Abstract
Abstract We show that the lowest-energy solution of the Hartree–Fock–Bogoliubov (HFB) equation has 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 for a method for solving the HFB equation to describe the ground state of odd-mass nuclei by employing a time-reversal antisymmetric 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 performed 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.
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