Atoms with the same atomic number Z and the same mass number A in different states of excitation, the higher states being metastable with respect to the ground state.
Nuclei usually exist in their ground state with the individual nucleons paired up subject to energy constraints. In some nuclides, for example resulting from radioactive decay, one or more nucleons can be excited into one or more higher spin states. These nuclei can revert back to the ground state by the emission of gamma radiation. If this emission is delayed by more than 1 μs, the nucleus is said to be a nuclear isomer and the process of releasing energy is known as isomeric transition.
There are two very different ways that such nuclei can possess spin. Either the nucleus rotates as a whole, or several nucleons can orbit the nucleus independently in a non-collective rotation. The latter case can result in the nucleons being trapped in high spin states such that they have much higher lifetimes. Nuclides with even-Z and even-N (i.e. with a whole number of He-4 nuclei) can also have high excess rotational spin due to alpha particles rotating independently around the nucleus. Examples here are 12C, 16O, 20Ne, and 24Mg.
Polonium-212 is an example where the isomer has a much longer halflife than the ground state. With a spin of 18, the half-life of 45 s is very much longer than the ground state half-life of 300 ns. The isomer can be considered as two neutrons and two protons orbiting around the doubly magic lead-82 nucleus. The high spin state decays by alpha emission which carries off the 18 units of spin.
Other examples are hafnium-178 (spin 16 due to 4 of the 78 nucleons orbiting the nucleus), tungsten-178 (spin 25 due to 8 unpaired nucleons orbiting the nucleus).
To distinguish between the excited and ground states, the symbols m, n, ... etc. are used to denote metastable states. The first metastable state is denoted by m, the second by n etc. Sometimes the symbol g is used to denote the ground state. In the Karlsruhe Nuclide Chart, in addition there is a symbol sf which is used to denote spontaneous fission isomers.