Comment on “Exact three-dimensional wave function and the on-shell<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:math>matrix for the sharply cut-off Coulomb potential: Failure of the standard renormalization factor”

Kouzakov, Konstantin; Popov, Yuri V.; Shablov, V. L.

doi:10.1103/physrevc.81.019801

Cited by 4 publications

(3 citation statements)

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“…To the best of our knowledge this formula has been derived here for the first time. The representation for the scattering amplitude obtained in the recent paper [16] was derived from the incorrect form of the wave function in the region r ≤ R [17] and cannot be considered as a contra result. The complete solution for the scattering problem for the potential V R is given in this paper for the first time.…”

Section: Discussionmentioning

confidence: 99%

“…However, the derivations made in [16] have been performed only for a particular value of the coordinate r = 0. It was not proven that the solution obtained in [16] is valid for all values of r. In the comment [17] it was shown by direct calculations that the three-dimensional result of [16] is erroneous. A further discussion of the results of [16] and their relation to the results of [12] can be found in [18].…”

Section: Definition Of the Problemmentioning

confidence: 99%

“…Consider an infinitely differentiable test function f (u) ∈ C ∞ (−1, 1). By multiplying both sides of (17) with f (u) and integrating over u, we obtain…”

Section: The Scattering Problem For the Potential V Rmentioning

confidence: 99%

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The impact of sharp screening on the Coulomb scattering problem in three dimensions

Yakovlev

Volkov

Yarevsky

et al. 2010

J. Phys. A: Math. Theor.

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The scattering problem for two particles interacting via the Coulomb potential is examined for the case where the potential has a sharp cut-off at some distance. The problem is solved for two complementary situations, firstly, when the interior part of the Coulomb potential is left in the Hamiltonian and, secondly, when the long-range tail is considered as the potential. The partial wave results are summed up to obtain the wavefunction in three dimensions. It is shown that in the domains where the wavefunction is expected to be proportional to the known solutions, the proportionality is given by an operator acting on the angular part of the wavefunction. The explicit representation for this operator is obtained in the basis of Legendre polynomials. We proposed a driven Schrödinger equation including an inhomogeneous term of the finite range with purely outgoing asymptotics for its solution in the case of the three-dimensional scattering problem with long-range potentials.

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Section: Discussionmentioning

confidence: 99%