A new treatment of nonlocality in scattering process

Abstract

Nonlocality in the scattering potential leads to an integro-differential equation.In this equation nonlocality enters through an integral over the nonlocal potential kernel. The resulting Schroedinger equation is usually handled by approximating r,r'-dependence of the nonlocal kernel. The present work proposes a novel method to solve the integro-differential equation. The method, using the mean value theorem of integral calculus, converts the nonhomogeneous term to a homogeneous term. The effective local potential in this equation turns out to be energy independent, but has relative angular momentum dependence. This method has high accuracy and is valid for any form of nonlocality. As illustrative examples, the total and differential cross sections for neutron scattering off 12C, 56Fe and 100Mo nuclei are calculated with this method in the low energy region (up to 10 MeV) and are found to be in good accord with the experiments.

arXiv comment14 pages, 12 figures, Accepted in Journal of Physics G: Nuclear and Particle Physics

References in corpus (3)

• Optical potential from first principles
• Green's Function for Nonlocal Potentials
• Solution of the Schrödinger equation containing a Perey-Buck nonlocality

Cited by in corpus (5)

• Critical view of nonlocal nuclear potentials in alpha decay
• SWANLOP : Scattering waves off nonlocal optical potentials in the presence of Coulomb interactions
• Exact scattering waves off nonlocal potentials under Coulomb interaction within Schrödinger's integro-differential equation
• Manifestation of deformation and nonlocality in $\alpha$ and cluster decay
• Taylor approximation to treat nonlocality in scattering processes