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تسجيل مستخدم جديدUser Manual for MOLSCAT, BOUND and FIELD, Version 2020.0: programs for quantum scattering properties and bound states of interacting pairs of atoms and molecules
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MOLSCAT is a general-purpose package for performing non-reactive quantum scattering calculations for atomic and molecular collisions using coupled-channel methods. Simple atom-molecule and molecule-molecule collision types are coded internally and additional ones may be handled with plug-in routines. Plug-in routines may include external magnetic, electric or photon fields (and combinations of them). Simple interaction potentials are coded internally and more complicated ones may be handled with plug-in routines. BOUND is a general-purpose package for performing calculations of bound-state energies in weakly bound atomic and molecular systems using coupled-channel methods. It solves the same sets of coupled equations as MOLSCAT, and can use the same plug-in routines if desired, but with different boundary conditions. FIELD is a development of BOUND that locates external fields at which a bound state exists with a specified energy. One important use is to locate the positions of magnetically tunable Feshbach resonance positions in ultracold collisions. Versions of these programs before version 2019.0 were released separately. However, there is a significant degree of overlap between their internal structures and usage specifications. This manual therefore describes all three, with careful identification of parts that are specific to one or two of the programs.
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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 th
e 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 Schrodinger 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.
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. 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 partial wave (or total angular momentum) to calculate elastic and inelastic cross integral 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 characterize scattering resonances as a function of an external variable such as the magnetic field.
We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. We use a diagrammatic method to analytically derive the scattering properties of two polaritons. We identify parameter regimes where polariton-
polariton interactions are repulsive. Furthermore, in the regime of attractive interactions, we identify multiple two-polariton bound states, calculate their dispersion, and study the resulting scattering resonances. Finally, the two-particle scattering properties allow us to derive the effective low-energy many-body Hamiltonian. This theoretical platform is applicable to ongoing experiments.
The three-body system inside the unitary window is studied for three equal bosons and three equal fermions having $1/2$ spin-isospin symmetry. We perform a gaussian characterization of the window using a gaussian potential to define trajectories for
low-energy quantities as binding energies and phase shifts. On top of this trajectories experimental values are placed or, when not available, quantities calculated using realistic potentials that are known to reproduce experimental values. The intention is to show that the gaussian characterization of the window, thought as a contact interaction plus range corrections, captures the main low-energy properties of real systems as for example three helium atoms or three nucleons. The mapping of real systems on the gaussian trajectories is taken as indication of universal behavior. The trajectories continuously link the physical points to the unitary limit allowing for the explanation of strong correlations between observables appearing in real systems and which are known to exist in that limit. In the present study we focus on low-energy bound, scattering and virtual states.
These notes were written for a set of three lectures given in a school at the Max Planck Institute for the Physics of Complex Systems in October/2017 before the workshop Critical Stability of Quantum Few-Body Systems. These lectures are primarily ded
icated to the students and represent a very idiosyncratic vision of the author, mainly in the last part of the text related to applications. These notes are only a tentative to show a technique, among many others, to solve problems in a very rich area of the contemporary physics - the Few-Body Physics - many times unknown by a considerable part of the students.
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