Abstract Modified effective range theory is applied as a tool to determine bound and virtual state energies in low-energy positron elastic scattering by atoms and molecules. This is achieved by the S-matrix continuation into the complex momentum plane, allowing to identify poles related to shallow energy states. The influence of the long-range polarization potential (∼r −4) on the bound and virtual-state pole positions is analyzed for noble gases and nonpolar molecules such as H2, N2, and CH4. The quantitative relations between the S-matrix poles and the s-wave scattering length accounting for dipole polarization are introduced.Abstract Modified effective range theory is applied as a tool to determine bound and virtual state energies in low-energy positron elastic scattering by atoms and molecules. This is achieved by the S-matrix continuation into the complex momentum plane, allowing to identify poles related to shallow energy states. The influence of the long-range polarization potential (∼r −4) on the bound and virtual-state pole positions is analyzed for noble gases and nonpolar molecules such as H2, N2, and CH4. The quantitative relations between the S-matrix poles and the s-wave scattering length accounting for dipole polarization are introduced.

Journal of Physics CommunicationsApr 1, 20242 citations

Elements of the Scattering Theory

WORLD SCIENTIFIC eBooksSep 1, 20080 citations

Ising Spectroscopy II: Particles and poles at T>Tc

Alexander B. Zamolodchikov

I discuss particle content of the Ising field theory (the scaling limit of the Ising model in a magnetic field), in particular the evolution of its mass spectrum under the change of the scaling parameter. I consider both real and pure imaginary magnetic field. Here I address the high-temperature regime, where the spectrum of stable particles is relatively simple (there are from one to three particles, depending on the parameter). My goal is to understand analytic continuations of the masses to the domain of the parameter where they no longer exist as the stable particles. I use the natural tool -- the $2\to 2$ elastic scattering amplitude, with its poles associated with the stable particles, virtual and resonance states in a standard manner. Concentrating attention on the "real" poles (those corresponding to stable and virtual states) I propose a scenario on how the pattern of the poles evolves from the integrable point $T=T_c,\ H\neq 0$ to the free particle point $T>T_c,\ H=0$ , and then, along the pure imaginary $H$ , to the Yang-Lee critical point. Waypoints along this evolution path are located using TFFSA data. I also speculate about likely behavior of some of the resonance poles.I discuss particle content of the Ising field theory (the scaling limit of the Ising model in a magnetic field), in particular the evolution of its mass spectrum under the change of the scaling parameter. I consider both real and pure imaginary magnetic field. Here I address the high-temperature regime, where the spectrum of stable particles is relatively simple (there are from one to three particles, depending on the parameter). My goal is to understand analytic continuations of the masses to the domain of the parameter where they no longer exist as the stable particles. I use the natural tool -- the $2\to 2$ elastic scattering amplitude, with its poles associated with the stable particles, virtual and resonance states in a standard manner. Concentrating attention on the "real" poles (those corresponding to stable and virtual states) I propose a scenario on how the pattern of the poles evolves from the integrable point $T=T_c,\ H\neq 0$ to the free particle point $T>T_c,\ H=0$, and then, along the pure imaginary $H$, to the Yang-Lee critical point. Waypoints along this evolution path are located using TFFSA data. I also speculate about likely behavior of some of the resonance poles.

arXiv:1310.4821Oct 17, 201316 citations

Resonances and scattering in the classical limit

J. M. Combes, Pierre Duclos, Ruedi Seiler

Jan 1, 19841 citation

Elementary Theory of Scattering

Ajoy Kumar Ghatak, S. Lokanathan

Springer eBooksJan 1, 20041 citation

2\to 2

elastic scattering amplitude, with its poles associated with the stable particles, virtual and resonance states in a standard manner. Concentrating attention on the "real" poles (those corresponding to stable and virtual states) I propose a scenario on how the pattern of the poles evolves from the integrable point

T=T_c,\ H\neq 0

to the free particle point

T>T_c,\ H=0

, and then, along the pure imaginary

H

, to the Yang-Lee critical point. Waypoints along this evolution path are located using TFFSA data. I also speculate about likely behavior of some of the resonance poles.