Abstract:
The connection between the homogeneous and inhomogeneous equations for the Coulomb
scattering wave function of two particles is investigated. It is shown that the form of
the equation depends on the method used to regularize the divergent integrals in the
homogeneous part of the equation. This result is a generalization of the result obtained
by Van Iiaeringen for orbital angular momentum $l=0$. It is also shown to be helpful
to introduce a Coulomb asymptotic state in the momentum representation; this is the
inhomogeneous part of the equation and contains all the principal information about the
forward scattering of charged particles. Therefore, the Coulomb asymptotic states
can be used to find the behavior of the reaction amplitudes of charged particles near
singularities in $\cos\theta$, where $\theta$ is the scattering angle.
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