Computation of Compton profiles in a weak laser field

A modified numerical scheme for the evaluation of Compton profiles in a weak laser field, based on an expression by Jain and Tzoar [Phys. Rev. A 18, 538 (1978)], is derived. The scheme is based on the reciprocal form factor and is computationally preferable to the original method. The scheme requires either a numerical Fourier transformation or the calculation of a one-dimensional integral, both of which are easily achieved. We focus on the numerical integration, which is readily performed with a Gauss-Chebyshev quadrature. Stable results may be obtained by avoiding numerical derivatives. Some numerical tests are performed to study the convergence properties of the old and modified methods. The modified scheme is applied to study some atomic and molecular systems. The dependence of the profile modulation on the atomic number Z throughout the periodic table is established.