Scattering phase shifts and mixing angles for an arbitrary number of coupled channels on the lattice

Abstract

We present a lattice method for determining scattering phase shifts and mixing angles for the case of an arbitrary number of coupled channels. Previous nuclear lattice effective field theory simulations were restricted to mixing of up to two partial waves for scattering of two spin-$1/2$ particles, which is insufficient for analyzing nucleon-nucleus or nucleus-nucleus scattering processes. In the proposed method, the phase shifts and mixing angles are extracted from the radial wave functions obtained by projecting the three-dimensional lattice Hamiltonian onto the partial wave basis. We use a spherical wall potential as a boundary condition along with a channel-mixing auxiliary potential to construct the full-rank $S$ matrix. Our method can be applied to particles with any spin, but we focus here on scattering of two spin-$1$ bosons involving up to four coupled channels. For a considered test potential, the phase shifts and mixing angles extracted on the lattice are shown to agree with the ones calculated by solving the Schrödinger equation in the continuum.

arXiv comment14 pages, 9 figures, 1 table, corresponds to the published version in Phys. Rev. C

References in corpus (56)

• Modern Theory of Nuclear Forces
• Chiral effective field theory and nuclear forces
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Ab initio calculation of the Hoyle state
• Precision nucleon-nucleon potential at fifth order in the chiral expansion
• High-quality two-nucleon potentials up to fifth order of the chiral expansion
• Microscopic Clustering in Light Nuclei
• Scattering processes and resonances from lattice QCD
• Structure and rotations of the Hoyle state
• Multiple-channel generalization of Lellouch-Luscher formula
• Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order
• Lattice simulations for few- and many-body systems
• Evolution of shell structure in neutron-rich calcium isotopes
• Subleading contributions to the chiral three-nucleon force I: long-range terms
• Two-particle multichannel systems in a finite volume with arbitrary spin
• Three-particle scattering amplitudes from a finite volume formalism
• Subleading contributions to the chiral three-nucleon force II: Short-range terms and relativistic corrections
• A method to measure the antikaon-nucleon scattering length in lattice QCD
• Ab initio alpha-alpha scattering
• In-Medium Similarity Renormalization Group with Chiral Two- Plus Three-Nucleon Interactions
• Relating the finite-volume spectrum and the two-and-three-particle $S$ matrix for relativistic systems of identical scalar particles
• Three particle quantization condition in a finite volume: 2. general formalism and the analysis of data
• Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
• Ab initio calculation of the spectrum and structure of ${}^{16}$O
• Ab-initio Gorkov-Green's function calculations of open-shell nuclei
• Scalar mesons in a finite volume
• Three-particle quantization condition in a finite volume: 1. The role of the three-particle force
• Chiral three-nucleon force at N^4LO I: Longest-range contributions
• Coupled-Channel $D\pi$, $D\eta$ and $D_s\bar{K}$ Scattering from Lattice QCD
• Lattice Effective Field Theory for Medium-Mass Nuclei
• Isoscalar $\pi \pi ,K\overline{K},\eta \eta$ scattering and the $\sigma ,f_0,f_2$ mesons from QCD
• Subleading contributions to the three-nucleon contact interaction
• Viability of carbon-based life as a function of the light quark mass
• Charge form factor and sum rules of electromagnetic response functions in Carbon-12
• Chiral three-nucleon force at N^4LO II: Intermediate-range contributions
• Two-pion exchange three-nucleon potential: O(q^4) chiral expansion
• Essential elements for nuclear binding
• Chiral dynamics of few- and many-nucleon systems
• Ab initio calculations of the isotopic dependence of nuclear clustering
• Four-nucleon force using the method of unitary transformation
• Lattice chiral effective field theory with three-body interactions at next-to-next-to-leading order
• Dependence of the triple-alpha process on the fundamental constants of nature
• The $b_1$ resonance in coupled $\pi \omega$, $\pi \varphi$ scattering from lattice QCD
• Dynamically-coupled partial-waves in $\rho \pi$ isospin-2 scattering from lattice QCD
• Two-particle scattering on the lattice: Phase shifts, spin-orbit coupling, and mixing angles
• Precise determination of lattice phase shifts and mixing angles
• Nucleon-deuteron scattering using the adiabatic projection method
• Anthropic considerations in nuclear physics
• Neutron-proton scattering with lattice chiral effective field theory at next-to-next-to-next-to-leading order
• Three-nucleon force at large distances: Insights from chiral effective field theory and the large-N_c expansion
• Dilute neutron matter on the lattice at next-to-leading order in chiral effective field theory
• Scattering cluster wave functions on the lattice using the adiabatic projection method
• Neutron-proton scattering at next-to-next-to-leading order in Nuclear Lattice Effective Field Theory
• Galilean invariance restoration on the lattice
• Lattice methods and the nuclear few- and many-body problem
• Lattice Improvement in Lattice Effective Field Theory

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