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The even-Z odd-N neutron-halo nuclei, which are the possible lightestneutron-halo nuclei heavier than $^{37}$Mg, are explored by studying theshell-structure unique in weakly-bound neutrons for spherical or deformedshape. It is pointed out that due to the narrowed N=50 spherical energy-gap anda 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-boundneutrons filling in those levels may be deformed and have a good chance to showdeformed s-wave halo. Promising candidates are $^{71}_{24}$Cr$_{47}$,$^{73}_{24}$Cr$_{49}$, $^{75}_{24}$Cr$_{51}$ and $^{77}_{26}$Fe$_{51}$ in thecase that those nuclei lie inside the neutron drip-line. An interestingpossibility of the deformed p-wave or s-wave halo is suggested also for thenucleus $^{53}_{18}$Ar$_{35}$.

Examining possible neutron-halo nuclei heaver than $^{37}$Mg