Nuclear Isomers at the Extremes of their Properties

Abstract: The longer-lived excited nuclear states, referred as nuclear isomers, exist due to the hindered decays owing to their peculiar nucleonic structural surroundings. Some of these conditions, being exceptionally rare and limited to achieve, elevate certain isomers to the status of extreme and unusual isomers among their kin. For example, the $E5$ coupling of single-particle orbitals is rare and so are $E5$ decaying isomers. This review delves into some of such remarkable isomers scattered across the nuclear landscape while highlighting the possibilities to find more of them. Unique properties of some of them, harbor the potential for transformative applications in medicine and energy. An exciting example is that of the lowest energy isomer known so far in $<sup>{229}$Th, which may help realize the dream of an ultra-precise nuclear clock in the coming decade. These isomers also offer an insight into the extremes of nuclear structure associated with them, which leads to their unusual status in energy, half-life, spin etc. The review attempts to highlight isomers with high-multipolarities, high-spins, high-energies, longest half-lives, extremely low energy, etc. A lack of theoretical understanding of the decay rates, half-lives and moments of these isomers is also pointed out.