Spin-echo small-angle scattering (SESANS) technique is a method to measure the structure of materials from nano- to micrmeter length scales. This method could be important for studying the packaging of DNA in the eukaryotic cell. We measured the SESANS function from chicken erythrocyte nuclei which is well fitted by the exponential function G(z) = exp(-z/ξ), where ξ is the correlation length of a nucleus (in experimental data ξ = 3, 3 μm). The exponential decay of G(z) corresponds to the logarithmic pair correlation function γ(r) = ln(ξ/r). As the sensitivity of the SESANS signal depends on the neutron wavelength, we propose the SESANS setup with the changeable wavelength in the range from 2 to 12 Å. Such option allows one to study in great detail the internal structure of the biological cell in the length scale from 10-2 μm to 10 μm.@en

Small-angle neutron scattering (SANS) on nuclei of chicken erythrocytes demonstrates the cubic dependence of the scattering intensity Q−3 in the range of momentum transfer Q∈10−3–10−2nm−1. Independent spin-echo SANS measurements give the spin-echo function, which is well described by the exponential law in a range of sizes (3×102)–(3×104) nm. Both experimental dependences reflect the nature of the structural organization of chromatin in the nucleus of a living cell, which corresponds to the correlation function γ(r)=ln(ξ/r) for r<ξ, where ξ=(3.69±0.07)×103 nm, the size of the nucleus. It has the specific scaling property of the logarithmic fractal γ(r/a)=γ(r)+ln(a), i.e., the scaling down by a gives an additive constant to the correlation function, which distinguishes it from the mass fractal, which is characterized by multiplicative constant.@en