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$nα$ Elastic Scattering: An Application of Variable Phase Approach to Local Potential

Anil Khachi

Abstract

Distance-dependent phase shifts, amplitude functions, and radial wave functions for neutron-alpha elastic scattering are studied using the Variable Phase Approach. The microscopic KKNN potential is employed to calculate scattering properties for the $S_{1/2}$, $P_{3/2}$, and $P_{1/2}$ partial waves over a range of laboratory energies. The variable phase equations are solved numerically using a fifth-order Runge-Kutta method, allowing a direct examination of how the nuclear interaction generates the scattering phase within the finite interaction region. The results exhibit physically consistent behavior of the phase shifts and yield well-behaved amplitude and wave functions. This study demonstrates that the Variable Phase Approach provides a physically transparent and reliable framework for describing neutron-alpha elastic scattering and for applications in inverse scattering problems.

$nα$ Elastic Scattering: An Application of Variable Phase Approach to Local Potential

Abstract

Distance-dependent phase shifts, amplitude functions, and radial wave functions for neutron-alpha elastic scattering are studied using the Variable Phase Approach. The microscopic KKNN potential is employed to calculate scattering properties for the , , and partial waves over a range of laboratory energies. The variable phase equations are solved numerically using a fifth-order Runge-Kutta method, allowing a direct examination of how the nuclear interaction generates the scattering phase within the finite interaction region. The results exhibit physically consistent behavior of the phase shifts and yield well-behaved amplitude and wave functions. This study demonstrates that the Variable Phase Approach provides a physically transparent and reliable framework for describing neutron-alpha elastic scattering and for applications in inverse scattering problems.

Paper Structure

This paper contains 6 sections, 11 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Interaction Potential
  4. Variable Phase Approach
  5. Results and Discussion
  6. Conclusion

Figures (2)

  • Figure 1: Scattering phase shifts as a function of laboratory energy for the $S_{1/2}$, $P_{1/2}$, and $P_{3/2}$ partial waves of neutron--alpha elastic scattering, obtained using the Variable Phase Approach with the KKNN potential. The corresponding effective interaction potentials for each channel are also shown. The differences between the partial waves reflect the roles of the central interaction, centrifugal barrier, and spin-orbit coupling in the n-$\alpha$ system.
  • Figure 2: Radial dependence of scattering quantities for neutron--alpha elastic scattering at laboratory energies $E_{\text{lab}} = 1$, 5, and 10 MeV. Top panels: distance-dependent phase shifts $\delta_\ell(r)$ showing the gradual buildup of the scattering phase within the interaction region and its saturation at large distances. Middle panels: corresponding amplitude functions $A_\ell(r)$, which remain finite and smooth over the entire radial domain. Bottom panels: reconstructed radial wave functions $u_\ell(r)$ exhibiting the expected nodal structure and asymptotic scattering behavior for each partial wave.