The minimum norm method for the determination of the charge density from elastic electron scattering data

Abstract

Unphysical behavior in the QR algorithm based least squares determination of the expansion coefficients of the charge density obtained from limited information about the charge form factor occurs when the spread of the singular values in the matrix relating these quantities becomes too large. Setting the smallest singular values equal to zero in the singular value decomposition used in the minimum norm method yields a much more reasonable determination of the charge density. Increasing the size of the basis without increasing the range of the prior information about the charge form factor leads to ambiguities in the determination of the charge density. Numerical results in an analytic model are presented.