Abstract
We studied the Coulombic transformation of potential in momentum space. The Coulombic transformation is defined as a unitary transformation in momentum space, which is equivalent of the Coulomb–Fourier transformation in coordinate space. The analytic continuation scheme avoids the difficulty which is occurred from the singularity of the Coulomb wave function in momentum space. We adopted the point method to perform the analytic continuation. The validity of the new scheme is checked by comparing with the analytic solution for the Malfliet-Tjon potential. Numerical calculation of the integration was done by separating into four intervals. We demonstrate the high accuracy of our calculation.
Highlights
In a few-body system consisting of pair charged particles Coulomb problem arises in momentum space because the diagonal components of the potential become singularities
Alt et al [1] gave the analytic expressions of Coulomb–Fourier transformation (CF) transformation for the Yukawa and Gaussian type potentials in coordinate space
By comparing with the analytic solution [1], we look into the accuracy of our numerical results
Summary
In a few-body system consisting of pair charged particles Coulomb problem arises in momentum space because the diagonal components of the potential become singularities. Coulomb–Fourier transformation (CF) is known as a prescription for the Coulomb problem. In a two-charged particle system, it is a unitary transformation which eliminates Coulomb potential from the original Hamitonian H into the transformed Hamiltonian H in the Coulombic momentum space. Alt et al [1] gave the analytic expressions of CF transformation for the Yukawa and Gaussian type potentials in coordinate space. The purpose of our study is here to demonstrate the accuracy of the numerical calculation of V(k , k) by mean of comparison with the analytic exact number [1]. Our numerical results will be shown in Sect.
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