Excited States of Even-Even Nuclei

A general survey of excited states of even-even nuclei yields the following results: The $n\mathrm{th}$ excited state has usually a spin $I\le 2n$. For $n=1\mathrm{}$, the assignment $I=2+\left(\mathrm{even}\mathrm{parity}\right)$ is compatible with experimental results for 66 out of 68 nuclei investigated. For $n=2\mathrm{}$, of 26 nuclei investigated, about one-third have $I=2+$, one-third $I=4+$, and one-third miscellaneous spins of both even and odd parities. The energy of the first excited state plotted against the number of protons or neutrons in the nucleus varies rather smoothly and reaches maxima at closed shells. Wherever the first excited state is very low, e.g., in the rare earths region and for the heavy elements from thorium up, the one-particle model for odd $A$ nuclei is likely to break down except for the ground state. The lack of isomers of odd proton nuclei below magic number 82 may be due to this fact. The average energy of the first excited state of the even-even core in this region is of the order of 0.1 Mev, whereas this energy is of the order of 0.5 Mev for the core of the corresponding odd neutron nuclei ($N<\mathrm{}82\mathrm{}$). Isomerism in even-even nuclei is discussed. The results are compared with theoretical predictions derived from an extended $j-j$ coupling model and from the liquid drop model of the nucleus.