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Perturbation Theory for Proton-Neutron Scattering: Perturbing the Energy

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Abstract

Using the time-independent Schrödinger equation with a velocity-dependent potential the energy dependence of the corresponding scattering phase shifts, when the energy is changed by a small amount ΔE from an arbitrary unperturbed value E 0, is studied. We expand kcot δ as a power series in ΔE and obtain analytic formulas for the effective range expansion parameters to all orders in the perturbing energy. Formulas for the corresponding wave function changes are also developed. At low energies the Bethe formula for the effective range is reproduced and an expression for the shape-dependent term is obtained. The derived formalism is relevant to fields like nuclear and atomic physics. Examples that demonstrate the effectiveness of the derived formalism are presented.

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Authors and Affiliations

  1. Department of Physics, University of Jordan, 11942, Amman, Jordan

    M. Al-Sayyed & M. I. Jaghoub

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  1. M. Al-Sayyed
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  2. M. I. Jaghoub
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Correspondence to M. I. Jaghoub.

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Al-Sayyed, M., Jaghoub, M.I. Perturbation Theory for Proton-Neutron Scattering: Perturbing the Energy. Int J Theor Phys 50, 3357–3367 (2011). https://doi.org/10.1007/s10773-011-0839-2

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  • DOI: https://doi.org/10.1007/s10773-011-0839-2

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