Calculation of resonances in the Coulomb three-body system with two disintegration channels in the adiabatic hyperspherical approach

Adiabatic Hyperspherical Representation for the Three-body Problem in Two Dimensions

We explore the three-body problem in two dimensions using the adiabatic hyperspherical representation. We develop the main equations in terms of democratic hyperangular coordinates and determine several symmetry properties and boundary conditions for both interacting and non-interacting solutions. From the analysis of the three-body effective potentials, we determine the threshold laws for low energy three-body recombination, collision-induced dissociation as well as inelastic atom-diatom collisions in two dimensions. Our results show that the hyperspherical representation can offer a simple a…

Analytical Expressions for a Hyperspherical Adiabatic Basis Suitable for a particular Three Particle Problem in 2 Dimensions

For a particular case of three-body scattering in two dimensions, and matching analytical expressions at a transition point, we obtain accurate solutions for the hyperspherical adiabatic basis and potential. We find analytical expressions for the respective, asymptotic, inverse logarithmic and inverse power potential behaviors, that arise as functions of the radial coordinate. The model that we consider is that of two particles interacting with a repulsive step potential, a third particle acting as a spectator. The model is simple but gives insight, as the 2-body interaction is long ranged in …

中子丰富氦同位素的共振和碰撞性质的绝热超球面表示研究

Resonances and collisional properties of neutron-rich helium isotopes in the adiabatic hyperspherical representation

本研究利用绝热超球面方法，分析中子丰富氦同位素的共振和碰撞性质，包括束缚态、散射态及核反应过程。

一维系统中二聚体-二聚体散射的超球面分析

Hyperspherical Analysis of Dimer-Dimer Scattering in One-Dimensional Systems

本研究针对一维量子系统二聚体-二聚体散射问题，采用绝热超球面表示结合慢变量离散化方法解决数值难题，经可积区域验证有效，并在不可积区域发现散射长度共振增强新特征，为低维少体量子物理研究提供了可靠工具。

Three-Body Recombination in One Dimension

We study the three-body problem in one dimension for both zero and finite range interactions using the adiabatic hyperspherical approach. Particular emphasis is placed on the threshold laws for recombination, which are derived for all combinations of the parity and exchange symmetries. For bosons, we provide a numerical demonstration of several universal features that appear in the three-body system, and discuss how certain universal features in three dimensions are different in one dimension. We show that the probability for inelastic processes vanishes as the range of the pair-wise interacti…

Complex collisions of ultracold molecules: a toy model

We introduce a model to study the collisions of two ultracold diatomic molecules in one dimension interacting via pairwise potentials. We present results for this system, and argue that it offers lessons for real molecular collisions in three dimensions. We analyze the distribution of the adiabatic potentials in the hyperspherical coordinate representation as well as the distribution of the four-body bound states in the adiabatic approximation (i.e. no coupling between adiabatic channels). It is found that while the adiabatic potential distribution transitions from chaotic to non-chaotic as th…