Measurements of the Thermal Neutron

Scattering Kernel

Li (Emily) Liu, Yaron Danon, Bjorn Becker, Devin P. Barry, Xin Li, Bin Wu

MANE, Rensselaer Polytechnic Institute

Alexander Kolesnikov

Oak Ridge National Lab/Spallation Neutron Source

Symposium on Nuclear Data for Criticality Safety and Reactor Applications, April 27, 2011.

2

Motivation and objectives

Approach-SEQUOIA

Present study

Results and discussions

Problems and Future study

Questions

3 M. Mattes and J. Keinert, Thermal Neutron Scattering Data for the Moderator Materials H2O, D2O and ZrHx in ENDF-6

Format and as ACE Library for MCNP(X) Codes, IAEA INDC(NDS)-0470, 2005.

IKE vs. ENDF/B-VI

Experimental Validation

4

The latest experimental data used was from 1973-1974!

M. Mattes and J. Keinert, Thermal Neutron Scattering Data for the Moderator Materials H2O, D2O and ZrHx in ENDF-6

Format and as ACE Library for MCNP(X) Codes, IAEA INDC(NDS)-0470, 2005.

Bischoff, F., et al., “Low Energy Neutron Inelastic

Scattering”, RPI-328-87, 1967.

The world’s most powerful neutron source, the $1.4 billion Spallation Neutron Source

At 1.4MW, SNS produces neutron flux ~8 times higher than ISIS, previous the

highest flux spallation neutron source in the world. SNS will feature 24 beamlines

for physics, chemistry, biology, materials research. www.sns.gov

Production of Neutrons for Materials

Research

• Reactors reaching a flux level limited by heat dissipation

• Pulsed source flux level not limited of heat dissipation, but pending further development of accelerator and target/moderator technology

• High peak flux and the time structure are advantageous to many applications

• Coproduction of epithermal, thermal and cold neutrons

SNS Instrument Beam Lines

8

1st

experiment proposed 2nd

experiment

SEQUOIA Fine-Resolution Fermi Chopper Spectrometer

Atomic-scale dynamics at thermal and epithermal energies – translations, rotations,

and vibrations.

EI = 10 to 2000 meV, 900 3He detector tubes,wide temperature/pressure capabilities

Horizontal -30 to -3 and 3 to 60, Vertical -30 to -3 and 3 to 30

Flux: > 1×105 neutrons/cm2s

E/EI ~ 1%

SEQUOIA spectrometer

Direct Geometry ToF

Fix the incident energy EI and use time of flight to determine the final energy EF

Detectors Moderator

Monochromating

chopper LC

LI

LF Sample

Phase time

at chopper

Flight time

at sample

Final flight

time

Energy transfer

E = EI - EF

18 m

2 m

5.5 m

F

FIF

E

LTTT 2284

I

II

E

LT 2284

I

CC

E

LT 2284

[msec]

[m]

[meV]

Ef kf

Sample

Ei ki

momentum = hk energy = (hk)2/(2m)

k=2p/l

Q = ki - kf

hw = Ei - Ef

Measure the number of scattered neutrons

as a function of Q and w

depends ONLY on the sample

Scattering Geometry

14

2 2Q / 2mkT

/ kT

S , kTS Q,

w

w

Transformation from S(Q,w) to S(α,).

where kT is the temperature in eV.

d2H

ddw 2N

H

4p

k f

kiSH(Q,w)

Experiment Measures Double Differential Cross Section

=> Dynamic Structure Factor S(Q,w)

(the Van Hove scattering function for quasi-elastic and inelastic

scattering)

Elastic

16

Inelastic Scattering from molecular vibrations

If atoms oscillate around fixed positions:

-intermediate scattering function I(q,t) has

oscillating component;

-the dynamic structure factor S(q,w) has an

inelastic component shifted in energy E=ħw. Also

significant elastic component is present.

Quasi-elastic Scattering from translation, rotation and conformation-jump motions

If atoms change their position:

-I(q,t) decays with a rate that is inversely

proportional to characteristic relaxation time of the

motion t;

-S(q,w) has quasielastic component (broadening of

the elastic line) with the width inversely proportional

to t. Depending on type of motion, elastic component

can be present.

)],([),( tQIFTQS w

17

Summary of the 1st SEQUOIA experiment (~ 4 days)

EI (eV) H2O PE Empty Can Vanadium

0.055 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs

0.16 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs

0.25 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs

0.6 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs

1 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs

3 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs

5 ~ 2 hrs ~ 2 hrs ~2-3 hrs ~2 hrs

Sample sizes: The vanadium sample is 50x50x2.12 mm3 size in the neutron beam. The

actual samples of H2O and PE were 0.1 mm thick samples, which means 50x 50x 0.1 mm3

in the neutron beam.

Temperature: Room – 27 oC.

Scattered angles : 5, 10, 15, 20, 35, 40, 45, 50, and 55 degrees.

Data Reduction

18

Vanadium White

CanEmpty from Counts - Sample from Counts

Counts vs. scattered energy is normalized

through vanadium file to double differential cross

section vs. scattered energy.

19 Esch et al., The Temperature Dependence of Neutron Inelastic Scattering

from Water, Nuclear Science and Engineering: 46, 223-235, 1971.

Ei=160 meV

20 Esch et al., The Temperature Dependence of Neutron

Inelastic Scattering from Water, Nuclear Science and

Engineering: 46, 223-235, 1971.

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 7500.01

0.1

1

10

100

S(Q

,w)

(ba

rn/s

r e

V)

Ef (meV)

40o

25o

14o

10o

Ei=600 meV

Etrans=40~130 meV: intermolecular librational vibrations of water

Etrans=200 meV: intramolecular H-O-H bending vibrations

Etrans=400~450 meV: intramolecular stretching O-H modes (symmetric and asymmetric)

0 50 100 150 200 250 300

1x104

2x104

3x104

4x104

5x104

6x104

7x104

8x104

d

dX

S [

co

un

ts]

E' [meV]

Exp. V (25 deg., 160 meV)

MCNP V (25 deg., 160 meV, normalized to Exp)

0 50 100 150 200 250 300

100

101

102

103

104

105

106

dd

XS

[co

un

ts]

E' [meV]

Exp. V (25 deg., 160 meV)

MCNP V (25 deg., 160 meV, normalized to Exp)

Vanadium

Discussions-H2O

0 20 40 60 80 100 120 140 160 180 200 220

2

10

100

1000

3000

dd

XS

[b

/sr/

eV

]

E' [meV]

Exp. (10 deg., 160 meV)

Exp. (old RPI, 10 deg., 154 meV)

ENDF/B VII (10 deg., 160 meV, E/E

i ~2.3%)

0 20 40 60 80 100 120 140 160 180 200 220

5

10

100

1000

2000

dd

XS

[b

/sr/

eV

]

E' [meV]

Exp. (15 deg., 160 meV)

Exp. (old RPI, 14 deg., 154 meV)

ENDF/B VII (15 deg., 160 meV, E/E

i ~2.3%)

0 20 40 60 80 100 120 140 160 180 200 220

5

10

100

1000

2000

dd

XS

[b

/sr/

eV

]

E' [meV]

Exp. (25 deg., 160 meV)

Exp. (old RPI, 25 deg., 154 meV)

ENDF/B VII (25 deg., 160 meV, E/E

i ~2.3%)

0 20 40 60 80 100 120 140 160 180 200 220

5

10

100

1000

dd

XS

[b

/sr/

eV

]

E' [meV]

Exp. (40 deg., 160 meV)

Exp. (old RPI, 40 deg., 154 meV)

ENDF/B VII (40 deg., 160 meV, E/E

i ~2.3%)

Discussions-H2O

0 20 40 60 80 100 120 140 160 180 200 220

5

10

100

1000

dd

XS

[b

/sr/

eV

]

E' [meV]

Exp. (40 deg., 160 meV)

ENDF/B VII (37.5 deg., 160 meV, E/E

i ~0.0%)

ENDF/B VII (40.0 deg., 160 meV, E/E

i ~2.3%)

ENDF/B VII (42.5 deg., 160 meV, E/E

i ~5.0%)

0 20 40 60 80 100 120 140 160 180 200 220

5

10

100

1000

dd

XS

[b

/sr/

eV

]

E' [meV]

Exp. (40 deg., 160 meV)

ENDF/B VII (37.5 deg., 160 meV, E/E

i ~2.3%)

ENDF/B VII (40.0 deg., 160 meV, E/E

i ~2.3%)

ENDF/B VII (42.5 deg., 160 meV, E/E

i ~2.3%)

2

4

Temperature Dependent Neutron Scattering Cross

Sections for Polyethylene

R. Hilla and C.-Y. Liu, arXiv:nucl-th/0309011v2

Discussions-PE

0 50 100 150 200 250 300 350 4000.01

0.1

1

10

100

1000

S(Q

,w)

(ba

rn/s

r e

V)

Ef (meV)

10o

40o

25o

14o

0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 7500.01

0.1

1

10

100

S(Q

,w)

(ba

rn/s

r e

V)

Ef (meV)

10o

40o

25o

14o

0 50 100 150 200 250 3000.1

1

10

100

1000

S(Q

,w)

(ba

rn/s

r e

V)

Ef (meV)

10o

40o

25o

14o

Ei=160 meV

Ei=250 meV

Ei=600 meV

Etrans=360 meV: stretching vibrations of (covalent bond) C-H modes

Etrans=170 meV: bending C-H modes

Etrans=90~130 meV: other intramolecular vibrations

26

Problems and future study

Include time-independent background and multiple-scattering corrections into data reduction.

Analyze all data of H2O and PE.

Insufficient angle coverage of SEQUOIA. We will use ARCS (the Wide Angular-Range Chopper Spectrometer) in addition to SEQUOIA.

Proper identification of the reasons associated with the discrepancies.

27

Acknowledgement

Thanks for your attention.

Questions?

28 0 50 100 150 200 250 300

0

10

20

30

40

50

60

70

80

E = 231 meV; theta = 60 deg.

dd

XS

[b

/sr/

eV

]

E' [meV]

ENDF/B VII calculation

ENDF/B VI calculation

ENDF/B VI (Mattes paper)

IKE (Mattes paper)

Bischoff et al. (Mattes paper)

0 50 100 150 200

0

10

20

30

40

50

60

70

80

90

100

110

E = 154 meV; theta = 60 deg.

dd

XS

[b

/sr/

eV

]

E' [meV]

ENDF/B VII calculation

ENDF/B VI calculation

ENDF/B VI (Mattes paper)

IKE (Mattes paper)

Bischoff et al. (Mattes paper)