Construction of an equivalent energy-dependent potential by a Taylor series expansion
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CONSTRUCTION OF AN EQUIVALENT ENERGY-DEPENDENT POTENTIAL BY A TAYLOR SERIES EXPANSION A. K. Behera,∗ B. Khirali,∗ U. Laha,∗ and J. Bhoi†
To construct a phase-equivalent energy-dependent local potential corresponding to a sum of local and nonlocal interactions, we use a simple method for expanding the wave function in a Taylor series up to the third order. We apply the constructed potentials to calculate the scattering phase shifts using the phase equation. The results for scattering in nucleon–nucleon, α–nucleon, and α–α systems agree reasonably well with the standard data.
Keywords: Coulomb–Yamaguchi potential, Taylor series expansion, phase-equivalent potentials, phase equation, nucleon–nucleon system, α–nucleon system, α–α system DOI: 10.1134/S0040577920100086
1. Introduction Our understanding of physical processes in the microscopic realm is largely based on the quantum theory of scattering. Experimental information about nucleon–nucleon, nucleon–nucleus and nucleus–nucleus systems is obtained from their scattering data. This is supplemented by the properties of bound states of these systems. In hadron–hadron scattering, the recoil of hadrons due to particle exchange can hardly be ignored, and the interaction cannot be represented by one radial variable. Therefore, such interactions are represented by nonlocal potentials V (r, r ) of two variables. A phenomenological local potential is replaced with a nonlocal potential in the subatomic region with no loss of generality. There are several phenomenological local potentials for describing these systems in the literature [1]–[23]. In this context, the phase shifts predicted by several groups have undergone minor changes although the methods used differ. The low-energy α–nucleon and α–α elastic scattering is important in the cluster model description of nuclei. Results for the α–nucleon and α–α scattering were previously reported in several publications [24]–[39]. Analysis of the phase shift involves a large number of free parameters in most cases and requires solving the Schr¨ odinger equation numerically using a high-speed computer. In [40] and [41] in the context of nucleon–nucleus scattering without an electromagnetic interaction, the Taylor expansion method was used to find the effectiveness of corrections of a higher (third) order to the scattering phase shifts. In contrast to this, we consider a simple nuclear model involving only two parameters along with the electromagnetic interaction to demonstrate the usefulness of localization of a potential that is a sum of local and nonlocal potentials by a Taylor series expansion of the wave function up to the third order. ∗
Department of Physics, National Institute of Technology, Jamshedpur, India, e-mail: [email protected], [email protected], [email protected] (corresponding author). †
Department of Physics, Veer Surendra Sai University of Technology, Odisha, India, e-mail: [email protected].
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreti
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