Abstract
Solution of the radial Schrodinger equation for the Woods–Saxon potential together with spin–orbit interaction, coulomb and centrifugal terms by using usual Nikiforov–Uvarov (NU) method is not possible. Here, we have presented a new NU procedure with which we are able to solve this Schrodinger equation and any other one-dimensional ones with any shape of the potential profile. For this purpose, we have combined the NU method with numerical fitting schema. The energy eigenvalues and corresponding eigenfunctions for various values of n, l, and j quantum numbers have been obtained. Good agreement with experimental values is also achieved. We have calculated the 1/2+ state energy with more accuracy (our absolute error = 0.023 MeV and Hagen et al. absolute error = 0.0918 MeV), while Hagen et al. have calculated the 5/2+ state energy with higher accuracy (our absolute error = 0.71 MeV and Hagen et al. absolute error = 0.0337 MeV). Our wave functions are in agreement with Kim et al.’s work, too.
Highlights
In the study of the breakup of 17F into proton ? 16O, some potential model for 17F has been used previously such as Woods–Saxon potential with spin–orbit and coulomb potentials [1] and M3Y interaction model [2]
Adding the coulomb potential and solution of the Schrodinger equation by Nikiforov– Uvarov method is the main goal of the present work
To make the application of the NU method simpler and the checking of the validity of solution unnecessary, we present a shortcut for the method
Summary
In the study of the breakup of 17F into proton ? 16O, some potential model for 17F has been used previously such as Woods–Saxon potential with spin–orbit and coulomb potentials [1] and M3Y interaction model [2]. Solution of the Schrodinger equation including the above potentials has been done by the numerical methods in the above-mentioned works. Pahlavani et al have solved the Schrodinger equation including Woods–Saxon potential with spin–orbit and centrifugal terms by Nikiforov–Uvarov method [3]. They did not include the coulomb term to their calculations. D, l, and N denote, respectively, the space dimension, total angular momentum and the number of particles, l is one of particle masses, and x is the hyper-radius If we write this equation for 17F as the combination of a proton and an inert 16O core with spin 0.
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