The even-Z odd-N neutron-halo nuclei, which are the lightest neutron-halo nuclei heavier than Mg-37, are explored by studying the shell structure unique in weakly bound neutrons for spherical or deformed shapes. It is pointed out that due to the narrowed N = 50 spherical energy gap and a few resulting close-lying neutron one-particle levels, 1g(9/2), 3s(1/2), and 2d(5/2), for spherical shape, nuclei with some weakly bound neutrons filling in those levels may be deformed and have a good chance to show deformed s-wave halos. Promising candidates are Cr-71(24)47, Cr-73(24)49, Cr-75(24)51, and Fe-77(26)51 in the case that those nuclei lie inside the neutron drip line. An interesting possibility of the deformed p-wave or s-wave halos is suggested also for the nucleus Ar-53(18)35.
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