Projection of good quantum numbers for reaction fragments

Bulgac, Aurel

doi:10.1103/PhysRevC.100.034612

Title: Projection of good quantum numbers for reaction fragments

Abstract

In reactions the wave packets of the emerging products normally are not eigenstates of particle number operators or any other conserved quantities and their properties are entangled. I describe here a particle projection technique in parts of space, which eschews the need to evaluate Pfaffians in the case of overlap of generalized Slater determinants or Hartree-Fock-Bogoliubov type of vacua. The extension of these formulas for calculating either angular momentum or particle projected energy distributions of the reaction fragments are presented as well. The generalization to simultaneous particle and angular momentum projection of various reaction fragment observables is straightforward.

Authors:

^[1]

Univ. of Washington, Seattle, WA (United States)

Publication Date:: Mon Sep 16 00:00:00 EDT 2019

Research Org.:: Texas A & M Univ., College Station, TX (United States)

Sponsoring Org.:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1608951

Grant/Contract Number:: NA0003841; FG02-97ER41014

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review C

Additional Journal Information:: Journal Volume: 100; Journal Issue: 3; Journal ID: ISSN 2469-9985

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Bulgac, Aurel. Projection of good quantum numbers for reaction fragments.  United States: N. p., 2019. 
Web.  doi:10.1103/PhysRevC.100.034612.

Copy to clipboard


                    Bulgac, Aurel. Projection of good quantum numbers for reaction fragments.  United States.  https://doi.org/10.1103/PhysRevC.100.034612

Copy to clipboard


                    Bulgac, Aurel. Mon .  
"Projection of good quantum numbers for reaction fragments".  United States.  https://doi.org/10.1103/PhysRevC.100.034612.  https://www.osti.gov/servlets/purl/1608951.

Copy to clipboard


                    
@article{osti_1608951,

  title        = {Projection of good quantum numbers for reaction fragments},

  author       = {Bulgac, Aurel},

  abstractNote = {In reactions the wave packets of the emerging products normally are not eigenstates of particle number operators or any other conserved quantities and their properties are entangled. I describe here a particle projection technique in parts of space, which eschews the need to evaluate Pfaffians in the case of overlap of generalized Slater determinants or Hartree-Fock-Bogoliubov type of vacua. The extension of these formulas for calculating either angular momentum or particle projected energy distributions of the reaction fragments are presented as well. The generalization to simultaneous particle and angular momentum projection of various reaction fragment observables is straightforward.},

  doi          = {10.1103/PhysRevC.100.034612},

  journal      = {Physical Review C},

  number       = 3,

  volume       = 100,

  place        = {United States},

  year         = {Mon Sep 16 00:00:00 EDT 2019},

  month        = {Mon Sep 16 00:00:00 EDT 2019}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Accepted Manuscript (DOE)

Publisher's Version of Record

https://doi.org/10.1103/PhysRevC.100.034612

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 9 works

Citation information provided by
Web of Science

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
journal, May 1935

Einstein, A.; Podolsky, B.; Rosen, N.
Physical Review, Vol. 47, Issue 10
DOI: 10.1103/PhysRev.47.777

Generator coordinate method applied to nuclei in the transition region
journal, May 1966

Onishi, Naoki; Yoshida, Shiro
Nuclear Physics, Vol. 80, Issue 2
DOI: 10.1016/0029-5582(66)90096-4

Symmetry Restoration in Hartree-Fock-Bogoliubov Based Theories
journal, January 2012

Bertsch, G. F.; Robledo, L. M.
Physical Review Letters, Vol. 108, Issue 4
DOI: 10.1103/PhysRevLett.108.042505

Angular momentum of fission fragments
journal, March 2019

Bertsch, G. F.; Kawano, T.; Robledo, L. M.
Physical Review C, Vol. 99, Issue 3
DOI: 10.1103/PhysRevC.99.034603

Renormalization of the Hartree-Fock-Bogoliubov Equations in the Case of a Zero Range Pairing Interaction
journal, January 2002

Bulgac, Aurel; Yu, Yongle
Physical Review Letters, Vol. 88, Issue 4
DOI: 10.1103/PhysRevLett.88.042504

Evaluation of overlaps between arbitrary fermionic quasiparticle vacua
journal, March 2012

Avez, B.; Bender, M.
Physical Review C, Vol. 85, Issue 3
DOI: 10.1103/PhysRevC.85.034325

The canonical form of an antisymmetric tensor and its application to the theory of superconductivity
journal, December 1962

Bloch, Claude; Messiah, Albert
Nuclear Physics, Vol. 39
DOI: 10.1016/0029-5582(62)90377-2

Why does the sign problem occur in evaluating the overlap of HFB wave functions?
journal, April 2018

Mizusaki, Takahiro; Oi, Makito; Shimizu, Noritaka
Physics Letters B, Vol. 779
DOI: 10.1016/j.physletb.2018.02.012

Angular momentum of fission fragments
journal, June 2001

Mikhailov, I. N.; Quentin, P.; Briançon, Ch.
Physics of Atomic Nuclei, Vol. 64, Issue 6
DOI: 10.1134/1.1383626

Particle Transfer Reactions with the Time-Dependent Hartree-Fock Theory Using a Particle Number Projection Technique
journal, November 2010

Simenel, Cédric
Physical Review Letters, Vol. 105, Issue 19
DOI: 10.1103/PhysRevLett.105.192701

Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states
journal, June 2014

Hu, Qing-Li; Gao, Zao-Chun; Chen, Y. S.
Physics Letters B, Vol. 734
DOI: 10.1016/j.physletb.2014.05.045

Number of particles in fission fragments
journal, August 2019

Verriere, Marc; Schunck, Nicolas; Kawano, Toshihiko
Physical Review C, Vol. 100, Issue 2
DOI: 10.1103/PhysRevC.100.024612

Grassmann integral and Balian–Brézin decomposition in Hartree–Fock–Bogoliubov matrix elements
journal, August 2013

Mizusaki, Takahiro; Oi, Makito; Chen, Fang-Qi
Physics Letters B, Vol. 725, Issue 1-3
DOI: 10.1016/j.physletb.2013.07.005

Particle transfer reactions with the time-dependent Hartree-Fock theory using a particle number projection technique
text, January 2010

Simenel, Cédric
arXiv
DOI: 10.48550/arxiv.1008.3033

Symmetry restoration in Hartree-Fock-Bogoliubov based theories
text, January 2011

Bertsch, G. F.; Robledo, L. M.
arXiv
DOI: 10.48550/arxiv.1108.5479

Evaluation of overlaps between arbitrary Fermionic quasiparticle vacua
text, January 2011

Avez, Benoît; Bender, Michael
arXiv
DOI: 10.48550/arxiv.1109.2078

Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states
text, January 2013

Hu, Qing-Li; Gao, Zao-Chun; Chen, Y. S.
arXiv
DOI: 10.48550/arxiv.1307.6905

Why does the sign problem occur in evaluating the overlap of HFB wave functions?
text, January 2017

Mizusaki, Takahiro; Oi, Makito; Shimizu, Noritaka
arXiv
DOI: 10.48550/arxiv.1711.00369

Angular momentum of fission fragments
text, January 2018

Bertsch, G. F.; Kawano, T.; Robledo, Lm.
arXiv
DOI: 10.48550/arxiv.1810.13429

Symmetry-Projected Hartree-Fock-Bogoliubov Equations
text, January 1999

Sheikh, Javid A.; Ring, Peter
arXiv
DOI: 10.48550/arxiv.nucl-th/9907065

Works referencing / citing this record:

Counting statistics in finite Fermi systems: Illustrations with the atomic nucleus
journal, January 2020

Lacroix, Denis; Ayik, Sakir
Physical Review C, Vol. 101, Issue 1
DOI: 10.1103/physrevc.101.014310

Similar Records in DOE PAGES and OSTI.GOV collections:

Generation, dynamics, and correlations of the fission fragments' angular momenta

Journal Article Scamps, Guillaume ; Bertsch, George - Physical Review. C

The generation of angular momentum in fissioning nuclei is not well understood. The predictions of different models disagree, particularly concerning the correlation between the fragments' angular momenta. In this article, a time-dependent collective Hamiltonian model is proposed to treat the generation of the angular momentum in the fission fragments due to the quantum uncertainty principle as well as the dynamics of the collective wave function during and after scission. The model is constructed in the framework of the frozen Hartree-Fock approximation using a Skyrme energy functional to extract deformations of the fission fragments as well as the interactions in a derived collective Hamiltonian. The fission reactions studied aremore »« less
https://doi.org/10.1103/physrevc.108.034616
VAMPIR describes shape coexistence in nuclei

Book Faessler, A

The measurements of shape coexistence of the Vanderbilt-Oak Ridge-LSU-Georgia-Tech-Group is shortly reviewed for the Hg isotopes and the mass 70 region. Then this contribution concentrates on the description of shape coexistence with the help of refined self-consistent fields plus correlations. The basic approach is VAMPIR which starts from an angular momentum, proton and neutron number and parity projected Hartree-Fock-Bogoliubov quasi-particle Slater determinant. VAMPIR stands for Variation After Mean field Projection In Realistic models spaces. Minimization of orthogonalized projected HFB states yields also shape coexistence exited states of the same symmetries. Those states can then be diagonalized to include correlations (excitedmore »« less
Quantum number projection at finite temperature via thermofield dynamics

Journal Article Tanabe, K ; Nakada, H ; Department of Physics, Faculty of Science, Chiba University, Inage, Chiba 263-8522 - Physical Review. C, Nuclear Physics

Applying thermofield dynamics, we reformulate the exact quantum number projection in the finite-temperature Hartree-Fock-Bogoliubov theory. Explicit formulas are derived for the simultaneous projection of particle number and angular momentum, in parallel to the zero-temperature case. We also propose a practical method for the variation-after-projection calculation, by approximating entropy consistently with the Peierls inequality. Using quantum number projection in finite-temperature mean-field theory will be useful for studying the effects of quantum fluctuations associated with the conservation laws on thermal properties of nuclei.
https://doi.org/10.1103/PhysRevC.71.024314
Technical aspects of the evaluation of the overlap of Hartree-Fock-Bogoliubov wave functions

Journal Article Robledo, L M - Physical Review. C, Nuclear Physics

Several technical aspects concerning the evaluation of the overlap between two mean-field wave functions of the Hartree-Fock-Bogoliubov type are discussed. The limit when several orbitals become fully occupied is derived as well as the formula to reduce the dimensionality of the problem when exactly empty orbitals are present. The formalism is also extended to deal with different bases for each of the wave functions. Several practical results concerning the evaluation of pfaffians, as well as the canonical decomposition of norm overlaps, are also discussed in the Appendices.
https://doi.org/10.1103/PHYSREVC.84.014307
Nuclear structure theory in spin- and number-conserving quasiparticle configuration spaces: First applications

Journal Article Schmid, K W ; Gruemmer, F ; Faessler, A - Phys. Rev. C; (United States)

In the first part of the present series of two papers we discussed several nuclear structure models all working in configuration spaces consisting of spin- and number-projected quasiparticle determinants. In the present paper a particular version of the numerically simplest of these models is presented. This model approximates the nuclear wave functions by linear combinations of the angular momentum- and particle number-projected Hartree-Fock-Bogoliubov vacuum and the equally spin- and number-projected two quasiparticle excitations with respect to it. The model allows the use of realistic two body interactions and rather large model spaces. It can hence be applied to a largemore »« less
https://doi.org/10.1103/PhysRevC.29.308

Similar Records

Title: Projection of good quantum numbers for reaction fragments

Abstract

Citation Formats

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? journal, May 1935

Generator coordinate method applied to nuclei in the transition region journal, May 1966

Symmetry Restoration in Hartree-Fock-Bogoliubov Based Theories journal, January 2012

Angular momentum of fission fragments journal, March 2019

Renormalization of the Hartree-Fock-Bogoliubov Equations in the Case of a Zero Range Pairing Interaction journal, January 2002

Evaluation of overlaps between arbitrary fermionic quasiparticle vacua journal, March 2012

The canonical form of an antisymmetric tensor and its application to the theory of superconductivity journal, December 1962

Why does the sign problem occur in evaluating the overlap of HFB wave functions? journal, April 2018

Angular momentum of fission fragments journal, June 2001

Particle Transfer Reactions with the Time-Dependent Hartree-Fock Theory Using a Particle Number Projection Technique journal, November 2010

Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states journal, June 2014

Number of particles in fission fragments journal, August 2019

Grassmann integral and Balian–Brézin decomposition in Hartree–Fock–Bogoliubov matrix elements journal, August 2013

Particle transfer reactions with the time-dependent Hartree-Fock theory using a particle number projection technique text, January 2010

Symmetry restoration in Hartree-Fock-Bogoliubov based theories text, January 2011

Evaluation of overlaps between arbitrary Fermionic quasiparticle vacua text, January 2011

Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states text, January 2013

Why does the sign problem occur in evaluating the overlap of HFB wave functions? text, January 2017

Angular momentum of fission fragments text, January 2018

Symmetry-Projected Hartree-Fock-Bogoliubov Equations text, January 1999

Counting statistics in finite Fermi systems: Illustrations with the atomic nucleus journal, January 2020

Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
journal, May 1935

Generator coordinate method applied to nuclei in the transition region
journal, May 1966

Symmetry Restoration in Hartree-Fock-Bogoliubov Based Theories
journal, January 2012

Angular momentum of fission fragments
journal, March 2019

Renormalization of the Hartree-Fock-Bogoliubov Equations in the Case of a Zero Range Pairing Interaction
journal, January 2002

Evaluation of overlaps between arbitrary fermionic quasiparticle vacua
journal, March 2012

The canonical form of an antisymmetric tensor and its application to the theory of superconductivity
journal, December 1962

Why does the sign problem occur in evaluating the overlap of HFB wave functions?
journal, April 2018

Angular momentum of fission fragments
journal, June 2001

Particle Transfer Reactions with the Time-Dependent Hartree-Fock Theory Using a Particle Number Projection Technique
journal, November 2010

Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states
journal, June 2014

Number of particles in fission fragments
journal, August 2019

Grassmann integral and Balian–Brézin decomposition in Hartree–Fock–Bogoliubov matrix elements
journal, August 2013

Particle transfer reactions with the time-dependent Hartree-Fock theory using a particle number projection technique
text, January 2010

Symmetry restoration in Hartree-Fock-Bogoliubov based theories
text, January 2011

Evaluation of overlaps between arbitrary Fermionic quasiparticle vacua
text, January 2011

Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states
text, January 2013

Why does the sign problem occur in evaluating the overlap of HFB wave functions?
text, January 2017

Angular momentum of fission fragments
text, January 2018

Symmetry-Projected Hartree-Fock-Bogoliubov Equations
text, January 1999

Counting statistics in finite Fermi systems: Illustrations with the atomic nucleus
journal, January 2020