Neutron Interferometry and Optics Facility for Precision

Scattering LengthD.L. Jacobson, M. Arif, P. Huffman

K. Schoen, S.A. Werner, T. Black

W.M. Snow

Introduction to Neutron Optics

• Neutron optical methods

• Energies for Thermal Neutrons are typically 5 meV – 80 meV

• Energies for Cold Neutrons are typically 0.5 meV - 20meV

The Neutrongum -2410 (13)1.67492716)55(80086649157.1

sec)9.1(7.46min14sec)9.1(7.886

gausseVBN123 10(16)6.0307739410)26(04187564.1)5(9130427.1

]/[],[],Å[],[ -1 smvTHzfkmeVE

22

2 (41)v5.22703710(32)4.13566727 5(43)81.8042012

)11(0721246252 fk.E

(44)3956.03398

v

= 0.2 nm, E = 20 meV, v = 2000 m/s

The rule of two’s

Optical Potential

.4221 222

mmmmmm

ir

iNbN

innn

Information Gained

• The coherent scattering length, b, may be determined from accurate measurement of– Index of refraction along with– Density– Composition

• Separate measurement of scattering cross section allows determination of the spin dependent scattering lengths

Neutron Optical Methods

Technique Accuracy

Gravity Reflectometry 0.02%

Prism Refraction 0.03%

Dynamical diffraction 0.02%

Interferometry 0.005%

Transmission 0.1%

Christiansen Filter 0.1%

Mirror Reflection 1%

Bragg Reflection 1%

Neutron Interferometry

• 1964 – Perfect crystal interferometer co-invented by Bonse and Hart for x-rays

• 1974 – First demonstration of a working neutron interferometer Helmut Rauch, Wolfgang Treimer and Ulric Bonse.

• 1975 – Gravitationally induced quantum interferference by Collela, Overhauser and Werner

Versatility of Interferometry Method

• Can make accurate measurements for– solids– liquids– gases

• Small quantities of constituents required

• Accuracy is comparable to and in principle better than all other methods

Interferometer

Neutron

Beam

Sample

Phase Shifter

Detectors

H-beam

O-beam

Sample

Top View

Neutron wave functioncoherently split byBragg diffraction.

3Hedetectors

Phase Shifter

H-beam

O-beampath I

path II

Perfect Crystal Interferometer

• Cut from a single ingot of > 17 MW silicon.• Three to four blades are machined and

left attached to a common silicon base to maintain the perfect registry of all atoms in the crystal.

• The NIST crystals are cut such that the SI (111) lattice planes are are perpendicular to the surfaces of the blades.

• Each crystal blade acts as a beam splitter in the transmission Laue-Bragg reflection geometry.

10 cm

n

D

Phase Shift Outgoingwave front

Incidentwave front

optV

Sample

n

D

Re{

}R

e{

}

path I

path II

• Phase shifts are measured by rotating a quartz phase flag tracing out the interferogram shown below. The data is fitted to a sinusoid allowing the phase difference between when the gas cell is in the interferometer and when it is removed to be determined. This is done back to back within a 40 minute period to allow the systematic overall time dependent phase drift to be removed.

-3 -2 -1 0 1 2 30

100

200

300

400

500

600

700

800 cell out cell in + D2 gas

(deg)

-6.28 -3.14 0.00 3.14 6.28

(rad)

• The phase shifter is rotated by an amount and neutrons are counted in the two 3He detectors.

Phase Shift Measurement

• The phase shifter is rotated by an amount and neutrons are counted in the two 3He detectors.

• Relative optical path length between path I and path II is a function of the phase shifter angle .

Phase Shift Measurement

CONSTANTNb

B

B22

2

sincos

sinsin2

• The phase shifter is rotated by an amount and neutrons are counted in the two 3He detectors.

• Relative optical path length between path I and path II is a function of the phase shifter angle .

• Data is fitted to this function allowing the initial phase shift to be deterimined.

Phase Shift Measurement

CONSTANTNb

B

B22

2

sincos

sinsin2

iBAI cos

• The phase shifter is rotated by an amount and neutrons are counted in the two 3He detectors.

• Relative optical path length between path I and path II is a function of the phase shifter angle .

• Data is fitted to this function allowing the initial phase shift to be deterimined.

• A sample placed in path I induces a phase shift sample.

Phase Shift Measurement

CONSTANTNb

B

B22

2

sincos

sinsin2

sampleiBAI cos

iBAI cos

Cell Design• Cell machined with the NIST high speed milling

machine.

• Cell dimensions measured by John Stoup Precision Engineering Division (821)using the NIST Coordinate Measuring Machine:

– Deff = 1.067(1) cm

• Finite element analysis of cell deformation at 13 bar of of filling pressure calculated by Christopher Brocker (NIST CNR)

– Distortion < 1 mm

• Picture of the assembled gas cell shown with a scale for size comparison.

-10 -5 0 5 100.1

0.2

0.3

0.4

0.5

0.6

Vertical Position (mm)-4 -2 0 2 4

0.48

0.50

0.52

0.54

0.56

0.58

0.60

Horizontal Position (mm)

Cell Alignment

• The cell was designed to have nearly zero phase shift. This presented a problem in aligning the cell, which was solved by aligning a separate quartz plate (see the figure below) that was kinematically mounted on the same holder as the gas cell. The alignment parabolas are shown below. This cell design allows 1° of misalignment for a 0.01% relative uncertainty. Actual alignment was 1 to 2 orders of magnitude better.

Rotation Alignment

• Rotational scan of the quartz alignment flag.

-10 -5 0 5 10

-2

0

2

4

6

(deg)

Tilt Alignment

• Tilt scan of the quartz alignment flag.

-10 -5 0 5 10-3

-2

-1

0

(deg)

- Wavelength measurement

• Measured with Si crystal• Si lattice constant known with

uncertainty much lower than 0.001%

-6 -4 -2 0 2 4 6

25.62

25.64

25.66

25.68

25.70

25.72

25.74

Analyzer Tilt (deg)

-27 -26 -25 25 26 27

400

600

800

1000

1200

1400

1600

anti-parallel parallel

2B

(deg)

Typical 2B scans from which thewavelength was determined

Optimization parabola of the 2B scans.The minumum indicates the correct tiltsetting of the analyzer crystal.

N - Atom Density• Combined pressure and temperature measurements were made during the

experiment. Using the virial equation the atom density was determined for each measurement of the phase shift due to the gas.

– Nvirial = 2 Nideal / (1 + BP P + CP P2 + ...)

• The data shows the presence of a small leak that occurred internally between the pressurized gas cell and the vacuum cell. The final phase shift data was corrected point by point for this leak and so this effect could only introduce a systematic error less than 0.005%. Well below the uncertainty target of 0.02%.

• The composition of the gas was analyzed using Raman spectroscopy to determine the concentration of the only significant contaminant HD. The HD concentration was determined to be 0.301(12) %.

Composition

• Raman spectroscopy– Sensitive to HD content

• Mass spectroscopy– Sensitive to all masses– New system for which the

ionization efficiencies were not well known

Results and Conclusions

• The value reported here for the scattering length measurement for hydrogen and deuterium represents a complete account of all the systematic and statistical effects that were taken into account to arrive at the value listed here. These values compare quite well with the weighted averages of all previous measurements. The measurement of the deuterium scattering length falls within one standard deviation of this weighted average. The value of the hydrogen scattering length is within 3.5 sigma of the weighted average. The discrepancy with hydrogen may well be due to improper accounting of systematic uncertainties in previous measurements that will become apparent with more detailed statistical analysis not completed at this time.

Deuterium Measurements in Time

• Measurements of the scattering length of hydrogen and deuterium through out time. Weighted average does not include the NIST result and is shown for the sake of comparison with the previous values.

1950 1960 1970 1980 1990 2000

6.4

6.5

6.6

6.7

6.8

Year of Measurement

Many Methods Bragg Diffraction Christiansen filter

Gravity reflectometry Total reflection Interferometry Transmission

Previous weighted average Current weighted average

Hydrogen Measurements in Time

Future Experiment - depends on signal to noise ratio i.e. more gas or more

neutrons (currently uncertainty is 210-4).– More gas improves signal and noise remains the same

(improvements of by 5 or 10 are possible)• Increasing the pressure P

• Increasing the wavelength • Increasing the path length D

– More neutrons requires facilities with a broader phase space acceptance (improvements by factor of 10 possible)

Future Experiment• N – Depends on P and T measurement and

composition– Pressure (currently 1 10-4) can be improved by factor of

100 with piston measurement– Temperature (currently 2 10-4) can be improved by factor

of 50 with better absolute resistance measurements.– Composition measurements can be improved to reduce

uncertainty in HD concentrations using Raman spectroscopy.

- Measurements of 510-5 level or below are possible

• D – Increasing cell path length by 5 cm to 10 cm.– decreases the relative uncertainty (currently 1 10-4) by the

same amount.