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Precision measurement of the neutron scattering length

interferometer setup to measure scattering The neutron interferometer is able to directly measure the neutron index of refraction, n, of solids, liquids or gases. Since the coherent scattering length b is the only variable parameter in the calculation of n we usually just refer to b. This is also because the same b is important in scattering problems which do not involve n. When a uniform slab or volume of material (the sample) is placed in the beam on either path I or path II the neutrons experience a phase shift given by:

Deltaphi = 2pi(n - 1)D/lambda   ,

where D is the effective slab thickness relative to the beam and lambda is the neutron deBroglie wavelength (between 0.2 nm and 0.5 nm). Although n differs from unity by 1 part in 106 the phase shift, Delta phi~20,000°, can be measured with a relative standard uncertainty of about 0.001 %. However, this low uncertainty can be offset by systematic uncertainties such as the placement of the sample in the interferometer. To avoid these problems the NIOF uses a method first introduced by Ioffe and Vrana [Phys. Lett. A231, 319 (1997)]. This method is based on a rather simple idea. Following along with fig. 1, one first places the sample in position 1 to measure the phase shift Delta phi1. The sample is then parallel transported (indicated by the yellow arrow in fig. 1) to position 2 where the phase shift, Delta phi2, is measured. Then the sample is rotated to some angle script epsilon and this sequence is repeated again. Each time we take the difference of the phase shifts, Theta = Delta phi1 - Delta phi2, for each angle script epsilon of the sample. This is plotted in fig. 2a. In fig. 2a we see that the difference of the phase shifts, Theta, is a parabola which has a minimum for the angle at which the slab is perfectly aligned in both beams. Moreover it can be shown that the difference phase shift, Theta(script epsilon0), measured at the minimum of this parabola, is insensitive to systematic alignment uncertainties to a relative uncertainty of 0.0005 % for solid samples a few millimeters thick. If a similar operation is performed on the tilt of the sample, labeled gamma in fig. 2b, one sees that again a symmetric difference in the phase shifts allow the sample tilt to be perfectly aligned (see fig. 2b). Usually the main uncertainties arise from the incomplete knowledge of the sample composition, the non-uniformity in the sample density and non-parallel surfaces of the sample. The last two uncertainties are systematic uncertainties which can't be corrected for, and therefore, limit this method to a relative standard uncertainty of > 0.005 %.

2a. Sample rotation and 2b. Sample tilt

Fig. 2. Phase shift difference parabolas used to determine the sample alignment.

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  Online: November 1998