Toward extremes of angular momentum: Application of the Pfaffian algorithm in realistic calculations

Abstract

In a calculation of rotated matrix elements with angular momentum projection, the generalized Wick's theorem may encounter a practical problem of combinatorial complexity when the configurations have more than four quasi-particles (qps). The problem can be solved by employing the Pfaffian algorithm generally applicable to calculations of matrix elements for Hartree-Fock-Bogoliubov states with any number of qps. This breakthrough in many-body techniques enables studies of high-spin states in a shell-model framework. As the first application of the Pfaffian algorithm, the configuration space of the Projected Shell Model is expanded to include 6-qp states for both positive and negative parities. Taking ${}^{166}$Hf as an example, we show that 6-qp states become the main configuration of the yrast band beyond spin $I\approx 34\hslash$, which explains the observed third back-bending in moment of inertia. Structures of multi-qp high-$K$ isomers in ${}^{176}$Hf are analyzed as another example.

arXiv comment6 pages, 3 figures, 1 table. Accepted version to appear in PRC-Rapid Communication

References in corpus (13)

• Nuclear Ground-State Masses and Deformations
• Enhanced Stability of Superheavy Nuclei due to High-Spin Isomerism
• The sign of the overlap of HFB wave functions
• Symmetry restoration in Hartree-Fock-Bogoliubov based theories
• Ideal magnetohydrodynamic simulations of unmagnetized dense plasma jet injection into a hot strongly magnetized plasma
• Multi-phonon $\gamma$-vibrational bands in odd-mass nuclei studied by triaxial projected shell model approach
• Evaluation of overlaps between arbitrary Fermionic quasiparticle vacua
• Mixing of quasiparticle excitations and gamma-vibrations in transitional nuclei
• Matrix elements of one-body and two-body operators between arbitrary HFB multi-quasiparticle states
• Numeric and symbolic evaluation of the pfaffian of general skew-symmetric matrices
• Technical aspects of the evaluation of the overlap of Hartree- Fock- Bogoliubov wave functions
• A new formulation to calculate general HFB matrix elements through Pfaffian
• Norm-overlap formula of Hartree-Fock-Bogoliubov states with odd number parity

Cited by in corpus (11)

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• Urca Cooling in Neutron Star Crusts and Oceans: Effects of Nuclear Excitations
• Systematic study of near yrast band structures in odd-mass ${}^{125-137}$Pr and ${}^{127-139}$Pm isotopes
• Extended triaxial projected shell model approach for odd-neutron nuclei
• An effective and efficient algorithm for the Wigner rotation matrix at high angular momenta
• Projected shell model description of nuclear level density: Collective, pair-breaking, and multiquasiparticle regimes in even-even nuclei
• Description of ${}^{93}$Nb stellar electron-capture rates by the Projected Shell Model
• A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations
• New angular momentum coupling method based on Wigner rotation theory