Classification of Nuclear Isomers

Abstract

The lifetime-energy relations of Axel and Dancoff and the $\frac{K}{L}$ ratios calculated by Hebb and Nelson are shown to yield spin differences $\Delta I$ which are one unit too high for long-lived electric transitions ($\Delta I\ge 3$). These transitions are also slower than expected from Weisskopf's one-particle model and have approximately the same lifetime as magnetic transitions of equal $\Delta I$. The lifetimes of magnetic transitions agree approximately with Weisskopf's formula. If the statistical weight of the initial state is introduced into the lifetime formula, the "scatter" of the square of the matrix elements is greatly reduced for these transitions. Most long-lived isomers show $M4\mathrm{}$ transitions, in agreement with shell theory. Some isomeric transitions which were previously assumed to show no parity change are now interpreted as $E3\mathrm{}$. Their occurrence in the $1g_{\frac{9}{2}}$ shell may be explained by assuming that for the configurations ${\left(g_{\frac{9}{2}}\right)}^{3,5, or 7}$, 7/2+ and $g_{\frac{9}{2}}$ states are comparable in energy. The 7/2+ state is lower in more than half of the cases. Empirical curves of $\frac{K}{L}$ ratios plotted against $\frac{Z^2}{E}$ are given. They are consistently lower than the existing theoretical curves based on nonrelativistic calculations of internal conversion coefficients. Spins of metastable and ground states are assigned for a number of nuclei. For even-even nuclei the following rule is found: the first excited state usually has spin 2 and even parity. The only mixed transitions found are $M1+E2\mathrm{}$. Sufficiently many $E3\mathrm{}$ transitions are established to permit the conclusion that electric transitions are slower for odd-neutron nuclei than for odd-proton nuclei. This gives strong support to a one-particle model. Among electric transitions only some $E2\mathrm{}$ transitions are faster than expected on the one-particle model. This is interpreted as a cooperative phenomenon, related to the existence of large quadrupole moments.