Angular momentum reduction for physical amplitudes in the three-body problem
Abstract
We give here an approach to the angular momentum reduction that is tailed to be appropriate for the multichannel structure of the three-body problem. Wherever possible we work directly with the physical scattering amplitudes. We obtain concrete partial-wave expansions of elastic, rearrangement, and breakup amplitudes. For these amplitudes we obtain a coupled two-variable integral equation. The effects of parity, time reversal, and rotational invariance are fully discussed. Finally, we provide expressions for the multichannel partial-wave cross sections, asymptotic coordinate-space wave functions, off-shell unitarity, and the partial-wave version of the optical theorem as well as phase-shift parametrizations of the amplitudes.
- Authors:
-
- Stanford Univ., CA (United States)
- Publication Date:
- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1442899
- Report Number(s):
- SLAC-PUB-1289
Journal ID: ISSN 0556-2813; PRVCAN
- Grant/Contract Number:
- AC02-76SF00515
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. C, Nuclear Physics
- Additional Journal Information:
- Journal Volume: 9; Journal Issue: 2; Journal ID: ISSN 0556-2813
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Citation Formats
Bollé, D., and Osborn, T. A. Angular momentum reduction for physical amplitudes in the three-body problem. United States: N. p., 1974.
Web. doi:10.1103/PhysRevC.9.441.
Bollé, D., & Osborn, T. A. Angular momentum reduction for physical amplitudes in the three-body problem. United States. https://doi.org/10.1103/PhysRevC.9.441
Bollé, D., and Osborn, T. A. Fri .
"Angular momentum reduction for physical amplitudes in the three-body problem". United States. https://doi.org/10.1103/PhysRevC.9.441. https://www.osti.gov/servlets/purl/1442899.
@article{osti_1442899,
title = {Angular momentum reduction for physical amplitudes in the three-body problem},
author = {Bollé, D. and Osborn, T. A.},
abstractNote = {We give here an approach to the angular momentum reduction that is tailed to be appropriate for the multichannel structure of the three-body problem. Wherever possible we work directly with the physical scattering amplitudes. We obtain concrete partial-wave expansions of elastic, rearrangement, and breakup amplitudes. For these amplitudes we obtain a coupled two-variable integral equation. The effects of parity, time reversal, and rotational invariance are fully discussed. Finally, we provide expressions for the multichannel partial-wave cross sections, asymptotic coordinate-space wave functions, off-shell unitarity, and the partial-wave version of the optical theorem as well as phase-shift parametrizations of the amplitudes.},
doi = {10.1103/PhysRevC.9.441},
journal = {Physical Review. C, Nuclear Physics},
number = 2,
volume = 9,
place = {United States},
year = {Fri Feb 01 00:00:00 EDT 1974},
month = {Fri Feb 01 00:00:00 EDT 1974}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journalFigures / Tables:
Fig. 1: Angular Conventions for Three Body Momentum Variables
All figures and tables
(1 total)
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Three-Body Model of and Deuteron-Alpha-Particle Scattering
journal, November 1969
- Shanley, Paul E.
- Physical Review, Vol. 187, Issue 4
Primary Singularities, Asymptotic Wave Functions and Unitarity in the Three-Body Problem
journal, October 1973
- Osborn, T. A.; Bollé, D.
- Physical Review C, Vol. 8, Issue 4
Complete angular momentum analysis of Fadde'ev-Lovelace equations based on non-central pair forces
journal, October 1970
- Stingl, M.; Rinat (Reiner), A. S.
- Nuclear Physics A, Vol. 154, Issue 3
Faddeev Equations for Realistic Three-Nucleon Systems. I. Complete Angular Momentum Reduction and Antisymmetrization of States
journal, September 1970
- Harper, E. P.; Kim, Y. E.; Tubis, A.
- Physical Review C, Vol. 2, Issue 3
Optimal equations for three particle scattering
journal, December 1971
- Osborn, T. A.; Kowalski, K. L.
- Annals of Physics, Vol. 68, Issue 2
New Reduction of the Faddeev Equations and Its Application to the Pion as a Three-Particle Bound State
journal, August 1965
- Ahmadzadeh, A.; Tjon, J. A.
- Physical Review, Vol. 139, Issue 4B
Three-nucleon calculations with realistic forces
journal, December 1970
- Malfliet, R. A.; Tjon, J. A.
- Annals of Physics, Vol. 61, Issue 2
Reduction of the Finite-Range Three-Body Problem in Two Variables
journal, July 1966
- Osborn, T.; Noyes, H. Pierre
- Physical Review Letters, Vol. 17, Issue 4
A non-exhaustive restatement of the angular momentum reduction in the three-body problem
journal, April 1973
- El Baz, E.; Fayard, C.; Lamot, G. -H.
- Acta Physica Academiae Scientiarum Hungaricae, Vol. 33, Issue 2
Angular-momentum reduction of the faddeev equations
journal, June 1969
- Balian, R.; Brézin, E.
- Il Nuovo Cimento B Series 10, Vol. 61, Issue 2
Tensor force in the separable potential model of neutron-deuteron collisions
journal, December 1969
- Sloan, Ian H.
- Nuclear Physics A, Vol. 139, Issue 2
The Faddeev equations for spin-dependent forces: calculation of 9Be binding energy
journal, December 1970
- Grubman, Ronald; Witten, Thomas
- Nuclear Physics A, Vol. 158, Issue 1
Theoretical angular distributions and polarizations in the three-body problem
journal, May 1971
- Fayard, C.; Lamot, G. H.; El Baz, E.
- Il Nuovo Cimento A, Vol. 3, Issue 1
Angular momentum states for three relativistic particles
journal, April 1962
- Wick, G. C.
- Annals of Physics, Vol. 18, Issue 1
Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.