Generation of excitedKbands in heavy nuclei

Abstract

It is known that coupling an intrinsic excitation of integer spin and positive parity ${I}^{+}$ to a rotor having a degenerate set of states ${L}^{\ensuremath{\pi}}={0}^{+},{2}^{+},{4}^{+},...,$ generates a series of $K$ bands. A given value of ${I}^{+}$ gives rise to several bands labeled by ${K}^{+}={0}^{+},{1}^{+},{2}^{+},...,{I}^{+}$, that is, a total of ($I+1$) such bands, in the spectrum of the combined system. We discuss how a binary cluster model of an excited core orbited by a spinless cluster can approximate these conditions. A crucial point is that the radial wave functions of relative motion are very similar for low $L$, and their radial coupling integrals even more so, such that the wave functions play the model role of a common intrinsic state for the lowest excited states of the system. If the core has a ${0}^{+}$ ground state and a low-lying ${2}^{+}$ excited state, then lifting the degeneracy leads to a ground state ${K}^{+}={0}^{+}$ band and low-lying excited ${K}^{+}={0}^{+}$, ${1}^{+}$, and ${2}^{+}$ bands. Although these are all seen in light nuclei, the ${K}^{+}={1}^{+}$ band is conspicuous by its apparent absence in heavy nuclei, and we urge experimental groups to reexamine their data for signs of it.