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. 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.

arXiv comment14 pages, 2 figures, 1 table

References in corpus (13)

• Effective interaction for pf-shell nuclei
• Monte Carlo evaluation of path integrals for the nuclear shell model
• Configuration mixing of angular-momentum projected triaxial relativistic mean-field wave functions
• Triaxial projected shell model approach
• N3LO NN interaction adjusted to light nuclei in ab exitu approach
• Nuclear Shell Model by the Quantum Monte Carlo Diagonalization Method
• Three-dimensional angular momentum projection in relativistic mean-field theory
• Symmetry-Projected Hartree-Fock-Bogoliubov Equations
• Spin projection in the shell model Monte Carlo method and the spin distribution of nuclear level densities
• Demonstration of the auxiliary-field Monte Carlo approach for sd-shell nuclei
• RPA vs. exact shell-model correlation energies
• Variation after full projection with triaxially deformed nuclear mean field
• Angular Momentum Projected Configuration Interaction with Realistic Hamiltonians

Cited by in corpus (17)

• Symmetry restoration in mean-field approaches
• Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• The union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double-beta decay
• Convergence and efficiency of angular momentum projection for many-body systems
• The nucleon-pair approximation for nuclei from spherical to deformed regions
• Nuclear states projected from a pair condensate
• An effective and efficient algorithm for the Wigner rotation matrix at high angular momenta
• Nucleon-pair coupling scheme in Elliott's SU(3) model
• Benchmarking projected Hartree-Fock as an approximation
• Nucleon-pair truncation of the shell model for medium-heavy nuclei
• A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations
• Nuclear spectra from low-energy interactions
• Exact sum rules with approximate ground states
• $SO(3)$ quadratures in angular-momentum projection
• The pervasiveness of shape coexistence in nuclear pair condensates
• New angular momentum coupling method based on Wigner rotation theory