https://arxiv.org/pdf/cond-mat/0410417.pdf

Universality in few-body systems with large scattering length

The theory of reactive (rearrangement) scattering for three atoms in three physical dimensions using adiabatically adjusting, principal axes hyperspherical (APH) coordinates is given. The relationships of the APH coordinates to Delves and Jacobi coordinates are given, and the kinetic energy operator is shown to be relatively simple. Procedures for solving the equations via either an exact coupled channel (CC) method or an optimum centrifugal sudden (CSAPH) approximation are given as well as procedures for applying scattering boundary conditions. Surface functions of two angles are obtained using a finite element method with an optimized, nonuniform mesh, and the CC equations are solved using the efficient VIVAS method. Sample CC results are given for the H3 system. The present approach has the advantages that all arrangements are treated fully equivalently; it is a principal axis system, so that both axes and internal coordinates swing smoothly with the reactions; it is directly applicable to both symmetric and unsymmetric systems and mass combinations and all total angular momenta; it gives convenient mappings for visualization of potential energy surfaces and wave functions; only regular radial solutions are required; all coordinate matching is by simple projection; and the expensive parts of the calculation are energy independent, so that, once they are done, the scattering matrices can be rapidly generated at the large numbers of energies needed to map out reactive thresholds and resonances. Accurate reactive scattering calculations are now possible for many chemically interesting reactions that were previously intractable.

Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. Theory

The three-nucleon continuum: achievements, challenges and applications

This article reviews theoretical and experimental advances in Efimov physics, an array of quantum few-body and many-body phenomena arising for particles interacting via short-range resonant interactions, that is based on the appearance of a scale-invariant three-body attraction theoretically discovered by Vitaly Efimov in 1970 This three-body effect was originally proposed to explain the binding of nuclei such as the triton and the Hoyle state of carbon-12, and later considered as a simple explanation for the existence of some halo nuclei It was subsequently evidenced in trapped ultra-cold atomic clouds and in diffracted molecular beams of gaseous helium These experiments revealed that the previously undetermined three-body parameter introduced in the Efimov theory to stabilise the three-body attraction typically scales with the range of atomic interactions The few- and many-body consequences of the Efimov attraction have been since investigated theoretically, and are expected to be observed in a broader spectrum of physical systems

http://iopscience.iop.org/article/10.1088/1361-6633/aa50e8/pdf

Efimov physics: a review

A method is presented for accurately solving the Schrodinger equation for the reactive collision of an atom with a diatomic molecule in three dimensions on a single Born–Oppenheimer potential energy surface. The Schrodinger equation is first expressed in body‐fixed coordinates. The wavefunction is then expanded in a set of vibration–rotation functions, and the resulting coupled equations are integrated in each of the three arrangement channel regions to generate primitive solutions. Next, these are smoothly matched to each other on three matching surfaces which appropriately separate the arrangement channel regions. The resulting matched solutions are linearly combined to generate wavefunctions which satisfy the reactance and scattering matrix boundary conditions, from which the corresponding R and S matrices are obtained. The scattering amplitudes in the helicity representation are easily calculated from the body fixed S matrices, and from these scattering amplitudes several types of differential and int...

/pdf/quantum-mechanical-reactive-scattering-for-three-dimensional-34fx4i3tyz.pdf

L.M. Delves

Papers

Tertiary and general-order collisions

Elastic and inelastic scattering of neutrons by deuterons near the inelastic threshold