Vladimir Roudnev

Benchmark helium dimer and trimer calculations with a public few-body code

We present detailed calculations of bound and scattering states of dimers and trimers of He to produce highly accurate data and to test a non-relativistic three-body code currently in development for public distribution. For these systems, uncertainties and inaccuracies in the fundamental constants frequently used in published works can substantially exceed numerical errors. Our benchmark calculations include specific estimates of the numerical accuracy of the calculations and also explore sensitivity to fundamental constants and their uncertainties. The use of an inexact coupling constant in the previous calculations leads to 0.08% error for the ground state energy, 0.3% error for the excited state energy and up to 0.15% error for the atom–dimer scattering length in the system of three 4He atoms. The corresponding errors for the asymmetric 4He23He system are 0.3% for the bound state energy and 0.03% for the atom–dimer scattering length.

Universal resonant ultracold molecular scattering

The elastic scattering amplitudes of indistinguishable, bosonic, strongly-polar molecules possess universal properties at the coldest temperatures due to wave propagation in the long-range dipole-dipole field. Universal scattering cross sections and anisotropic threshold angular distributions, independent of molecular species, result from careful tuning of the dipole moment with an applied electric field. Three distinct families of threshold resonances also occur for specific field strengths, and can be both qualitatively and quantitatively predicted using elementary adiabatic and semi-classical techniques. The temperatures and densities of heteronuclear molecular gases required to observe these univeral characteristics are predicted. PACS numbers: 34.50.Cx, 31.15.ap, 33.15.-e, 34.20.-b

Resonance phenomena in ultracold dipole?dipole scattering

Elastic scattering resonances occurring in ultracold collisions of either bosonic or fermionic polar molecules are investigated. The Born–Oppenheimer adiabatic representation of the two-body dynamics provides both a qualitative classification scheme and a quantitative WKB quantization condition that predicts several sequences of resonant states. It is found that the near-threshold energy dependence of ultracold collision cross sections varies significantly with the particle exchange symmetry, with bosonic systems showing much smoother energy variations than their fermionic counterparts. Resonant variations of the angular distributions in ultracold collisions are also described.

Helium trimer calculations with a public quantum three-body code

We present an illustration of using a quantumthree-body code being prepared for public release. The code is based on iterative solving of the three-dimensional Faddeev equations. The code is easy to use and allows users to perform highly-accurate calculations of quantum three-body systems. The previously known results for He3 ground state are well reproduced by the code.

Automatic grid construction for few-body quantum-mechanical calculations

Abstract An algorithm for generating optimal nonuniform grids for solving the two-body Schrodinger equation is developed and implemented. The shape of the grid is optimized to accurately reproduce the low-energy part of the spectrum of the Schrodinger operator. Grids constructed this way are applicable to more complex few-body systems where the number of grid points is a critical limitation to numerical accuracy. The utility of the grid generation for improving few-body calculations is illustrated through an application to bound states of He trimers.