Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Three-particle scattering rates and singularities of the T matrix. II.

Vladimir S. Potapov, John R. Taylor

Published Dec 1, 1977• 11 citations
Publisher

Abstract

We evaluate the contributions of double-scattering singularities to three-particle scattering rates. It is shown that these contributions are finite and consistent with the physical interpretation of double-scattering processes. The "double-scattering regions" of momentum space where these processes contribute are calculated, and it is shown that in these regions the double-scattering contributions dominate and the regular part of the $T$ matrix can be neglected.

DOI
10.1103/physreva.16.2276

Related papers

Three-particle scattering rates and singularities of the T matrix. I.

Vladimir S. Potapov, John R. Taylor

We construct a quantum ensemble to describe nonrelativistic three-particle scattering, and derive expressions for the observable scattering rates. These expressions are seen to reduce to the familiar expressions involving the modulus squared of the $T$ matrix, provided the final momenta are chosen to avoid the disconnected and double-scattering singularities. We show that our expressions remain finite in the neighborhood of the disconnected singularities, and that the predicted rates are consistent with the physical interpretation of the disconnected processes.

Physical Review A•Dec 1, 1977•16 citations

Scattering Faddeev calculations in the double continuum

Romain Guérout

We use the configuration-space Faddeev formalism to study scattering of three particles in the double continuum where all particles are free. All scattering processes, starting from and ending in both single and double continua, are collected in a unique matrix. We apply our method to the benchmark system of neutron-deuteron scattering.

quant-pharXiv:2604.12516•Apr 15, 2026

Double-Photon Contributions to Multiple-Photon Processes

Norah V. Cohan, Hendrik F. Hameka

It is shown that in evaluating the transition probability of a multiple-photon process involving more than two photons, the contributions of the part of the interaction Hamiltonian that is quadratic in the vector potential of the radiation field may be neglected if the vector potential of the radiation field is assumed to be constant in the region of space that we consider.

Physical Review•Nov 25, 1966•17 citations

Finite Cross Section for Three-Particle Scattering

M. Yamazaki

In the scattering of three free incident particles, a finite cross section for the double scattering has to be defined differently from the processes other than the double scattering. That is, we want to maintain that, in order to obtain a definite quantity being connected to the experimental observation, a particular definition of the cross section has to be required for the double scattering owing to a particular time dependence of its scattering rate. Our definition differs from the ones given recently by others in a form depending on some macroscopic quantities.1), 2) In the previous paper (refered as I in the following)3), we have attained to a finite cross section by working on the basis of the wave packet formalism, while we want to give here a clear-cut derivation in a simple and familear form.

Progress of Theoretical Physics•Mar 1, 1979•0 citations

Singular Three-Body Amplitudes in the Theory of the Third Virial Coefficient

Roger F. Dashen, Shang-keng Ma

We have shown earlier how the virial coefficients can be expressed in terms of traces taken over products of multiparticle (on-energy-shell) scattering matrices. The traces are to be taken in the angular-momentum representation instead of the momentum representation to avoid the infinite forward N-particle scattering amplitude for N > 2 caused by certain singular diagrams. Here, we analyze and sum the contribution of the singular diagrams to the third virial coefficient. It is also shown that one can get the same result if off-shell amplitudes in the momentum representation are utilized.

Journal of Mathematical Physics•Apr 1, 1970•36 citations

Diffractive scattering of three particles in one dimension: A simple result for weak violations of the Yang-Baxter equation

Austen Lamacraft

We study scattering of three equal-mass particles in one dimension. Integrable interactions are synonymous with nondiffractive scattering, meaning that the set of incoming momenta for any scattering event coincides with the set of outgoing momenta. A system is integrable if the two-particle scattering matrix obeys the Yang-Baxter equation. Nonintegrable interactions correspond to diffractive scattering, where the set of outgoing momenta may take on all values consistent with energy and momentum conservation. Such processes play a vital role in the kinetics of one-dimensional gases, where binary collisions are unable to alter the distribution function. When integrability is broken weakly, the result is a small diffractive scattering amplitude. Our main result is a simple formula for the diffractive part of the scattering amplitude, when the violation of the Yang-Baxter equation is small. Although the derivation is given for $\ensuremath{\delta}$-function interactions, the result depends only on the two-particle scattering matrix, and should therefore also apply to finite-range interactions close to integrable.

arXiv:1211.4110•Physical Review A•Jan 16, 2013•26 citations
We evaluate the contributions of double-scattering singularities to three-particle scattering rates. It is shown that these contributions are finite and consistent with the physical interpretation of double-scattering processes. The "double-scattering regions" of momentum space where these processes contribute are calculated, and it is shown that in these regions the double-scattering contributions dominate and the regular part of the TTT matrix can be neglected.
We construct a quantum ensemble to describe nonrelativistic three-particle scattering, and derive expressions for the observable scattering rates. These expressions are seen to reduce to the familiar expressions involving the modulus squared of the TTT matrix, provided the final momenta are chosen to avoid the disconnected and double-scattering singularities. We show that our expressions remain finite in the neighborhood of the disconnected singularities, and that the predicted rates are consistent with the physical interpretation of the disconnected processes.
In the scattering of three free incident particles, a finite cross section for the double scattering has to be defined differently from the processes other than the double scattering. That is, we want to maintain that, in order to obtain a definite quantity being connected to the experimental observation, a particular definition of the cross section has to be required for the double scattering owing to a particular time dependence of its scattering rate. Our definition differs from the ones given recently by others in a form depending on some macroscopic quantities.1), 2) In the previous paper (refered as I in the following)3), we have attained to a finite cross section by working on the basis of the wave packet formalism, while we want to give here a clear-cut derivation in a simple and familear form.
We have shown earlier how the virial coefficients can be expressed in terms of traces taken over products of multiparticle (on-energy-shell) scattering matrices. The traces are to be taken in the angular-momentum representation instead of the momentum representation to avoid the infinite forward N-particle scattering amplitude for N > 2 caused by certain singular diagrams. Here, we analyze and sum the contribution of the singular diagrams to the third virial coefficient. It is also shown that one can get the same result if off-shell amplitudes in the momentum representation are utilized.
We study scattering of three equal-mass particles in one dimension. Integrable interactions are synonymous with nondiffractive scattering, meaning that the set of incoming momenta for any scattering event coincides with the set of outgoing momenta. A system is integrable if the two-particle scattering matrix obeys the Yang-Baxter equation. Nonintegrable interactions correspond to diffractive scattering, where the set of outgoing momenta may take on all values consistent with energy and momentum conservation. Such processes play a vital role in the kinetics of one-dimensional gases, where binary collisions are unable to alter the distribution function. When integrability is broken weakly, the result is a small diffractive scattering amplitude. Our main result is a simple formula for the diffractive part of the scattering amplitude, when the violation of the Yang-Baxter equation is small. Although the derivation is given for $\ensuremath{\delta}$-function interactions, the result depends only on the two-particle scattering matrix, and should therefore also apply to finite-range interactions close to integrable.