The nucleon-pair approximation for nuclei from spherical to deformed regions

Abstract

In this paper we model low-lying states of atomic nuclei in the nucleon-pair approximation of the shell model, using three approaches to select collective nucleon pairs: the generalized seniority scheme, the conjugate gradient method, and the Hartree-Fock approach. We find the collective pairs obtained from the generalized seniority scheme provides a good description for nearly spherical nuclei, and those from the conjugate gradient method or the Hartree-Fock approach work well for transitional and deformed nuclei. Our NPA calculations using collective pairs with angular momenta 0, 2, and 4 (denoted by $SDG$ pairs) reproduce the nuclear shape evolution in the $N=26$ isotones, ${}^{46}$Ca, ${}^{48}$Ti, ${}^{50}$Cr, and ${}^{52}$Fe, and yield good agreement with full configuration-interaction calculations of low-lying states in medium-heavy transitional and deformed nuclei: ${}^{44-48}$Ti, ${}^{48}$Cr, ${}^{50}$Cr, ${}^{52}$Fe, ${}^{60-64}$Zn, ${}^{64,66}$Ge, ${}^{84}$Mo, and ${}^{108-112}$Xe. Finally, using the $SDGI$-pair approximation we describe low-lying states of ${}^{112,114}$Ba, cases difficult to reach by conventional configuration-interaction methods.

References in corpus (21)

• The Shell Model as Unified View of Nuclear Structure
• Shell model study of the isobaric chains A=50, A=51 and A=52
• A Full $PF$ Shell Model Study of a~=~48 Nuclei
• Quantum Phase Transition in the Shape of Zr isotopes
• Spherical Shell Model description of rotational motion
• Factorization in large-scale many-body calculations
• Microscopic Formulation of Interacting Boson Model for Rotational Nuclei
• Coexistence of spherical states with deformed and superdeformed bands in doubly magic 40-Ca; A shell model challenge
• An Update of B(E2) Evaluation for 0+1 -> 2+1 Transitions in Even-Even Nuclei near N~Z~28
• Intertwined Quantum Phase Transitions in the Zr Isotopes
• The subtle connection between shape coexistence and quantum phase transition. The Zr case
• BIGSTICK: A flexible configuration-interaction shell-model code (updated)
• RPA vs. exact shell-model correlation energies
• Measurable bounds for Entanglement of Formation
• Quadrupole dominance in the light Sn and in the Cd isotopes
• Nucleons pair shell model in M-scheme
• Projection of angular momentum via linear algebra
• Nucleon-pair approximation with matrix representation
• From deformed Hartree-Fock to the nucleon-pair approximation
• Two-neutron transfer reactions and shape phase transitions in the microscopically-formulated interacting boson model
• Variational approach for pair optimization in the nucleon pair approximation

Cited by in corpus (3)

• Nuclear states projected from a pair condensate
• Nucleon-pair truncation of the shell model for medium-heavy nuclei
• Band-like structures and quartets in deformed N=Z nuclei