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

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.