Examining possible neutron-halo nuclei heavier than ${}^{37}\mathbf{Mg}$

The even-$Z$ odd-$N$ neutron-halo nuclei, which are the lightest neutron-halo nuclei heavier than ${}^{37}\mathrm{Mg}$, 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 ${}_{24}{}^{71}\mathrm{Cr}_{47}, {}_{24}{}^{73}\mathrm{Cr}_{49}, {}_{24}{}^{75}\mathrm{Cr}_{51}$, and ${}_{26}{}^{77}\mathrm{Fe}_{51}$ 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 ${}_{18}{}^{53}\mathrm{Ar}_{35}$.

Figure 1

Calculated one-particle energies for neutrons in the potential given by the core nucleus ${}_{26}{}^{76}\mathrm{Fe}_{50}$ as a function of axially symmetric quadrupole deformation parameter $\beta$. Bound one-particle energies at $\beta =0$ are $-6.56, -6.14, -5.39, -1.53$, and $-0.05$ MeV for the $2p_{3/2}, 1f_{5/2}, 2p_{1/2}, 1g_{9/2}$, and $3s_{1/2}$ levels, respectively, while one-particle resonant $2d_{5/2}, 2d_{3/2}$, and $1g_{7/2}$ levels are obtained at 0.25, 1.62, and 3.12 MeV (denoted by filled circles) with the widths of 0.024, 1.92, and 0.13 MeV, respectively. The ${\mathrm{\Omega }}^{\pi }=1/2^{+}$ resonant level connected to the $2d_{5/2}$ level at $\beta =0$ cannot be obtained as a one-particle resonant level for $\beta >0.007$. Three bound ${\mathrm{\Omega }}^{\pi }=1/2^{+}$ levels are denoted by the asymptotic quantum numbers on the prolate side [14], $\left[N{n}_z\mathrm{\Lambda }\mathrm{\Omega }\right]$ = [440 1/2], [431 1/2], and [420 1/2], although the wave functions of those levels plotted in this figure are quite different from those expressed by the asymptotic quantum numbers. The neutron numbers 40, 48, and 50, which are obtained by filling all lower lying levels, are indicated with circles, for reference. For simplicity, calculated widths of one-particle resonant levels are not shown. The parity of levels can be seen from the $\ell$ values denoted at $\beta =0$; $\pi ={(-1)}^{\ell }$. One-particle resonant energies for $\beta \ne 0$ are not always plotted if they are not important for the present discussions.

Figure 2

Calculated one-particle energies for neutrons in the potential given by the core nucleus ${}_{18}{}^{52}\mathrm{Ar}_{34}$ as a function of axially symmetric quadrupole deformation. Bound one-particle energies at $\beta =0$ are $-5.99, -3.18, -1.63$, and $-0.31$ MeV for the $1f_{7/2}, 2p_{3/2}, 2p_{1/2}$, and $1f_{5/2}$ levels, respectively, while one-particle resonant $1g_{9/2}$ level is obtained at 2.69 MeV with the width of 0.061 MeV. The $2d_{5/2}$ level is not obtained as a one-particle resonant level for this potential. The neutron numbers 28 and 34, which are obtained by filling all lower lying levels, are indicated with circles. One-particle resonant energies for $\beta \ne 0$ are not always plotted if they are not important for the present discussions.