A new measurement of the neutron-<sup>3</sup>He incoherent scattering length

Prepared by F. Wietfeldt, Tulane University, for the DNP webpage

Scientists from Tulane University, the National Institute of Standards and Techology (NIST), and the University of North Carolina, Wilmington recently completed a precision measurement of the incoherent neutron scattering length of helium-3 using the NIST Interferometry and Optics Facility at the NIST Center for Neutron Research. The incoherent scattering length is a measure of the spin-dependence of the low-energy interaction potential between a free neutron and a helium-3 atom, a rare isotope of helium whose nucleus contains two protons and one neutron. This quantity is important for testing theories that describe the strong-force potential between neutrons and protons, and for interpreting neutron scattering measurements of quantum excitations in liquid helium.


A schematic representation of the experiment (not to scale). The dashed lines indicate the neutron wave paths. The interference signal was measured by a helium-3 proportional counter marked C3.

The experiment used a neutron interferometer, a device that splits and separates the matter wave of a single neutron using Bragg diffraction in a single silicon crystal. The two wave paths are then combined to produce an interference signal, analogous to a diffraction pattern of light waves. The phase of this interference signal gives a direct measurement of the phase shift of the neutron wave caused by its interaction with the target.


Typical interference signals for the two neutron flip states. The incoherent neutron scattering length of the target is proportional to the phase difference between these.

In this case the target is polarized helium-3 gas. The neutron beam is also polarized. The incoherent scattering length is proportional to the change in the neutron phase shift as the neutron polarization direction is flipped from parallel to antiparallel relative to the target polarization. Due to the physical and environmental constraints of the interferometer setup, the helium-3 targets were polarized remotely using spin-exchange optical pumping, a method where a rubidium vapor is optically pumped using polarized laser light, and the resulting spin polarization is transferred from rubidium to helium-3 via atomic collisions. Each target was contained in a small cell, 42 mm in length, made of boron-free glass to reduce neutron absorption. The gas pressure in the cell was 1.8 bar, a compromise between the needs for high density to maximize the phase shift and low density to limit neutron loss in the strongly absorbing helium-3. The spin relaxation time of the targets were long (up to 115 hours) so that they could be transported to the interferometer and remain polarized in a weak magnetic field for measurements that lasted several days. This was the first successful use of a polarized target in a neutron interferometer.


A summary of the triplet (a1) and singlet (a0) neutron scattering lengths of helium-3. The three blue bands are coherent scattering length measurements using unpolarized helium-3. The green bands, including this work, are measurements of the incoherent scattering length. The theoretical point shown is from Reference [1].

This result was published in a recent issue of Physical Review Letters [2]. It is in good agreement with the latest theory, represented by a recent theoretical calculation using the Argonne AV18 + Urbana 9 potential model, but it disagrees with a previous experimental measurement that used a very different method, pseudomagnetic spin rotation.

Work supported by the National Science Foundation and the National Institute of Standards and Technology (U.S. Dept. of Commerce), Principal Investigator: Fred Wietfeldt, Tulane University


[1] H.M. Hofmann and G.M. Hale, Phys. Rev. C 68, 021002 (2003).
[2] M.G. Huber, M. Arif, T.C. Black, W.C. Chen, T.R. Gentile, D.S. Hussey, D. A. Pushin, F.E. Wietfeldt, and L. Yang, Phys. Rev. Lett. 102, 200401 (2009).