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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-reversalsymmetry is conserved in the HFB Hamiltonian without null eigenvalues. Based onthis finding, we give a rigorous foundation of a method for solving the HFBequation to describe the ground state of odd-mass nuclei by employing atime-reversal anti-symmetric constraint operator to the Hamiltonian, where oneobtains directly the ground state as a self-consistent solution of thecranked-HFB-type equation. Numerical analysis is done for the neutron-rich Mgisotopes with a reasonable choice for the operator, and it is demonstrated thatthe anomalous increase in the matter radius of $^{37}$Mg is well described whenthe last neutron occupies a low angular-momentum orbital in the framework ofthe nuclear energy-density-functional method, revealing the deformed halostructure.

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