Isomerism in Nuclei

 

A small proportion of nuclei exhibit highly-excited metastable [isomeric] states coexisting at low excitation energy. Isomeric states in nuclei have unique and unusual properties that can provide new insights into nuclear shell structure and nuclear shapes. They are of special interest because of the possibility of using stimulated isomer decay for energy storage or for building gamma-ray lasers.

Three classes of isomers are observed, shape isomers, spin isomers, and K isomers. In contrast to shape isomers, which are due to a large change in deformation as seen in fission isomerism, spin and K isomers result from the angular momentum coupling of a few valence nucleons. Study of collective bands based on isomeric states is of considerable interest in order to understand the spin dependence of the goodness of the approximate symmetries leading to isomerism. We have used Gammasphere plus CHICO to make such studies of rotational bands built on isomeric states that were populated by Coulomb excitation or transfer reactions in nuclei such as $^{168,170}$Er and $^{178,180,182}$Hf [1,2]. In addition we have studied isomeric states in several neutron-rich medium-mass nuclei populated by nuclear fission, as well as 184W by multi-nucleon transfer and 136Ba by deep inelastic reactions [3,4].

The projection $K$ of the angular momentum on the symmetry axis of a deformed nucleus appears to be approximately conserved as evidenced by the existence of $K$ isomeric states in many nuclei in the mass 180 region. Electromagnetic transitions must obey the $K$-selection rule MATH $\leq \lambda $ if $K$ is a good quantum number, as can exist in axial symmetric nuclei. Recent studies in Lu, Hf, Ta, W and Os isotopes have shown highly $K$-forbidden transitions are hindered rather than strictly forbidden and the hindrance factor is strongly correlated with the degree of forbiddenness, MATH, implying partial breakdown of the $K$-selection rule. Our recent Coulomb excitation study using 650 MeV $^{136}$Xe ions, searched for direct population of the in-band transitions of the rotational bands based on high-spin $K$ isomers in $^{178} $Hf. Rotational band states based on three high-$K$ isomers were observed; $K^{\pi }=6^{+}$ ($t_{\frac{1}{2}}=77$ ns) up to spin $13^{+}$, $K^{\pi }=8^{-}$ ($4$ s) up to spin $14^{-}$, and, unexpectedly, the $K^{\pi }=16^{+} $ ($31$ y) up to spin $20^{+}.$ The Coulomb excitation yields show unambiguously that although the decays are highly $K$-forbidden at the band heads, there is a rapid increase in $K$-mixing with increase in spin resulting in isomer population via the higher-spin rotational band states. Moreover, this measurement showed that three distinctly different mechanisms are responsible for population of these three isomeric bands as illustrated below. The $K^{\pi }=6^{+}$ isomeric band is populated equally by two-step and three step allowed transition as well as $\sim 10\%$ by $K$-forbidden direct excitation. The $K^{\pi }=8^{-}$ isomeric band is populated primarily by direct $K$-forbidden $E3$ excitation from the ground-state band. The unexpected population of the $K^{\pi }=16^{+}$ isomeric band occurs by direct $K-$forbidden $\gamma $-ray feeding from around the spin 20 state in the ground band. These exciting results appear to finally solve a question that as remained unanswered for two decades. This result has been confirmed by a follow up experiment using a $^{178}$Hf beam at ATLAS to measure the excitation function for Coulomb excitation of the $K^{\pi }=16^{+}$ ($31$ y) isomer in order to determine individual $E2$ matrix elements coupling the high-spin rotational band states based on the ground and $K^{\pi }=16^{+}$ states.

The extremely rare odd-odd nucleus $^{180}$Ta survives in nature in its long-lived isomeric state ($I=9^{-}$, $E^{\ast }=75.3$ keV, MATH yr) rather than its short-lived ground state ($I=1^{+}$, T$_{1/2}$=8.15 h). The nucleosynthesis leading to the natural abundance of this isotope is not understood. Depopulation of this isomer via intermediate states, suggested by recent activation experiments using either real or virtual photons, has important implications in understanding the population and survival of this isomer in stellar environments. The $\Delta K=8$ decay of the isomer to the ground band implies the existence of appreciable K mixing. The depopulation of this $K^{\pi }=9^{-}$ state and population of the isomeric bands in $^{178}$Hf probably are closely related questions. A rapid increase in $K$-mixing, similar to what has been observed in $^{178}$Hf, could explain the $^{180}$Ta isomer depopulation. Further studies are in progress.


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1)A. B. Hayes, D. Cline, C.Y. Wu, M.W. Simon, R. Teng, J. Gerl, Ch. Schlegel,, H.J. Wollersheim, A.O. Macchiavelli, K. Vetter, P. Napiorkowski, J. Srebrny,
Phys. Rev. Lett. 89 (2002)242501.

2) C.Y. Wu, D. Cline, M.W. Simon, R. Teng, K. Vetter, M.P. Carpenter, R.V.F. Janssens, I. Wiedenhover, Phys. Rev. C 61, 021305(R) (2000), and Phys. Rev, C68 044305 (2003).

3) J.J. Valiente-Dubon et al, Phys. Rev C69 024316 (2004)

4) C. Wheldon et al, European Physical Journal A19 xxx (2004)

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