Bound and field: Programs for calculating bound states of interacting pairs of atoms and molecules

Abstract

The bound program calculates the bound states of a complex formed from two interacting particles using coupled-channel methods. It is particularly suitable for the bound states of atom–molecule and molecule–molecule van der Waals complexes and for the near-threshold bound states that are important in ultracold physics. It uses a basis set for all degrees of freedom except R, the separation of the centres of mass of the two particles. The Schrödinger equation is expressed as a set of coupled equations in R. Solutions of the coupled equations are propagated outwards from the classically forbidden region at short range and inwards from the classically forbidden region at long range, and matched at a point in the central region. Built-in coupling cases include atom + rigid linear molecule, atom + vibrating diatom, atom + rigid symmetric top, atom + asymmetric or spherical top, rigid diatom + rigid diatom, and rigid diatom + asymmetric top. Both programs provide an interface for plug-in routines to specify coupling cases (Hamiltonians and basis sets) that are not built in. With appropriate plug-in routines, bound can take account of the effects of external electric, magnetic and electromagnetic fields, locating bound-state energies at fixed values of the fields. The related program field uses the same plug-in routines and locates values of the fields where bound states exist at a specified energy. As a special case, it can locate values of the external field where bound states cross scattering thresholds and produce zero-energy Feshbach resonances. Plug-in routines are supplied to handle the bound states of a pair of alkali-metal atoms with hyperfine structure in an applied magnetic field. Program summaryProgram Titles:bound and fieldProgram Files doi:http://dx.doi.org/10.17632/rtzgf5mwpn.1Licensing provisions: GPLv3Programming language: Fortran 90External routines/libraries: LAPACK, BLASNature of problem: Solve the Schrödinger equation to locate the bound states of an interacting pair of atoms or molecules as a function of energy (for bound) or external field (for field).Solution method: The Schrödinger equation is expressed in terms of coupled equations in the interparticle distance, R. Solutions of the coupled-channel equations are propagated outwards from the classically forbidden region at short range and inwards from the classically forbidden region at long range, and matched at a point in the central region. Bound states exist at energies where one of the eigenvalues of the log-derivative matching matrix is zero. bound calculates the number of bound states in a specified range of energy and then converges on the bound-state energies. field operates in a similar manner to bound but converges on bound states as a function of external field at fixed energy, or energy fixed with respect to a field-dependent threshold energy. The programs can also generate bound-state wavefunctions if desired.Unusual features:1. The programs include Hamiltonians for simple atom–molecule and molecule–molecule interactions, and provide an interface that allows users to specify Hamiltonians and basis sets for more complex systems. This interface allows users to include multiple external fields in the Hamiltonian.2. The programs can propagate very efficiently to long range, making them particularly suited to locating very high-lying bound states.