Projection of angular momentum via linear algebra
Abstract
Projection of many-body states with good angular momentum from an initial state is usually accomplished by a three-dimensional integral. Here, we show how projection can instead be done by solving a straightforward system of linear equations. We demonstrate the method and give sample applications to $$^{48}$$Cr and $$^{60}$$Fe in the $pf$ shell. This new projection scheme, which is competitive against the standard numerical quadrature, should also be applicable to other quantum numbers such as isospin and particle number.
- Authors:
-
- San Diego State Univ., San Diego, CA (United States). Dept. of Physics
- Publication Date:
- Research Org.:
- San Diego State Univ., CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP)
- OSTI Identifier:
- 1430220
- Alternate Identifier(s):
- OSTI ID: 1410865
- Grant/Contract Number:
- FG02-03ER41272
- Resource Type:
- 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; mean-field; angular momentum projection
Citation Formats
Johnson, Calvin W., and O'Mara, Kevin D. Projection of angular momentum via linear algebra. United States: N. p., 2017.
Web. doi:10.1103/PhysRevC.96.064304.
Johnson, Calvin W., & O'Mara, Kevin D. Projection of angular momentum via linear algebra. United States. https://doi.org/10.1103/PhysRevC.96.064304
Johnson, Calvin W., and O'Mara, Kevin D. Fri .
"Projection of angular momentum via linear algebra". United States. https://doi.org/10.1103/PhysRevC.96.064304. https://www.osti.gov/servlets/purl/1430220.
@article{osti_1430220,
title = {Projection of angular momentum via linear algebra},
author = {Johnson, Calvin W. and O'Mara, Kevin D.},
abstractNote = {Projection of many-body states with good angular momentum from an initial state is usually accomplished by a three-dimensional integral. Here, we show how projection can instead be done by solving a straightforward system of linear equations. We demonstrate the method and give sample applications to $^{48}$Cr and $^{60}$Fe in the $pf$ shell. This new projection scheme, which is competitive against the standard numerical quadrature, should also be applicable to other quantum numbers such as isospin and particle number.},
doi = {10.1103/PhysRevC.96.064304},
journal = {Physical Review C},
number = 6,
volume = 96,
place = {United States},
year = {Fri Dec 01 00:00:00 EST 2017},
month = {Fri Dec 01 00:00:00 EST 2017}
}
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Works referenced in this record:
On the use of general symmetry-projected Hartree–Fock–Bogoliubov configurations in variational approaches to the nuclear many-body problem
journal, April 2004
- Schmid, K. W.
- Progress in Particle and Nuclear Physics, Vol. 52, Issue 2
Variation after projection with a triaxially deformed nuclear mean field
journal, December 2015
- Gao, Zao-Chun; Horoi, Mihai; Chen, Y. S.
- Physical Review C, Vol. 92, Issue 6
Recent development of Monte Carlo shell model and its application to no-core calculations
journal, August 2013
- Abe, T.; Maris, P.; Otsuka, T.
- Journal of Physics: Conference Series, Vol. 454
Angular momentum projected configuration interaction with realistic Hamiltonians
journal, January 2009
- Gao, Zao-Chun; Horoi, Mihai
- Physical Review C, Vol. 79, Issue 1
N3LO NN interaction adjusted to light nuclei in ab exitu approach
journal, October 2016
- Shirokov, A. M.; Shin, I. J.; Kim, Y.
- Physics Letters B, Vol. 761
Projected Hartree-Fock Spectra of -Shell Nuclei
journal, April 1967
- Gunye, M. R.; Warke, Chindhu S.
- Physical Review, Vol. 156, Issue 4
A symmetry-conserving description of odd nuclei with the Gogny force: Particle number and angular-momentum projection with self-consistent blocking
journal, September 2016
- Borrajo, M.; Egido, J. L.
- The European Physical Journal A, Vol. 52, Issue 9
Triaxial Projected Shell Model Approach
journal, May 1999
- Sheikh, J. A.; Hara, K.
- Physical Review Letters, Vol. 82, Issue 20
Effective interaction for -shell nuclei
journal, May 2002
- Honma, M.; Otsuka, T.; Brown, B. A.
- Physical Review C, Vol. 65, Issue 6
Fortran code of the Projected Shell Model: feasible shell model calculations for heavy nuclei
journal, August 1997
- Sun, Yang; Hara, Kenji
- Computer Physics Communications, Vol. 104, Issue 1-3
Demonstration of the auxiliary-field Monte Carlo approach for sd -shell nuclei
journal, March 1994
- Ormand, W. E.; Dean, D. J.; Johnson, C. W.
- Physical Review C, Vol. 49, Issue 3
Configuration mixing of angular-momentum-projected triaxial relativistic mean-field wave functions
journal, April 2010
- Yao, J. M.; Meng, J.; Ring, P.
- Physical Review C, Vol. 81, Issue 4
Nuclear Shell Model by the Quantum Monte Carlo Diagonalization Method
journal, October 1996
- Honma, Michio; Mizusaki, Takahiro; Otsuka, Takaharu
- Physical Review Letters, Vol. 77, Issue 16
Quadrupole collectivity in N≈28 nuclei with the angular momentum projected generator coordinate method
journal, January 2002
- Rodríguez-Guzmán, R.; Egido, J.; Robledo, L.
- Physical Review C, Vol. 65, Issue 2
Quality of the restricted variation after projection method with angular momentum projection
journal, April 2005
- Rodríguez, Tomás R.; Egido, J. L.; Robledo, L. M.
- Physical Review C, Vol. 71, Issue 4
Microscopic description of high-spin states: Quantum-number projections of the cranked Hartree-Fock-Bogoliubov self-consistent solution
journal, January 1999
- Enami, K.; Tanabe, K.; Yoshinaga, N.
- Physical Review C, Vol. 59, Issue 1
Exact angular momentum projection of cranked Hartree-Fock-Bogoliubov wave functions
journal, August 1982
- Hara, K.; Hayashi, A.; Ring, P.
- Nuclear Physics A, Vol. 385, Issue 1
Projected Shell Model and High-Spin Spectroscopy
journal, December 1995
- Hara, Kenji; Sun, Yang
- International Journal of Modern Physics E, Vol. 04, Issue 04
Monte Carlo evaluation of path integrals for the nuclear shell model
journal, October 1993
- Lang, G. H.; Johnson, C. W.; Koonin, S. E.
- Physical Review C, Vol. 48, Issue 4
Shell-model description of neutron-rich pf-shell nuclei with a new effective interaction GXPF 1
journal, April 2005
- Honma, M.; Otsuka, T.; Brown, B. A.
- The European Physical Journal A, Vol. 25, Issue S1
Three-dimensional angular momentum projection in relativistic mean-field theory
journal, April 2009
- Yao, J. M.; Meng, J.; Ring, P.
- Physical Review C, Vol. 79, Issue 4
Spin Projection in the Shell Model Monte Carlo Method and the Spin Distribution of Nuclear Level Densities
journal, October 2007
- Alhassid, Y.; Liu, S.; Nakada, H.
- Physical Review Letters, Vol. 99, Issue 16
Symmetry-projected Hartree–Fock–Bogoliubov equations
journal, February 2000
- Sheikh, Javid A.; Ring, Peter
- Nuclear Physics A, Vol. 665, Issue 1-2
Random phase approximation vs exact shell-model correlation energies
journal, September 2002
- Stetcu, Ionel; Johnson, Calvin W.
- Physical Review C, Vol. 66, Issue 3
Works referencing / citing this record:
Convergence and efficiency of angular momentum projection
journal, November 2018
- Johnson, Calvin W.; Jiao, Changfeng
- Journal of Physics G: Nuclear and Particle Physics, Vol. 46, Issue 1