POTHEA: A program for computing eigenvalues and eigenfunctions and their first derivatives with respect to the parameter of the parametric self-adjoined 2D elliptic partial differential equation

A FORTRAN 77 program is presented for calculating with the given accuracy eigenvalues, surface eigenfunctions and their first derivatives with respect to a parameter of the parametric self-adjoined 2D elliptic partial differential equation with the Dirichlet and/or Neumann type boundary conditions on a finite two-dimensional region. The program calculates also potential matrix elements that are integrals of the products of the surface eigenfunctions and/or the first derivatives of the surface eigenfunctions with respect to a parameter. Eigenvalues and matrix elements computed by the POTHEA program can be used for solving the bound state and multi-channel scattering problems for a system of coupled second order ordinary differential equations with the help of the KANTBP program (Chuluunbaatar et al., 2007). Benchmark calculations of eigenvalues and eigenfunctions of the ground and first excited states of a Helium atom in the framework of a coupled-channel hyperspherical adiabatic approach are presented. As a test desk, the program is applied to the calculation of the eigensolutions of a 2D boundary value problem, their first derivatives with respect to a parameter and potential matrix elements used in the benchmark calculations. Program title: POTHEA Catalogue identifier: AESX_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AESX_v1_0.html Program obtainable from: Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of bits in distributed program, including test data, etc.: 36 929 No. of lines in distributed program, including test data, etc.: 3 756 Distribution format: tar.gz Programming language: FORTRAN 77 Computer: Personal computer Operating system: Unix/Linux, Windows RAM: depends on (a)the number of differential equations,(b)the number and order of finite elements, and(b)the number of eigensolutions required.Classification: 2.7 External routine: SSPACE [1], GAULEG [2] Nature of problem: Solutions of boundary value problems (BVPs) for the elliptic partial differential equations (PDEs) of the Schrödinger type find wide application in molecular, atomic and nuclear physics, for example, in three-dimensional tunneling of a diatomic molecule incident upon a potential barrier, fission model of collision of heavy ions, fragmentation of light nuclei, a hydrogen atom in magnetic field, photoionization of Helium like atoms, one photon ionization of atoms, electron-impact ionization of molecular hydrogen and phot