Hartree-Fock-Bogoliubov theory for odd-mass nuclei with a time-odd constraint and application to deformed halo nuclei

Abstract

We show that the lowest-energy solution of the Hartree-Fock-Bogoliubov (HFB) equation has the even particle-number parity as long as the time-reversal symmetry is conserved in the HFB Hamiltonian without null eigenvalues. Based on this finding, we give a rigorous foundation of a method for solving the HFB equation to describe the ground state of odd-mass nuclei by employing a time-reversal anti-symmetric constraint operator to the Hamiltonian, where one obtains directly the ground state as a self-consistent solution of the cranked-HFB-type equation. Numerical analysis is done for the neutron-rich Mg isotopes with a reasonable choice for the operator, and it is demonstrated that the anomalous increase in the matter radius of ${}^{37}$Mg is well described when the last neutron occupies a low angular-momentum orbital in the framework of the nuclear energy-density-functional method, revealing the deformed halo structure.

arXiv comment34 pages, 4 figures, to appear in PTEP

References in corpus (37)

• Unpaired Majorana fermions in quantum wires
• Systematic study of deformed nuclei at the drip lines and beyond
• Neutron halo in deformed nuclei
• Time-dependent density-functional description of nuclear dynamics
• Odd-Even Staggering of Nuclear Masses: Pairing or Shape Effect?
• Correlations beyond the mean field in Magnesium isotopes: Angular momentum projection and configuration mixing
• Microscopic justification of the Equal Filling approximation
• A new effective interaction for $0\hslash \omega$ shell model calculations in the sdpf valence space
• Deformed relativistic Hartree Bogoliubov theory in continuum
• Time-odd components in the mean field of rotating superdeformed nuclei
• Odd-even mass differences from self-consistent mean-field theory
• The merging of the islands of inversion at N=20 and N=28
• One-quasiparticle States in the Nuclear Energy Density Functional Theory
• Continuum Linear Response in Coordinate Space Hartree-Fock-Bogoliubov Formalism for Collective Excitations in Drip-line Nuclei
• Deformation of Nuclei Close to the Two-Neutron Drip Line in Mg Region
• The sign of the overlap of HFB wave functions
• Nuclear landscape in covariant density functional theory
• Pairing correlations. Part 1: description of odd nuclei in mean-field theories
• Broyden's Method in Nuclear Structure Calculations
• Deformed nuclear halos
• Ground-state properties of neutron-rich Mg isotopes
• Axially symmetric Hartree-Fock-Bogoliubov Calculations for Nuclei Near the Drip-Lines
• Deformed Coordinate-Space Hartree-Fock-Bogoliubov Approach to Weakly Bound Nuclei and Large Deformations
• Solution of the Skyrme-Hartree-Fock-Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis. (IV) HFODD (v2.07f): a new version of the program
• Time-odd mean fields in covariant density functional theory I. Non-rotating systems
• Coordinate Space HFB Calculations for the Zirconium Isotope Chain up to the Two-Neutron Dripline
• Shape fluctuations in the ground and excited 0+ states of 30Mg and 32Mg
• Time-odd mean fields in the rotating frame: microscopic nature of nuclear magnetism
• Deformed one-quasiparticle states in covariant density functional theory
• Intertwined effects of pairing and deformation on neutron halos in magnesium isotopes
• Hartree-Fock-Bogoliubov Theory of Polarized Fermi Systems
• Low-lying dipole resonance in neutron-rich Ne isotopes
• Role of deformation in odd-even staggering in reaction cross sections for ${}^{30,31,32}$Ne and ${}^{36,37,38}$Mg isotopes
• Deformation around neutron-rich Cr isotopes in axially symmetric Skyrme-Hatree-Fock-Bogoliubov method
• Role of low-$l$ component in deformed wave functions near the continuum threshold
• Skyrme-QRPA calculations for low-lying excitation modes in deformed neutron-rich nuclei
• Simultaneous analysis of matter radii, transition probabilities, and excitation energies of Mg isotopes by angular-momentum-projected configuration-mixing calculations

Cited by in corpus (11)

• Deformed relativistic Hartree-Bogoliubov theory in continuum with a point-coupling functional. II. Examples of odd Nd isotopes
• Missed prediction of the neutron halo in ${}^{37}$Mg
• Angular momentum projection in the deformed relativistic Hartree-Bogoliubov theory in continuum
• Role of triaxiality in deformed halo nuclei
• $\beta$-decay half-lives as an indicator of shape-phase transition in neutron-rich Zr isotopes with particle-vibration coupling effect
• Pairing and nonaxial-shape correlations in $N=150$ isotones
• Isovector spin susceptibility: Isotopic evolution of collectivity in spin response
• Nonspherical Pauli-forbidden states in deformed halo nuclei: Impact on the ${}^7\mathrm{Be}+p$ resonant states in the particle rotor model
• Spin-triplet proton-neutron pair in spin-dipole excitations
• Electron wave functions in beta-decay formulas revisited (II): Completion including recoil-order and induced currents
• Isovector giant monopole and quadrupole resonances in a Skyrme energy density functional approach with axial symmetry