Direct analysis of small-angle smeared intensity tails. I. General results

The leading asymptotic terms of small-angle slit-smeared intensities, at large momentum transfer h = (4π/λ)sin (θ/2), are obtained from the pinhole intensities by an integral transform whose kernel is the beam-height profile determined by the slits used in a Kratky camera. This profile, directly measurable, generally shows a trapezoidal shape characterized by Q₀, the end point of its horizontal plateau, and Q₁, the momentum-transfer value beyond which it vanishes. It results that any pinhole contribution, monotonically decreasing as 1/h^α, after being smeared, decreases as 1/­h^(α−1) in the region h < Q₀, while the power exponent monotonically increases from (α − 1) to α in the outer h region. The actual change explicitly depends on the slit length. On the contrary, the oscillatory damped contributions cos (hδ)/h⁴ and sin (hδ)/h⁴, after being smeared, remain close, whatever the slit length, to those resulting from the smearing with an ideal slit.