Since the 1940s, scientists have been seeking to expand the periodic table by smashing atomic nuclei together to create heavier elements. They have been successful in making and detecting elements with up to 118 protons, although only 111 are officially acknowledged. The issue, however, is that these heavy nuclei resist combination and are highly unstable even when combination is successful, lasting just fractions of a second before decaying in many instances.
And yet, physicists are hopeful that superheavy and stable nuclei may be synthesized because theoretical models suggest that nuclei with particular numbers of protons (Z) and neutrons (N), called "magic numbers; are unusually stable. One step in determining these magic Z numbers is measuring the exact energy levels in the higher shells.
Rolf-Dietmar Herzberg and his team from the University of Liverpool have given theorists some data to chew on by examining high-energy states of the element nobelium using the particle accelerator of the University of Jvyäskylä, Finland. The findings work out to an energy level so energetic that it could be filled only by elements beyond position 114 in the periodic table. The research involved producing excited versions of nobelium and then monitoring produced energy when the atoms relax back to a non-excited state.

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An alternative to magic numbers by wyldeling :: NR7 :: Show
In addition to "magic numbers", there are nuclear isomers that are exceptionally stable. The June 2005 edition of Physics Today (sorry, subscribers only) discussed several elements that have metastable nuclear states. Metastable states by themselves are unusual because they are excited states that take a long time to decay to the ground state, and hence the term meta-stable. They take a long time because a direct transition from the the metastable state to the ground state is often forbidden by quantum mechanical selection rulesrule, so the system has to make a transition to a state that does allow the transition to the ground state. An interesting example is the curious case of 180mTantalum. For Tantalum, the ground state itself is unstable, with a half-life of only 8 hours. The metastable state has a half-life of approx. 1015 years, which is only a lower limit since no actual decays have been observed. Specifically, the metastable state has a spin-parity of 9-, while the ground state has a spin-parity of 1+, so the transition is forbidden. However, it could transition from 9- to 2+ and then to 1+, but the transition requires a multipoleexpansion transition with E7 or M8 character, which have never been seen. (E1, E2, E3, … dipole, quadrupole, octopole, … E refers to electric, M to magnetic.)