in a three-body model with realistic Forces: Separable versus nonseparable approach
Abstract
Background: Deuteron induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d, p) reactions may be viewed as three-body reactions and described with Faddeev techniques. Purpose: Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. However, it needs to be demonstrated that their solution based on separable interactions agrees exactly with solutions based on nonseparable forces. Methods: Momentum space Faddeev equations are solved with nonseparable and separable forces as coupled integral equations. Results: The ground state of 6Li is calculated via momentum space Faddeev equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)-4He force. For the latter the Pauli-forbidden S-wave bound state is projected out. This result is compared to a calculation in which the interactions in the two-body subsystems are represented by separable interactions derived in the Ernst-Shakin-Thaler (EST) framework. Conclusions: We find that calculations based on the separable representation of the interactions and the original interactions give results that agree to four significant figures for the binding energy, provided that energy and momentum support points of the EST expansion are chosen independently. The momentum distributionsmore »
- Authors:
-
- Michigan State Univ., East Lansing, MI (United States). National Superconducting Cyclotron Lab. and Dept. of Physics and Astronomy
- Ohio Univ., Athens, OH (United States). Inst. of Nuclear and Particle Physics and Dept. of Physics and Astronomy
- Julich Research Centre, JHCP and JARA-HPC (Germany). Inst. of Plasma Physics and Nuclear Physics
- Publication Date:
- Research Org.:
- Michigan State Univ., East Lansing, MI (United States); Ohio Univ., Athens, OH (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF); German Research Foundation (DFG); National Natural Science Foundation of China (NSFC)
- Contributing Org.:
- Julich Supercomputing Centre (JSC) (Germany); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
- OSTI Identifier:
- 1463321
- Alternate Identifier(s):
- OSTI ID: 1414847
- Grant/Contract Number:
- NA0002132; NSF-PHY-1520972; NSF-PHY-1520929; FG02-93ER40756; 11621131001; TRR110; AC02-05CH11231
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physical Review C
- Additional Journal Information:
- Journal Volume: 96; Journal Issue: 6; Journal ID: ISSN 2469-9985
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 73 NUCLEAR PHYSICS AND RADIATION PHYSICS; few-body systems; binding energies and masses; light nuclei; nuclear forces; H & He induced nuclear reactions; 6 ≤ A ≤ 19
Citation Formats
Hlophe, L., Lei, Jin, Elster, Ch., Nogga, A., and Nunes, F. M. Li6 in a three-body model with realistic Forces: Separable versus nonseparable approach. United States: N. p., 2017.
Web. doi:10.1103/PhysRevC.96.064003.
Hlophe, L., Lei, Jin, Elster, Ch., Nogga, A., & Nunes, F. M. Li6 in a three-body model with realistic Forces: Separable versus nonseparable approach. United States. https://doi.org/10.1103/PhysRevC.96.064003
Hlophe, L., Lei, Jin, Elster, Ch., Nogga, A., and Nunes, F. M. 2017.
"Li6 in a three-body model with realistic Forces: Separable versus nonseparable approach". United States. https://doi.org/10.1103/PhysRevC.96.064003. https://www.osti.gov/servlets/purl/1463321.
@article{osti_1463321,
title = {Li6 in a three-body model with realistic Forces: Separable versus nonseparable approach},
author = {Hlophe, L. and Lei, Jin and Elster, Ch. and Nogga, A. and Nunes, F. M.},
abstractNote = {Background: Deuteron induced reactions are widely used to probe nuclear structure and astrophysical information. Those (d, p) reactions may be viewed as three-body reactions and described with Faddeev techniques. Purpose: Faddeev equations in momentum space have a long tradition of utilizing separable interactions in order to arrive at sets of coupled integral equations in one variable. However, it needs to be demonstrated that their solution based on separable interactions agrees exactly with solutions based on nonseparable forces. Methods: Momentum space Faddeev equations are solved with nonseparable and separable forces as coupled integral equations. Results: The ground state of 6Li is calculated via momentum space Faddeev equations using the CD-Bonn neutron-proton force and a Woods-Saxon type neutron(proton)-4He force. For the latter the Pauli-forbidden S-wave bound state is projected out. This result is compared to a calculation in which the interactions in the two-body subsystems are represented by separable interactions derived in the Ernst-Shakin-Thaler (EST) framework. Conclusions: We find that calculations based on the separable representation of the interactions and the original interactions give results that agree to four significant figures for the binding energy, provided that energy and momentum support points of the EST expansion are chosen independently. The momentum distributions computed in both approaches also fully agree with each other.},
doi = {10.1103/PhysRevC.96.064003},
url = {https://www.osti.gov/biblio/1463321},
journal = {Physical Review C},
issn = {2469-9985},
number = 6,
volume = 96,
place = {United States},
year = {Tue Dec 26 00:00:00 EST 2017},
month = {Tue Dec 26 00:00:00 EST 2017}
}
Web of Science
Works referenced in this record:
Energy levels of light nuclei A = 5−10
journal, December 1988
- Ajzenberg-Selove, F.
- Nuclear Physics A, Vol. 490, Issue 1
Excluded bound state in the interaction and the three-body binding energies of and
journal, June 1982
- Lehman, D. R.
- Physical Review C, Vol. 25, Issue 6
Applications of Nuclear Science for Stewardship Science
journal, March 2013
- Cizewski, Jolie A.
- Journal of Physics: Conference Series, Vol. 420
Erratum: Nucleon polarization in three-body models of polarized
journal, July 1995
- Schellingerhout, N. W.; Kok, L. P.; Coon, S. A.
- Physical Review C, Vol. 52, Issue 1
Accurate nucleon-nucleon potential with charge-independence breaking
journal, January 1995
- Wiringa, R. B.; Stoks, V. G. J.; Schiavilla, R.
- Physical Review C, Vol. 51, Issue 1
Nucleon-Deuteron Scattering with $\Delta $ -Isobar Excitation, I: Test of Separable Expansion
journal, December 1998
- Nemoto, S.; Chmielewski, K.; Schellingerhout, N. W.
- Few-Body Systems, Vol. 24, Issue 4
Separable representation of energy-dependent optical potentials
journal, March 2016
- Hlophe, L.; Elster, Ch.
- Physical Review C, Vol. 93, Issue 3
Separable-potential three-body model of the system. II. ground state
journal, February 1978
- Lehman, D. R.; Rai, Mamta; Ghovanlou, A.
- Physical Review C, Vol. 17, Issue 2
Benchmark calculation of and scattering
journal, March 2017
- Viviani, M.; Deltuva, A.; Lazauskas, R.
- Physical Review C, Vol. 95, Issue 3
Testing the continuum-discretized coupled channels method for deuteron-induced reactions
journal, May 2012
- Upadhyay, N. J.; Deltuva, A.; Nunes, F. M.
- Physical Review C, Vol. 85, Issue 5
Deuteron stripping and pickup involving the halo nuclei and
journal, May 2009
- Deltuva, A.
- Physical Review C, Vol. 79, Issue 5
Angular-momentum reduction of the faddeev equations
journal, June 1969
- Balian, R.; Brézin, E.
- Il Nuovo Cimento B Series 10, Vol. 61, Issue 2
Scattering and break-up of deuterons on α-particles in a realistic three-body model
journal, August 1983
- Bang, J.; Benayoun, J. -J.; Gignoux, C.
- Nuclear Physics A, Vol. 405, Issue 1
Renormalization of one-pion exchange and power counting
journal, November 2005
- Nogga, A.; Timmermans, R. G. E.; Kolck, U. van
- Physical Review C, Vol. 72, Issue 5
Separable representation of the Bonn nucleon-nucleon potential
journal, February 1986
- Haidenbauer, J.; Koike, Y.; Plessas, W.
- Physical Review C, Vol. 33, Issue 2
Construction of high-quality NN potential models
journal, June 1994
- Stoks, V. G. J.; Klomp, R. A. M.; Terheggen, C. P. F.
- Physical Review C, Vol. 49, Issue 6
Neutron Single Particle Structure in and Direct Neutron Capture Cross Sections
journal, October 2012
- Kozub, R. L.; Arbanas, G.; Adekola, A. S.
- Physical Review Letters, Vol. 109, Issue 17
Constraint of the Astrophysical Destruction Rate at Stellar Temperatures
journal, May 2015
- Pain, S. D.; Bardayan, D. W.; Blackmon, J. C.
- Physical Review Letters, Vol. 114, Issue 21
Isospin dependent global nucleon-nucleus optical model at intermediate energies
journal, September 2009
- Weppner, S. P.; Penney, R. B.; Diffendale, G. W.
- Physical Review C, Vol. 80, Issue 3
Three-body Faddeev-Alt-Grassberger-Sandhas approach to direct nuclear reactions
journal, January 2009
- Deltuva, A.; Fonseca, A. C.
- Physical Review C, Vol. 79, Issue 1
Accurate charge-dependent nucleon-nucleon potential at fourth order of chiral perturbation theory
journal, October 2003
- Entem, D. R.; Machleidt, R.
- Physical Review C, Vol. 68, Issue 4
α- d resonances and the low-lying states of
journal, December 1992
- Eskandarian, A.; Afnan, I. R.
- Physical Review C, Vol. 46, Issue 6
Faddeev-type calculation of three-body nuclear reactions including core excitation
journal, July 2013
- Deltuva, A.
- Physical Review C, Vol. 88, Issue 1
Generalized Faddeev equations in the Alt-Grassberger-Sandhas form for deuteron stripping with explicit inclusion of target excitations and Coulomb interaction
journal, September 2012
- Mukhamedzhanov, A. M.; Eremenko, V.; Sattarov, A. I.
- Physical Review C, Vol. 86, Issue 3
Separable approximations of two-body interactions
journal, January 1983
- Haidenbauer, J.; Plessas, W.
- Physical Review C, Vol. 27, Issue 1
Benchmark test calculation of a four-nucleon bound state
journal, August 2001
- Kamada, H.; Nogga, A.; Glöckle, W.
- Physical Review C, Vol. 64, Issue 4
Halo Nucleus : A Spectroscopic Study via Neutron Transfer
journal, May 2012
- Schmitt, K. T.; Jones, K. L.; Bey, A.
- Physical Review Letters, Vol. 108, Issue 19
The Formal Theory of Scattering
journal, July 1953
- Gell-Mann, M.; Goldberger, M. L.
- Physical Review, Vol. 91, Issue 2
Pauli blocking in three-body models of halo nuclei
journal, January 2000
- Thompson, I. J.; Danilin, B. V.; Efros, V. D.
- Physical Review C, Vol. 61, Issue 2
Toward a complete theory for predicting inclusive deuteron breakup away from stability
journal, September 2017
- Potel, G.; Perdikakis, G.; Carlson, B. V.
- The European Physical Journal A, Vol. 53, Issue 9
R-matrix formulation and phase shifts for n-4He and p-4He scattering for energies up to 20 MeV
journal, January 1972
- Stammbach, Th.; Walter, R. L.
- Nuclear Physics A, Vol. 180, Issue 1
Direct reaction measurements with a Sn radioactive ion beam
journal, September 2011
- Jones, K. L.; Nunes, F. M.; Adekola, A. S.
- Physical Review C, Vol. 84, Issue 3
Nucleon polarization in three-body models of polarized
journal, December 1993
- Schellingerhout, N. W.; Kok, L. P.; Coon, S. A.
- Physical Review C, Vol. 48, Issue 6
A realistic three-body model of 6Li with local interactions
journal, January 1979
- Bang, J.; Gignoux, C.
- Nuclear Physics A, Vol. 313, Issue 1-2
Local and global nucleon optical models from 1 keV to 200 MeV
journal, January 2003
- Koning, A. J.; Delaroche, J. P.
- Nuclear Physics A, Vol. 713, Issue 3-4
Adiabatic approximation versus exact Faddeev method for ( ) and ( ) reactions
journal, September 2011
- Nunes, F. M.; Deltuva, A.
- Physical Review C, Vol. 84, Issue 3
Separable-potential three-body model of the system. I. ground state
journal, May 1974
- Ghovanlou, A.; Lehman, D. R.
- Physical Review C, Vol. 9, Issue 5
Separable representation of proton-nucleus optical potentials
journal, December 2014
- Hlophe, L.; Eremenko, V.; Elster, Ch.
- Physical Review C, Vol. 90, Issue 6
Compound-nuclear reaction cross sections from surrogate measurements
journal, March 2012
- Escher, Jutta E.; Burke, Jason T.; Dietrich, Frank S.
- Reviews of Modern Physics, Vol. 84, Issue 1
Separable representation of phenomenological optical potentials of Woods-Saxon type
journal, December 2013
- Hlophe, L.; Elster, Ch.; Johnson, R. C.
- Physical Review C, Vol. 88, Issue 6
Quality of the three-nucleon bound-state wave function from a two-nucleon separable expansion method
journal, June 1991
- Parke, W. C.; Koike, Y.; Lehman, D. R.
- Few-Body Systems, Vol. 11, Issue 2-3
The orthogonal projection method in scattering theory
journal, April 1978
- Kukulin, V. I.; Pomerantsev, V. N.
- Annals of Physics, Vol. 111, Issue 2
High-precision, charge-dependent Bonn nucleon-nucleon potential
journal, January 2001
- Machleidt, R.
- Physical Review C, Vol. 63, Issue 2
Separable Representations of Two-Body Interactions
journal, July 1973
- Ernst, D. J.; Shakin, C. M.; Thaler, R. M.
- Physical Review C, Vol. 8, Issue 1
A global nucleon optical model potential
journal, March 1991
- Varner, R. L.; Thompson, W. J.; McAbee, T. L.
- Physics Reports, Vol. 201, Issue 2
Predictions of the Paris N - N potential for three-nucleon continuum observables: Comparison of two approaches
journal, June 1990
- Cornelius, T.; Glöckle, W.; Haidenbauer, J.
- Physical Review C, Vol. 41, Issue 6
Separable representations of matrices valid in the vicinity of off-shell points
journal, May 1974
- Ernst, D. J.; Shakin, C. M.; Thaler, R. M.
- Physical Review C, Vol. 9, Issue 5
Bound state properties of Borromean halo nuclei: 6He and 11Li
journal, August 1993
- Zhukov, M. V.; Danilin, B. V.; Fedorov, D. V.
- Physics Reports, Vol. 231, Issue 4