Isomer spectroscopy in ${}^{133}\mathrm{Ba}$ and high-spin structure of ${}^{134}\mathrm{Ba}$

The transitional nuclei ${}^{134}\mathrm{Ba}$ and ${}^{133}\mathrm{Ba}$ are investigated after multinucleon transfer employing the high-resolution Advanced GAmma Tracking Array coupled to the magnetic spectrometer PRISMA at the Laboratori Nazionali di Legnaro, Italy, and after fusion-evaporation reaction at the FN tandem accelerator of the University of Cologne, Germany. The $J^{\pi }=19/2^{+}$ state at 1942 keV in ${}^{133}\mathrm{Ba}$ is identified as an isomer with a half-life of $66.6\left(20\right)\mathrm{ns}$ corresponding to a $B\left(E1\right)$ value of $7.7\left(4\right)\times {10}^{-6}{e}^2{\mathrm{fm}}^2$ for the $J^{\pi }=19/2^{+}$ to $J^{\pi }=19/2^{-}$ transition. The level scheme of ${}^{134}\mathrm{Ba}$ above the $J^{\pi }={10}^{+}$ isomer is extended to approximately 6 MeV. A pronounced backbending is observed at $\hslash \omega =0.38$ MeV along the positive-parity yrast band. The results are compared to the high-spin systematics of the $Z=56$ isotopes. Large-scale shell-model calculations employing the GCN50:82, SN100PN, SNV, PQM130, Realistic SM, and EPQQM interactions reproduce the experimental findings and elucidate the structure of the high-spin states. The shell-model calculations employing the GCN50:82 and PQM130 interactions reproduce alignment properties and provide detailed insight into the microscopic origin of this phenomenon in transitional ${}^{134}\mathrm{Ba}$.

Figure 1

(a) Partial level scheme of ${}^{133}\mathrm{Ba}$ including transitions feeding or deexciting the 1942-keV state which is subject of this paper. Transitions and excitation energies are given in keV. Intensities, energies, and spins are adopted from Ref. [20]. For the $J^{\pi }=19/2^{+}$ and $J^{\pi }=11/2^{-}$ [50] states, the corresponding $T_{1/2}$ values are given in the figure. (b) Level scheme assigned to ${}^{134}\mathrm{Ba}$ with the newly observed $\gamma$ rays above the $T_{1/2}=2.51\left(30\right)\mu \mathrm{s}$ ($J^{\pi }={10}^{+}$) and $T_{1/2}=48\left(5\right)\mathrm{ns}$ ($J^{\pi }=5^{-}$) isomers. Intensities are extracted from the HORUS data and normalized to the intensity of the 605-keV transition. The given half-lives of the $J^{\pi }=19/2^{+}$ state in ${}^{133}\mathrm{Ba}$ and of the $J^{\pi }=5^{-}$ and ${10}^{+}$ states in ${}^{134}\mathrm{Ba}$ were newly determined.

Figure 2

[(a) and (c)] Two-dimensional $E_{\gamma }$-time matrices showing the time distribution of coincident $\gamma$-ray transitions relative to the 424-keV transition. The applied two-dimensional gates are surrounded by thick solid red lines. (b) Prompt and (d) delayed one-dimensional $\gamma$-ray spectra with respect to the 424-keV transition. (e) Plot of the fitted intensities of the 681- and 890-keV $\gamma$-ray transitions in the $\gamma \gamma$ projection gated on the 424-keV transitions as a function of coincidence time windows. The solid lines correspond to the fitted time distribution [see Eq. (1)]. One data acquisition time unit (tick) corresponds to 12.5 ns. [(f)–(i)] Gated $E_{\gamma }\text{−}{E}_{\gamma }$-time distributions and final lifetime fits for gating combinations between ${\mathrm{LaBr}}_3$ and HPGe detectors. Half-lives are determined by exponential fits of the delayed component. The fit is drawn with a red solid line. The given half-lives include only the statistical uncertainties of the fits. For the total error see text.

Figure 3

(a) Doppler-corrected $\gamma$-ray spectrum gated on ${}^{134}\mathrm{Ba}$ identified with PRISMA in the ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ experiment. Random background is reduced with a gate on the prompt peak in the spectrum of time differences between AGATA and PRISMA. Inset (b) represents the mass spectrum of the Ba isotopes obtained with PRISMA. The applied mass gate on ${}^{134}\mathrm{Ba}$ is marked black.

Figure 4

Results of the HORUS experiment showing (a) $E_{\gamma }$-time matrix with respect to the $2^{+}\to 0^{+}$ 605-keV transition. (b) Time difference spectrum between the 668- and 605-keV transitions, extracted from the $E_{\gamma }$-time matrix. (c) One-dimensional HORUS $\gamma$-ray spectrum gated on the 605-keV transition. Transitions below the $J^{\pi }={10}^{+}$ isomer are predominantly visible. (d) Projection of a HORUS $\gamma \gamma$ matrix sorted by gating on negative timestamp differences relative to the timestamp of the delayed ground-state band of ${}^{134}\mathrm{Ba}$ with 605-, 796-, 810-, 625- or 121-keV transitions. Only transitions above the $J^{\pi }={10}^{+}$ isomer are visible. $\mathrm{Ge}(n,n\gamma$) edges are marked with $n$. See text for details.

Figure 5

$\gamma$-Ray spectra above the $J^{\pi }={10}^{+}$ isomer, gated on (a) 668, (b) 1193, and (c) 744 keV. (d) $\gamma \gamma$-coincidence spectra with a gate on the $5^{-}\to 4^{+}$ 585-keV transition. (e) Time spectrum between the 761–970–285-keV (prompt) and 585–796–605-keV (delayed) cascades with an exponential decay-curve fit (red solid line). The fitted half-life is 48(5) ns.

Figure 6

(a) Benchmark $\gamma \gamma$ angular correlations for the $4^{+}\to 2^{+}\to 0^{+}$ (796–605-keV) cascade in ${}^{134}\mathrm{Ba}$. Experimental values (data points) are compared to calculated angular-correlation functions $W({\mathrm{\Theta }}_1,{\mathrm{\Theta }}_2,\mathrm{\Phi })$ (lines) for six correlation groups using the code corleone [63, 64]. Investigation for (b) the newly established 668-1193-keV cascade and (c) the 285–970-keV cascade in ${}^{134}\mathrm{Ba}$.

Figure 7

Comparison of experimental energy spectra with the results of shell-model calculations for ${}^{134}\mathrm{Ba}$. (a) Experimental energy spectrum. The results obtained with the different interactions are separated in different columns: (b) GCN50:82, (c) SN100PN, (d) SNV, (e) PQM130, and (f) Realistic SM. For clarity, the states are separated into columns for the negative- and the positive-parity states.

Figure 8

Evolution of excited states along the even-mass $N=78$ isotones for (a) the positive-parity yrast states and (b) for the negative-parity yrast states. (c) Evolution of positive-parity yrast states along the $Z=56$ even-mass Ba isotopes. Newly discovered states in ${}^{134}\mathrm{Ba}$ are marked with thick lines. Data taken from Refs. [50, 94, 95, 96].

Figure 9

Evolution of net aligned angular momenta $i_x\left(\hslash \right)$ along the even-mass Ba chain as a function of rotational frequency $\hslash \omega$. Isotopes along the Ba chain exhibit two $S$ bands with (a) neutron-hole ($\nu h_{11/2}^{-2}$) and (b) proton ($\pi h_{11/2}^2$) configurations. (c) Summary of observed crossing frequencies between ground-state band and $S$ bands based on proton ($\pi$) and neutron ($\nu$) configurations for Ba isotops. The frequencies have been determined from net aligned angular momenta plots. Data extracted from Refs. [50, 96].

Figure 10

(a) Comparison between experimental and calculated total aligned angular momenta $I_x$ as a function of the rotational frequency $\hslash \omega$, employing GCN50:82, SN100PN, SNV, PQM130, and Realstic SM calculations for ${}^{134}\mathrm{Ba}$. Only a partial comparison with SN100PN and SNV is displayed since both interactions predict the $J^{\pi }=8_1^{+}$ state above the $J^{\pi }={10}_1^{+}$ state. [(b) and (c)] Calculated reduced quadrupole transition strengths for yrast $B\left(E2\right)$ values employing the GCN50:82 and SN100PN interactions. Experimental values are visualized as black filled dots, taken from Refs. [45, 48]. (b) The first calculations use the complete $gdsh$ valence space; (c) the second prohibit more than one proton in the $\pi h_{11/2}$ orbital.

Figure 11

(a) $E2$ map: Calculated excitation energy against spin of positive- and negative-parity states of ${}^{133}\mathrm{Ba}$ obtained by the SNV calculation. The widths indicate the $E2$ transition probabilities. Decomposition of the total angular momentum $I_{\pi }\otimes I_{\nu }$ in their proton and neutron components for $J^{\pi }=19/2_1^{+}$ and $J^{\pi }=19/2_1^{-}$ states in [(b) and (c)] ${}^{133}\mathrm{Ba}$ and [(e) and (f)] ${}^{131}\mathrm{Xe}$, employing the GCN50:82 (filled blue boxes) and the SN100PN interaction (empty red boxes). $J^{\pi }=19/2_1^{+}$ states arise from couplings of a $h_{11/2}^{-1}$ neutron-hole to the $J^{\pi }=5^{-}$ states in (d) ${}^{134}\mathrm{Ba}$ and (g) ${}^{132}\mathrm{Xe}$.