Article

# Quantum mechanical inverse scattering problem at fixed energy: a constructive method

11/2011; DOI: 10.4310/MAA.2011.v18.n1.a6

Source: arXiv

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**ABSTRACT:**In order to learn more about the precision of the inversion by the Cox–Thompson method, we investigated the inversion of phase shifts of a singular potential, namely of a Coulomb potential. Using asymptotically Riccati–Bessel functions as reference functions, we could only approximately reproduce the singularity of the Coulomb potential at the origin. We also show uncertainties in the inverted potential due to different minima in the minimization solution of the nonlinear equations of the Cox–Thompson procedure. As a result, we conclude that one has to take much care with the inversion of experimental phase shifts suffering from measurement errors.Journal of Physics A Mathematical and Theoretical 05/2010; 43(22):225302. · 1.77 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The Cox–Thompson inverse scattering method at fixed energy has been generalized to treat complex phase shifts derived from experiments. New formulae for relating phase shifts to shifted angular momenta are derived. The method is applied to phase shifts of known potentials in order to test its quality and stability and, further, it is used to invert experimental n-α and n-12C phase shifts.Journal of Physics G Nuclear and Particle Physics 05/2006; 32(6):849. · 5.33 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**Solution of the Cox-Thompson inverse scattering problem at fixed energy [1,2,3] is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are free of matrix inversion operations. This simplification is a result of treating only the input phase shifts of partial waves of a given parity. Therefore, the proposed method can be applied for identical particle scattering of the bosonic type (or for certain cases of identical fermionic scattering). The new formulae are expected to be numerically more efficient than the previous ones. Based on the semi-analytic equations an approximate method is proposed for the generic inverse scattering problem, when partial waves of arbitrary parity are considered.Modern Physics Letters B 11/2011; 22(23). · 0.48 Impact Factor

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