Molscat: A program for non-reactive quantum scattering calculations on atomic and molecular collisions

Abstract

molscat is a general-purpose program for quantum-mechanical calculations on nonreactive atom–atom, atom–molecule and molecule–molecule collisions. It constructs the coupled-channel equations of atomic and molecular scattering theory, and solves them by propagating the wavefunction or log-derivative matrix outwards from short range to the asymptotic region at long range. It then applies scattering boundary conditions to extract the scattering matrix (S matrix). 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, rigid diatom + asymmetric top, and diffractive scattering of an atom from a crystal surface. Interaction potentials may be specified either in program input (for simple cases) or with user-supplied routines. For the built-in coupling cases, molscat can loop over total angular momentum (partial wave) and total parity to calculate elastic and inelastic integral cross sections and spectroscopic line-shape cross sections. Post-processors are available to calculate differential cross sections, transport, relaxation and Senftleben–Beenakker cross sections, and to fit the parameters of scattering resonances. molscat also provides an interface for plug-in routines to specify coupling cases (Hamiltonians and basis sets) that are not built in; plug-in routines are supplied to handle collisions of a pair of alkali-metal atoms with hyperfine structure in an applied magnetic field. For low-energy scattering, molscat can calculate scattering lengths and effective ranges and can locate and characterise scattering resonances as a function of an external variable such as the magnetic field. Program summaryProgram Title:molscatProgram Files doi:http://dx.doi.org/10.17632/rtzgf5mwpn.1Licensing provisions: GPLv3Programming language: Fortran 90External routines/libraries: LAPACK, BLASNature of problem: Quantum-mechanical calculations of scattering properties for non-reactive collisions between atoms and molecules.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 to the asymptotic region. The program calculates scattering S matrices and uses them to calculate scattering properties including elastic, inelastic and line-shape cross sections.Unusual features:1. molscat contains numerous features to handle quantities important in low-energy collisions. It can propagate very efficiently to very long range, and it can calculate low-energy properties such as the scattering length (complex and energy-dependent if required) and the effective range.2. molscat can construct and solve sets of coupled equations using basis sets that are not eigenfunctions of the Hamiltonians of the colliding particles at long range. The propagation is carried out in the primitive basis set, and the solutions are transformed to the asymptotic basis set before applying long-range boundary conditions to extract the S matrix.3. molscat provides an interface that allows users to specify the coupled equations that arise from additional Hamiltonians and basis sets.4. molscat provides an interface that allows users to include multiple external fields in the Hamiltonian. This same interface also allows users to include a factor which scales the interaction potential, and to investigate how properties vary with this factor.5. molscat can locate and characterise low-energy Feshbach resonances either as a function of collision energy or as a function of external fields or of the potential scaling factor.