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Register a new userBound State Calculations for Three Atoms Without Explicit Partial Wave Decomposition
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A method to calculate the bound states of three-atoms without resorting to an explicit partial wave decomposition is presented. The differential form of the Faddeev equations in the total angular momentum representation is used for this purpose. The method utilizes Cartesian coordinates combined with the tensor-trick preconditioning for large linear systems and Arnoldis algorithm for eigenanalysis. As an example, we consider the He$_3$ system in which the interatomic force has a very strong repulsive core that makes the three-body calculations with standard methods tedious and cumbersome requiring the inclusion of a large number of partial waves. The results obtained compare favorably with other results in the field.
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The Faddeev equations for the three body bound state are solved directly as three dimensional integral equation without employing partial wave decomposition. The numerical stability of the algorithm is demonstrated. The three body binding energy is calculated for Malfliet-Tjon type potentials and compared with results obtained from calculations based on partial wave decomposition. The full three body wave function is calculated as function of the vector Jacobi momenta. It is shown that it satisfies the Schrodinger equation with high accuracy. The properties of the full wave function are displayed and compared to the ones of the corresponding wave functions obtained as finite sum of partial wave components. The agreement between the two approaches is essentially perfect in all respects.
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 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.
The orientation of water molecules is the key factor for the fast transport of water in small nanotubes. It has been accepted that the bidirectional water burst in short nanotubes can be transformed into unidirectional transport when the orientation of water molecules is maintained in long nanotubes under the external field. In this work, based on molecular dynamics simulations and first-principles calculations, we showed without external field, it only needs 21 water molecules to maintain the unidirectional single file water intrinsically in carbon nanotube at seconds. Detailed analysis indicates that the surprising result comes from the step by step process for the flip of water chain, which is different with the perceived concerted mechanism. Considering the thickness of cell membrane (normally 5-10 nm) is larger than the length threshold of the unidirectional water wire, this study suggests it may not need the external field to maintain the unidirectional flow in the water channel at the macroscopic timescale.
Supersonic beams are a prevalent source of cold molecules utilized in the study of chemical reactions, atom interferometry, gas-surface interactions, precision spectroscopy, molecular cooling and more. The triumph of this method emanates from the high densities produced in relation to other methods, however beam density remains fundamentally limited by interference with shock waves reflected from collimating surfaces. Here we show experimentally that this shock interaction can be reduced or even eliminated by cryo-cooling the interacting surface. An increase in beam density of nearly an order of magnitude was measured at the lowest surface temperature, with no further fundamental limitation reached. Visualization of the shock waves by plasma discharge and reproduction with direct simulation Monte Carlo calculations both indicate that the suppression of the shock structure is partially caused by lowering the momentum flux of reflected particles, and significantly enhanced by the adsorption of particles to the surface. We observe that the scaling of beam density with source pressure is recovered, paving the way to order of magnitude brighter cold molecular beams.
The main formalisms of partial level densities (PLD) used in preequilibrium nuclear reaction models, based on the equidistant spacing model (ESM), are considered. A collection of FORTRAN77 functions for PLD calculation by using 14 formalisms for the related partial-state densities is provided and 28 sample cases (
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