Multiple Scattering of X-Rays and Neutrons. I. A Recurrence Formula for the Taylor Series Expansion in the Calculation of Intensities

Abstract

This work reports on calculations of the deformation energy of a nucleus for nonlinear deformations. The working hypothesis is that, beyond the usual linear approximation, the nonlinear analysis yields soliton solutions moving on its surface. The potential barrier against the emission of a soliton is calculated within the macroscopic-microscopic method. The outer turning point of the barrier determines limitations on the geometrical and kinematical parameters for the formation of a surface soliton. For large asymmetry, the two-centre shell model is used to assign a structure to the soliton. Calculations for 248 No with the emission of a 40 Ca soliton are reported; likewise for 224 Th with the emission of 16 O. Except for necked shapes at the very first stages of soliton formation, the greatest portion of the deformation path displays rather compact configurations with large neck radii. These shape sequences correspond to allowable soliton velocities. Close to and just beyond the touching point configuration, where the shape becomes concave, the width and the velocity of the soliton approaches zero. The calculations suggest that the emission of a 40 Ca structure is quite probable due to a low potential barrier, whereas the emission of an 16 O-type soliton is rather unlikely due to the higher penetration barrier.

Approximate intensity solutions for the multiple diffraction of neutrons in a many-beam case

“…Moon & Shulrs differential equations, describing the change in power in the several beams traversing a layer of thickness dx at depth x below the surface of a crystal plate, can be written in the following concise form (Parente & Caticha-Ellis, 1974a):…”

“…In this work, approximate intensity solutions appropriate for a many-beam case are derived. The recurrence formula (Parente & Caticha-Ellis, 1974a) was employed in the derivations in order to allow intensity calculations when high absorption and high secondary extinction are present. MULTI, a computer program for the simulation of m.d.…”

Intensity ofN-beam X-ray diffraction: kinematical theory for a small crystal

“…Coppens (1968). After the strict solutions had been given for a few special cases at n = 2, 3, 4, 6 (Zachariasen, 1965), the formal solution of the equations for unlimited n was derived by Parente & Caticha-Ellis (1974) in the infinite order of the series expansion, and then applied in practice .…”

High-resolution synchrotron radiation Renninger scan to examine hybrid reflections in InGaP/GaAs(001)

“…Furthermore, with regard to the position and intensity of the RS peaks, two programs have been developed and successfully tested: (i) MULTX, by Salles da Costa et al (1992), which uses the theory of X-ray MD for mosaic crystals and the multiply diffracted intensities are calculated step by step as a function of the 9 angle. The program is based on the iterative method of Parente & Caticha-Ellis (1974) that uses the general term of the Taylor series, and allows for many-beam interactions to be simultaneously considered. MULTX has been implemented to simulate synchrotron radiation RS (Sasaki et al, 1996b) accounting for the ' polarization of the synchrotron radiation beam (perpendicular to the primary incidence plane) as well as the diffracted-beam path length for thin epilayered materials.…”