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The detailed investigation of new physical mechanisms which allows to extend the boundaries of particle-bound nuclear landscape beyond the traditional limits and lead to exotic nuclear shapes has been performed over recent years [1-5]. The increased role of the Coulomb interaction in the hyperheavy $(Z\geq 126)$ nuclei leads to the situation when toroidal shapes become more energetically favored than ellipsoidal ones: this provides a substantial increase of nuclear landscape [2,3]. Toroidal nuclei are stable with respect to breathing deformation, but their stability with respect of sausage deformations is established so far only in the $Z\sim 134, N\sim 210$ region for fat toroidal nuclei [1,2]. However, the analysis of toroidal shell structure indicates their potential stability for other combinations of protons and neutrons both for thin and fat toroidal nuclei [3]. In the cases when toroidal shapes become unstable, the ground states are represented by spherical shapes characterized by a substantial depletion of the density in the center of nucleus ("bubble" nuclei). This takes place in the $(Z\sim 138, N\sim 230)$, $(Z\sim 154, N\sim 308)$ and $(Z\sim 186, N\sim 406)$ islands of stability of spherical hyperheavy nuclei [1,3].
Rotational excitations provide an alternative mechanism of the extension of nuclear landscape beyond the limits defined at spin zero [4,5]. Both in hyperheavy and rotating nuclei, the collective coordinates play an important role in extending nuclear landscape. In hyperheavy nuclei, they (deformations) drive the nuclear systems from ellipsoidal-like to toroidal shapes. In rotating nuclei, the increase of collective coordinate (rotational frequency) triggers the transition of nucleonic configurations from particle-unbound to particle-bound. Strong Coriolis interaction acting on high-$N$ intruder orbitals is responsible for this transformation. This new physical mechanism has two important consequences. First, it leads to a substantial extension of the nuclear landscape beyond the spin zero proton and neutron drip lines. Second, exotic shapes such as giant proton halos in rotating proton-rich nuclei [5] and super-, hyper- and megadeformed shapes in rotating neutron-rich nuclei [4] are formed at high spin. Their formation is triggered by the occupation of high-$N$ intruder orbitals.
[1] A.V.Afanasjev, S.E.Agbemava and A.Gyawali, Phys. Lett. B 782, 533 (2018).
[2] S.E.Agbemava, A.V.Afanasjev, A.Taninah, and A.Gyawali, Phys. Rev. C 99, 034316 (2019).
[3] S.E.Agbemava and A.V.Afanasjev, Phys. Rev. C 103, 034323 (2021).
[4] A.V.Afanasjev, N.Itagaki, and D.Ray, Phys. Lett. B 794, 7 (2019).
[5] S.Teeti, A.V.Afanasjev, and A.Taninah, submitted to Phys. Rev. C and in preparation.
