Halos and changes of nuclear magicities have been extensively investigated in exotic nuclei during past decades. The newly discovered ${}^{39}\mathrm{Na}$ with the neutron number $N=28$ provides a new platform to explore such novel phenomena near the neutron dripline of the sodium isotopic chain. We study the shell property and the possible halo structure in ${}^{39}\mathrm{Na}$ within the deformed relativistic Hartree-Bogoliubov theory in continuum. It is found that the lowering of $2p$ orbitals in the spherical limit results in the collapse of the $N=28$ shell closure in ${}^{39}\mathrm{Na}$, and a well-deformed ground state is established. The pairing correlations and the mixing of $pf$ components driven by deformation lead to the occupation of weakly bound or continuum $p$-wave neutron orbitals. An oblate halo is therefore formed around the prolate core in ${}^{39,41}\mathrm{Na}$, making ${}^{39}\mathrm{Na}$ a single nucleus with the coexistence of several exotic structures, including the quenched $N=28$ shell closure, Borromean structure, deformed halo, and shape decoupling. The microscopic mechanisms behind the shape decoupling phenomenon and the development of halos towards dripline are revealed.

We investigate ground states properties of Pb isotopes located between neutron and proton drip-lines estimated by two-neutron (two-proton) separation energies and Fermi energies within the deformed relativistic Hartree-Bogoliubov theory in continuum. First, we report some candidates of nuclear shape coexistence in the isotope chain. They are accessed by calculating total energy as a function of the deformation parameter ${\beta }_2$, and for the coexistence candidates we take a few deformation regions bringing about minima of the energy within energy difference $\mathrm{\Delta }E<1$ MeV. Second, the Pb isotopes near neutron drip-lines are also investigated and compared to the results by other nuclear mass models. We find out 11 neutron emitters, ${}^{278\text{–}296,300}\mathrm{Pb}$, giving rise to the Pb peninsular near the neutron drip-line. Finally, by exploiting the neutron and proton density we deduce the neutron skin thickness (NST) of the Pb isotopes and compare to the available experimental data. The recent reports regarding the shape coexistence of ${}^{184,186,188}\mathrm{Pb}$ and the NST of ${}^{208}\mathrm{Pb}$ are shown to be well matched with the present results.

The shape of a nucleus is one of the fundamental nuclear properties. We perform a systematic investigation of bubble nuclei that also exhibit shape coexistence in Hf, W, Os, Pt, and Hg even-even isotopes using the deformed relativistic Hartree-Bogoliubov theory in continuum. For a systematic study, we first consider nuclear bubble structures and shape coexistence separately. We confirm that deformations and pairing correlations hinder bubble structures by comparing our results with those from relativistic continuum Hartree-Bogoliubov theory that assumes spherical symmetry in nuclei. We then predict candidate isotopes with both bubble structure and shape coexistence. We observe that the depletion fraction factor that characterizes bubble structure is mostly smaller in oblate deformation than in prolate, while some isotopes such as ${}^{206}\mathrm{Os}$ have bubble structures both in oblate and prolate deformations. We compare the proton single-particle energy levels for the candidates of shape coexistence both with only prolate bubble structure and with prolate and oblate bubble structures.

The possibilities of production of yet-undiscovered neutron-rich isotopes of Ca, Gd, Dy, Er, Yb, Hf, W, Os, Hg, Pb, and Th are explored in various multinucleon transfer reactions with stable and radioactive beams. The probable projectile-target combinations and bombarding energies to produce these neutron-rich isotopes are suggested for future experiments.

We investigate possible production of neutron-rich isotopes of nobelium. We calculate the production cross sections of ${}^{261–266}\mathrm{No}$ in the multinucleon transfer reactions of the same projectiles (${}^{36}\mathrm{S},{}^{40}\mathrm{Ar},{}^{48}\mathrm{Ca}$, and ${}^{50}\mathrm{Ti}$) and targets (${}^{254}\mathrm{Es}$ and ${}^{248–251}\mathrm{Cf}$) that were used in the previous study for the possible production of neutron-rich isotopes of Md. We find that the production cross sections of neutron-rich No isotopes are about an order of magnitude smaller than those for neutron-rich Md isotopes. By combining the results for the production of neutron-rich No and Md isotopes, we suggest simple expressions which can trace the isotopic trends of the production cross sections of heavy neutron-rich isotopes. The logarithm of the production cross section is proportional to isospin of projectile or target and the $Q$ value.