Rapid calculation of X-ray absorption correction factors for spheres to an accuracy of 0.05%

X-ray absorption factors A* for spherical samples were calculated in the range of the product of sphere radius R and linear absorption coefficient μ of 0 ≤ μR ≤ 2.5 and in the range of Bragg angle θ of 0° ≤ θ ≤ 90°. A new method that requires numerical integration over only one variable using high-accuracy values of A* recently calculated for cylinders was developed. A table of values of A* was tabulated. A full-range, curve-fitting procedure that is accurate to 0.05% also was developed for routine calculation of A*.