Neutron Interferometry and Optics Facility for Precision Scattering Length D.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 Neutron = 0.2 nm, E = 20 meV, v = 2000 m/s The rule of two’s

Optical Potential

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 TechniqueAccuracy Gravity Reflectometry0.02% Prism Refraction0.03% Dynamical diffraction0.02% Interferometry0.005% Transmission0.1% Christiansen Filter0.1% Mirror Reflection1% Bragg Reflection1%

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 – 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 function coherently split by Bragg diffraction. 3 He detectors  Phase Shifter  H-beam O-beam path 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 Outgoing wave front Incident wave front opt V  Sample nn D Re{  } 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.

The phase shifter is rotated by an amount  and neutrons are counted in the two 3 He detectors. Phase Shift Measurement

The phase shifter is rotated by an amount  and neutrons are counted in the two 3 He detectors. Relative optical path length between path I and path II is a function of the phase shifter angle . Phase Shift Measurement

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

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

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: –D eff = 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.

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.

Tilt Alignment Tilt scan of the quartz alignment flag.

- Wavelength measurement Measured with Si crystal Si lattice constant known with uncertainty much lower than 0.001%

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. –N virial = 2 N ideal / (1 + B P P + C P P ) 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.

Hydrogen Measurements in Time

Table 2. x denotes the mole fraction of each element i in the gas. Assuming that b D  b gas then we get where y denotes the uncertainty in the mole fraction x. Future Experiment  - depends on signal to noise ratio i.e. more gas or more neutrons (currently uncertainty is 2  ). –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  ) can be improved by factor of 100 with piston measurement –Temperature (currently 2  ) 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 5  level or below are possible D – Increasing cell path length by 5 cm to 10 cm. –decreases the relative uncertainty (currently 1  ) by the same amount.