Kern, Ralph (2021)
Isovector One-Quadrupole-Phonon Excitations of Heavy Vibrational Nuclei.
Technische Universität Darmstadt
doi: 10.26083/tuprints-00018581
Dissertation, Erstveröffentlichung, Verlagsversion

Kurzbeschreibung (Abstract)

The investigation and identification of mixed-symmetry states stand in the focus of this work. They are formed from collective vibrations and rotations of valence neutrons and protons, where the two nucleon groups oscillate partly out-of-phase with respect to each other. In vibrational nuclei, the $2^+_\mathrm{1,ms}$ state is the lowest-lying mixed-symmetry level.

For the $N=80$ isotones, the sub-shell closure at $Z=58$ highly effects the structure of the $2^+_\mathrm{1,ms}$ state. Up to $Z=56$, the isotones have isolated $2^+_\mathrm{1,ms}$ states, but for $^{138}$Ce ($Z=58$), it is strongly fragmented. This behaviour is explained by the valence-shell stabilization, which is lacking at the proton sub-shell closure $Z=58$. For addressing the question how the $2^+_\mathrm{1,ms}$ state behaves while going beyond the proton sub-shell closure, projectile Coulomb-excitation experiments were performed. They took place at HIE-ISOLDE at CERN using the $\gamma$-ray spectrometer Miniball with the radioactive ion beams of the $N=80$ isotones $^{140}$Nd and $^{142}$Sm. The enhanced $B(M1;2^+_3\to2^+_1)=0.26^{+0.11}_{-0.10}\,\mu_\mathrm{N}^2$ strength and the low upper limit $B(M1;2^+_4\to2^+_1)<0.04\,\mu_\mathrm{N}^2$ of $^{140}$Nd showed the restoration of the valence-shell stabilization at $Z=60$. From the $M1$ strength distribution, the quality of the $F$ spin of $^{140}$Nd was determined by the $F$-spin mixing matrix element $V_\mathrm{F-mix}<7^{+13}_{-7}\,\mathrm{keV}$. The reduced mixing matrix element supports the proposed restoration of the valence-shell stabilization. For $^{142}$Sm, the Coulomb-excitation analysis delivered an upper limit $B(M1;2^+_3\to2^+_1)<0.14^{+0.37}_{-0.01}\,\mu_\mathrm{N}^2$, which is not in conflict with the conclusions from the $^{140}$Nd experiment. A complementary $\gamma$-$\gamma$ correlation measurement after $\beta^+$/$\epsilon$ decay to determine the indispensable $E2$/$M1$ multipole-mixing ratio $\delta$ of the $2^+_3\to2^+_1$ transition of $^{142}$Sm was designed for the Heavy Ion Laboratory in Warsaw and accepted.

For the stable $^{202}$Hg, a projectile Coulomb-excitation experiment was conducted at the ATLAS facility at the ANL using the $\gamma$-ray spectrometer Gammasphere. Simultaneously, angular particle-$\gamma$ correlations were measured with the aim of deducing $\delta$. In $^{202}$Hg a pronounced $B(M1;2^+_7\to2^+_1)=0.18(8) \,\mu_\mathrm{N}^2$ with $\delta=0.06(4)$ was found, while an upper limit for the neighboring transition was obtained, $B(M1;2^+_8\to2^+_1)<0.027 \,\mu_\mathrm{N}^2$. For the first time in the mass region $A\approx200$, the $F$-spin mixing quality was determined, for $^{202}$Hg and $^{204}$Hg, $V_\mathrm{F-mix}=9(2)^{+3}_{-3}\,\mathrm{keV}$ and $11(1)^{+4}_{-5}\,\mathrm{keV}$, respectively.

Consequently, $F$ spin can be considered a sufficiently good approximate quantum number in the investigated nuclei of $N,Z=80$ near doubly-magic isotopes.

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