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

The leading asymptotic terms of small-angle slit-smeared intensities, at la rge momentum transfer h = (4 pi/lambda)sin (theta/2), are obtained from the pinhole intensities by an integral transform whose kernel is the beam-heig ht profile determined by the slits used in a Kratky camera. This profile, d irectly measurable, generally shows a trapezoidal shape characterized by Q( 0), the end point of its horizontal plateau, and Q(1), the momentum-transfe r value beyond which it vanishes. It results that any pinhole contribution, monotonically decreasing as 1/h(alpha), after being smeared, decreases as 1/h((alpha-1)) in the region h < Q(0), while the power exponent monotonical ly increases from (alpha - 1) to alpha in the outer h region. The actual ch ange explicitly depends on the slit length. On the contrary, the oscillator y damped contributions cos(h delta)/h(4) and sin(h delta)/h(4), after being smeared, remain close, whatever the slit length, to those resulting from t he smearing with an ideal slit.