Angular Momentum Eigenstates of the Isotropic 3-D Harmonic Oscillator: Phase-Space Distributions and Coalescence Probabilities
arXiv:2112.12269 · doi:10.1016/j.aop.2022.168960
Abstract
The isotropic 3-dimensional harmonic oscillator potential can serve as an approximate description of many systems in atomic, solid state, nuclear, and particle physics. In particular, the question of 2 particles binding (or coalescing) into angular momentum eigenstates in such a potential has interesting applications. We compute the probabilities for coalescence of two distinguishable, non-relativistic particles into such a bound state, where the initial particles are represented by generic wave packets of given average positions and momenta. We use a phase-space formulation and hence need the Wigner distribution functions of angular momentum eigenstates in isotropic 3-dimensional harmonic oscillators. These distribution functions have been discussed in the literature before but we utilize an alternative approach to obtain these functions. Along the way, we derive a general formula that expands angular momentum eigenstates in terms of products of 1-dimensional harmonic oscillator eigenstates.
arXiv comment31 pages, 4 figures; v2: typos fixed, reference added
References in corpus (25)
- Hadronization in heavy ion collisions: Recombination and fragmentation of partons
- Parton coalescence and antiproton/pion anomaly at RHIC
- Hadron production in heavy ion collisions: Fragmentation and recombination from a dense parton phase
- Parton coalescence at RHIC
- Quark Coalescence for Charmed Mesons in Ultrarelativistic Heavy-Ion Collisions
- Coalescence and flow in ultra-relativistic heavy ion collisions
- Coalescence Models For Hadron Formation From Quark Gluon Plasma
- Multi-quark hadrons from Heavy Ion Collisions
- Exotic Hadrons from Heavy Ion Collisions
- Light cluster production in intermediate energy heavy-ion collisions induced by neutron-rich nuclei
- Heavy baryon/meson ratios in relativistic heavy ion collisions
- Studying Exotic Hadrons in Heavy Ion Collisions
- Nuclear Clusters as a Probe for Expansion Flow in Heavy Ion Reactions at 10-15AGeV
- Light clusters production as a probe to the nuclear symmetry energy
- Light (anti-)nuclei production and flow in relativistic heavy-ion collisions
- Generating All Wigner Functions
- Spectra and flow of light nuclei in relativistic heavy ion collisions at RHIC and the LHC
- Jet Fragmentation via Recombination of Parton Showers
- Pentaquark baryon production at the Relativistic Heavy Ion Collider
- Recombination Models
- Elliptic flow of resonances at RHIC: probing final state interactions and the structure of resonances
- (2317) meson production at RHIC
- Hydrogen atom in phase space: The Wigner representation
- Modeling Cluster Production at the AGS
- Enhanced production of mesons in heavy ion collisions