-free access to cm anisotropy

with kinematical anisotropy being “switched off”

● EXPERIMENT: underway since July 2008

● FINAL AIM: find from experimental ΔΦ distribution the cms anisotropy (1 + A sin² θ) relative to FF spin

and by averaging over spin the cms anisotropy (1 + b cos² θcm) relative to fission axis.

Calculate n-spectra taking into account anisotropy b and compare to experiment

2008 Kaz 12