COLOSS: Complex-scaled Optical and couLOmb Scattering Solver

Abstract

We introduce COLOSS, a program designed to address the scattering problem using a bound-state technique known as complex scaling. In this method, the oscillatory boundary conditions of the wave function are transformed into exponentially decaying ones, accommodating the long-range Coulomb interaction. The program implements the general local optical potential and the Perey-Buck non-local optical potential, with all potential parameters included in a well-designed input format for ease of use. The design offers users direct access to compute S-matrices and cross-sections for scattering processes involving a projectile of any spin interacting with a spin-0 target. We provide thorough discussions on the precision of Lagrange functions and their benefits in evaluating matrix elements. Additionally, COLOSS incorporates two distinct rotation methods, making it adaptable to potentials without analytical expressions. Comparative results demonstrate that COLOSS achieves high accuracy when compared with the direct integration method, Numerov, underscoring its utility and effectiveness in scattering calculations.

Program summary

Program Title: COLOSS

CPC Library link to program files: https://doi.org/10.17632/ph4m98rpv2.1

Developer's repository link: https://github.com/jinleiphys/COLOSS

Licensing provisions: GPLv3

Programming language: Fortran

Nature of problem: The study of elastic scattering between nuclei is a fundamental problem in nuclear physics, key to understanding nuclear interactions and structure. Traditional methods for solving the Schrödinger equation in such contexts often require imposing boundary conditions at large distances, which can be computationally challenging and prone to inaccuracies, especially for reactions involving strong Coulomb interactions and complex potentials. The complex scaling method offers a robust alternative by transforming the scattered wave function from an oscillatory to an exponentially decaying form, thus eliminating the need for boundary conditions. However, implementing this method requires careful numerical handling and validation of the analytic properties of the involved potentials, such as the Woods-Saxon function, on the complex plane. Additionally, ensuring numerical stability and accuracy across different rotational techniques and integration methods is crucial. This study addresses these challenges by developing a program that leverages the complex scaling method, providing a flexible and accurate tool for calculating elastic scattering between nuclei. The program's ability to handle various optical model potentials and its validation against established methods like Numerov underscores its utility and reliability in nuclear physics research.

Solution method: To address the challenges in calculating elastic scattering between nuclei, we utilize the complex scaling method, which transforms the Schrödinger equation to simplify boundary conditions by converting the radial coordinate into the complex plane. This transformation changes the wave function from oscillatory to exponentially decaying. Our approach includes validating results against traditional methods like the Numerov algorithm to ensure accuracy. Additionally, we develop a flexible computational program capable of handling various optical model potentials, such as the Woods-Saxon potential, and performing complex scaling and integration efficiently. This method provides a robust, accurate, and computationally efficient solution for studying elastic scattering in nuclear physics.

Additional comments including restrictions and unusual features: Our method, while effective, has some restrictions and unusual features. The complex scaling method requires careful handling to avoid numerical instabilities, especially at large radial distances. Gauss-Legendre quadrature, chosen for its convergence, demands precise selection of points and weights. The computational program's flexibility to handle various optical model potentials, like the Woods-Saxon potential, adds complexity and requires thorough validation. Additionally, large-scale simulations may require significant computational resources. Despite these challenges, our approach provides precise and efficient solutions for elastic scattering in nuclear physics, though users must be cautious of potential numerical instabilities and complexities.