Abstract: We created software to simulate the Larmor precession in a setup for SESANS with adiabatic/radio frequency flippers in magnets designed to measure the time-of-flight on pulsed or stationary neutron sources. The values and spatial configurations of the magnetic fields of the existing prototype magnets we used as input data. For an empty setup, we calculate the polarization of a “divergent ribbon beam” 2 cm high, depending on the neutron wavelength λ. In the “scattering experiment”, we show how to convert λ to the “spin-echo length” δ. For λ = 10 Å, flippers at a distance of 140 cm and a radio frequency 1 MHz we find δ ≈ 10 μm. Extension to δ = 20 μm is realistic.

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This paper reports on the two-scale fractal structure of chromatin organization in the nucleus of the HeLa cell. Two neutron scattering methods, small-angle neutron scattering (SANS) and spin-echo SANS, are used to unambiguously identify the large-scale structure as being a logarithmic fractal with the correlation function (r) - ln(r/E). The smaller-scale structural level is shown to be a volume fractal with dimension DF = 2.41. By definition, the volume fractal is self-similar at different scales, while the logarithmic fractal is hierarchically changed upon scaling. As a result, the logarithmic fractal is more compact than the volume fractal but still has a rather high surface area, which provides accessibility at all length scales. Apparently such bi-fractal chromatin organization is the result of an evolutionary process of optimizing the compactness and accessibility of gene packing. As they are in a water solution, the HeLa nuclei tend to agglomerate over time. The large-scale logarithmic fractal structure of chromatin provides the HeLa nucleus with the possibility of penetrating deeply into the adjacent nucleus during the agglomeration process. The interpenetration phenomenon of the HeLa nuclei shows that the chromatin-free space of one nucleus is not negligible but is as large as the volume occupied by chromatin itself. It is speculated that it is the logarithmic fractal architecture of chromatin that provides a comfortable compartment for this most important function of the cell.

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Larmor precession has been used in the past in neutron spin-echo and neutron depolarisation. In the last decade, interest has been revived in the inclined front and end faces of the precession regions combined with the neutron-resonance spin-echo (NRSE) technique. Various techniques based on these inclined faces have been developed, such as spin-echo, small-angle neutron scattering (SESANS), off-specular neutron reflectometry using SESANS and high-resolution diffraction using Larmor precession. An overview will be given of the various state-of-the-art techniques.

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The use of π-flippers for correction of line integrals in Larmor-precession devices is described. The π-flippers consist of magnetised foils of the proper thickness, magnetised by the field of the precession device itself. Application of such π-flippers in a spin-echo small angle neutron scattering set-up with fields perpendicular and parallel to the beam direction is discussed. It appears that such flippers avoid corrections for the inhomogeneity of the field-line integrals, for the main part, in both options.

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Spin-echo small-angle neutron scattering of dilute dispersions of mono-disperse polystyrene spheres is measured. The spheres have radii of 60 and 100 nm. The measurements agree well in shape and absolute intensity with calculations. Multiple scattering is significant in these experiments and is easily taken into account. This is the first time that quantitative analysis of real-space small-angle neutron scattering is possible. The calculations show that this technique will have most applications in systems with strong scattering, which usually implies larger length scales.@en