An [formula omitted]-matrix package for coupled-channel problems in nuclear physics

Abstract

We present an R-matrix Fortran package to solve coupled-channel problems in nuclear physics. The basis functions are chosen as Lagrange functions, which permits simple calculations of the matrix elements. The main input is the coupling potentials at some nucleus–nucleus distances, specified by the program. The program provides the collision matrix and, optionally, the associated wave function. The present method deals with open and closed channels simultaneously, without numerical instability associated with closed channels. It can also solve coupled-channel problems for non-local potentials. Long-range potentials can be treated with propagation techniques, which significantly speed up the calculations. We first present an overview of the R-matrix theory, and of the Lagrange-mesh method. A description of the package and its installation on a UNIX machine is then provided. Finally, five typical examples are discussed. Program summaryProgram title: rmatrixCatalogue identifier: AEYP_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEYP_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 6090No. of bytes in distributed program, including test data, etc.: 86122Distribution format: tar.gzProgramming language: Fortran 90.RAM: Memory usage strongly depends on the nature of the problem (number of channels, size of the basis).Classification: 17.8.External routines: If available, the LAPACK library can be used for matrix inversion (faster than the sub-routine included in the package).Nature of problem: Solving coupled-channel problems for positive energies; the package provides the collision matrix and the associated wave function for given energy, spin and parity.Solution method: The coupled-channel system is solved with the R-matrix method, and Lagrange functions are adopted. Propagation of the R-matrix can be performed.Restrictions: For non-local potentials, the propagation technique cannot be used.Running time: strongly depends on the nature of the problem. For single-channel calculations, the running type is typically less than 1 s. For large scale calculations (typically more than 100 channels), the running time may increase up to several minutes on a multi-CPU Linux machine.