Two-quasiparticle states in $^{252,254}$No and the stability of superheavy nuclei

Two-quasiparticle (qp) states in shell-stabilized nuclei probe the levels that govern the stability of superheavy nuclei, test 2-qp energies from theory and, thereby, check their predictions of magic gaps. We have identified in $^{254}$No 2- and 4-qp isomers, with quantum numbers K$^{\pi }$ = 8$^{-}$ and (14$^{+})$, and a low-energy 2-qp K$^{\pi }$= 3$^{+}$ state, as well as a K$^{\pi }$ = 8$^{- }$isomer in$^{ 252}$No. The use of Woods-Saxon single-particle energies reproduces the experimental proton 2-qp energies in $^{254}$No. Some shortcomings in the 2-qp energies from self-consistent mean-field theories suggest that their predictions of magic gaps at Z=120 and 126 should be viewed with reservations. The resilient survival of superheavy nuclei with high Z, up to 118, well past the onset of spontaneous fission at Z=92, is an interesting phenomenon in nuclear and mesoscopic physics. This research was conducted by a collaboration from Argonne National Laboratory and the Universities of Massachusetts Lowell, Jyv\"{a}skyl\"{a}, K\"{o}ln, Liverpool, Maryland, Notre~Dame and Yale.