Identification of high-spin proton configurations in ${}^{136}\mathrm{Ba}$ and ${}^{137}\mathrm{Ba}$

The high-spin structures of ${}^{136}\mathrm{Ba}$ and ${}^{137}\mathrm{Ba}$ are investigated after multinucleon-transfer (MNT) and fusion-evaporation reactions. ${}^{136}\mathrm{Ba}$ is populated in a ${}^{136}\mathrm{Xe}+{}^{238}\mathrm{U}$ MNT reaction employing the high-resolution Advanced GAmma Tracking Array (AGATA) coupled to the magnetic spectrometer PRISMA at the Laboratori Nazionali di Legnaro, Italy, and in two ${}^9\mathrm{Be}+{}^{130}\mathrm{Te}$ fusion-evaporation reactions using the High-efficiency Observatory for $\gamma$-Ray Unique Spectroscopy (HORUS) at the FN tandem accelerator of the University of Cologne, Germany. Furthermore, both isotopes are populated in an elusive reaction channel in the ${}^{11}\mathrm{B}+{}^{130}\mathrm{Te}$ fusion-evaporation reaction utilizing the HORUS $\gamma$-ray array. The level scheme above the $J^{\pi }={10}^{+}$ isomer in ${}^{136}\mathrm{Ba}$ is revised and extended up to an excitation energy of approximately 5.5 MeV. From the results of angular-correlation measurements, the $E_x=3707$- and $E_x=4920$-keV states are identified as the bandheads of positive- and negative-parity cascades. While the high-spin regimes of both ${}^{132}\mathrm{Te}$ and ${}^{134}\mathrm{Xe}$ are characterized by high-energy ${12}^{+}\to {10}^{+}$ transitions, the ${}^{136}\mathrm{Ba}E2$ ground-state band is interrupted by negative-parity states only a few hundred keV above the $J^{\pi }={10}^{+}$ isomer. Furthermore, spins are established for several hitherto unassigned high-spin states in ${}^{137}\mathrm{Ba}$. The new results close a gap along the high-spin structure of $N<82$ Ba isotopes. Experimental results are compared to large-scale shell-model calculations employing the GCN50:82, Realistic SM, PQM130, and SN100PN interactions. The calculations suggest that the bandheads of the positive-parity bands in both isotopes are predominantly of proton character.

Figure 1

Comparison of high-spin states above (a) the $J^{\pi }={10}_1^{+}$ isomers along $N=80$ and (b) above the $J^{\pi }=19/2_1^{-}$ isomers along $N=81$. There is a significant lack of information on spin assignments in ${}^{136}\mathrm{Ba}$ and ${}^{137}\mathrm{Ba}$. Data taken from Refs. [3, 9, 15, 16, 18, 20, 21, 22, 23].

Figure 2

(a) Level scheme assigned to ${}^{136}\mathrm{Ba}$ in the present work. Transitions and excitation energies are given in keV. $\gamma$-ray intensities above the $J^{\pi }={10}^{+}$ isomer are deduced from the ${}^9\mathrm{Be}+{}^{130}\mathrm{Te}$ experiment and normalized to the 349-keV transition. (b) Level scheme assigned to ${}^{137}\mathrm{Ba}$ and normalized to the 275-keV transition. Transitions and excitation energies are taken from the previous work, using the same ${}^{11}\mathrm{B}+{}^{130}\mathrm{Te}$ experiment, presented in Ref. [20]. Tentative assignments are given in brackets and dashed lines. In both isotopes new spin/parity assignments are based on the spin/parity assignments of the isomeric 3357.3-keV state in ${}^{136}\mathrm{Ba}$ given in Ref. [14] and on the spin/parity assignments of the isomeric 2349.9-keV state in ${}^{137}\mathrm{Ba}$ given in Refs. [20, 21]. See text for details.

Figure 3

(a) Doppler-corrected $\gamma$-ray spectrum gated on ${}^{136}\mathrm{Ba}$ identified in PRISMA in the ${}^{136}\mathrm{Xe}+{}^{238}\mathrm{U}$ experiment. $\gamma$-ray energies are given in keV. (b) Mass spectrum of Ba isotopes identified with PRISMA. The applied mass gate on ${}^{136}\mathrm{Ba}$ is marked black. A gate on the prompt time peak between AGATA and PRISMA is applied to reduce random background.

Figure 4

Prompt $\gamma \gamma$ double-coincidence spectra from the first ${}^9\mathrm{Be}+{}^{130}\mathrm{Te}$ experiment (see Sec. 2b) with gates on (a) 349, (b) 848, (c) 328, and (d) 247 keV. Transitions above the $J^{\pi }={10}^{+}$ isomer are marked with asterisks. Coincidences are labeled by filled arrowheads. Contaminant transitions in the spectrum gated on the 328 keV stem from transitions in ${}^{135}\mathrm{Ba}$. $\gamma \gamma \gamma$ triple-coincidence spectra from the second ${}^9\mathrm{Be}+{}^{130}\mathrm{Te}$ experiment (see Sec. 2c) with (e) a double gate on 349 and 510 keV, a sum of double-gated triples coincidence spectra gated on (f) 566 and 510 and 566 and 349 keV, and a similar sum spectra gated on (g) 661 and 510 and 661 and 349 keV. Prompt $\gamma \gamma$ double-coincidence spectra with a gate on (h) 818 and (i) 349 keV from the ${}^{11}\mathrm{B}+{}^{130}\mathrm{Te}$ experiment (see Sec. 2d). The gate on 349 keV is contaminated with transitions from ${}^{137}\mathrm{La}$.

Figure 5

Benchmark angular distribution of (a) the 1052-keV ($19/2^{-}\to 15/2^{-}$) $\gamma$-ray transition and (b) the 391-keV ($21/2^{-}\to 19/2^{-}$) $\gamma$-ray transition, both in ${}^{135}\mathrm{Ba}$. Experimental values (data points) are compared to pure dipole and quadrupole hypotheses (solid lines). (c) Angular distribution of the 349-keV transition, feeding the $J^{\pi }={10}^{+}$ isomer in ${}^{136}\mathrm{Ba}$. Several pure dipole and quadrupole hypotheses (lines) are plotted. (d) Benchmark $\gamma \gamma$ angular correlations for the $5_1^{+}\to 4_1^{+}\to 2_1^{+}$ (727-773-keV) cascade in ${}^{132}\mathrm{Xe}$. Experimental values (data points) are compared to calculated angular-correlation functions $W({\mathrm{\Theta }}_1,{\mathrm{\Theta }}_2,\mathrm{\Phi }$) (lines) for eight correlation groups using the code corleone. Investigation for (e) the 510-349-keV cascade and (f) the 1214-349-keV cascade in ${}^{136}\mathrm{Ba}$. Several spin hypotheses are plotted.

Figure 6

Angular distributions of transitions in ${}^{137}\mathrm{La}$ and ${}^{137}\mathrm{Ba}$. Experimental distribution is obtained in the $\gamma$-ray spectra, gated on disoriented transitions below the isomers. (a) Benchmark angular distribution of the well-known 1172-keV ($23/2^{-}\to 19/2^{-}$) $\gamma$-ray transition in ${}^{137}\mathrm{La}$. The pure quadrupole hypothesis is well reproduced with this approach. Angular distribution of (b) 275- and (c) 1195-keV transition, decaying into the $19/2^{-}$ isomer in ${}^{137}\mathrm{Ba}$. Intensities are extracted from $\gamma \gamma$ coincident spectra with a gate on the $15/2^{-}\to 11/2^{-}$ transition. Several pure dipole and quadrupole hypotheses (lines) are plotted. (d) Benchmark $\gamma \gamma$ angular correlations for the $4_1^{+}\to 2_1^{+}\to 0_1^{+}$ (1048-818-keV) cascade in ${}^{136}\mathrm{Ba}$. Investigation for (e) the 289-275-keV cascade and (f) the 296-1195-keV cascade in ${}^{137}\mathrm{Ba}$. Several spin hypotheses are plotted.

Figure 7

Comparison of experimental energy spectra with the results of shell-model calculations for ${}^{136}\mathrm{Ba}$. Only states above the $J^{\pi }={10}^{+}$ state are displayed. For clarity, the states are separated into columns for positive- and negative-parity states, as well as for yrast and yrare states. (a),(b) Experimental energy spectra, shell-model results obtained with (c) GCN50:82, (d) PQM130, (e) realistic SM and, (f) SN100PN interactions.

Figure 8

Decomposition of the total wave function configuration into its proton and neutron components for several positive- and negative-parity states in (a)–(f) ${}^{136}\mathrm{Ba}$ and (g)–(l) ${}^{134}\mathrm{Xe}$, employing the GCN50:82 (filled blue boxes) and the SN100PN interaction (empty red boxes). Strongest components in the GCN50:82 interaction are labeled with corresponding percentages. The other configurations of both calculations are drawn with areas proportional to their percentages.

Figure 9

Decomposition of the total angular momentum of selected states of (a)–(f) ${}^{136}\mathrm{Ba}$ and (g)–(l) ${}^{134}\mathrm{Xe}$, using the GCN50:82 interaction (filled blue boxes) and the SN100PN interaction (empty red boxes) into their proton and neutron spins.

Figure 10

Comparison of experimental energy spectra with the results of shell-model calculations for ${}^{137}\mathrm{Ba}$. Only states above the $J^{\pi }=19/2^{-}$ state are displayed. For clarity, the states are separated into columns for positive- and negative-parity states, as well as for yrast and yrare excited states. (a),(b) Experimental energy spectra, shell-model results obtained with (c) GCN50:82, (d) PQM130, (e) realistic SM, and (f) SN100PN interactions.

Figure 11

Decomposition of the total angular momentum of selected states of ${}^{137}\mathrm{Ba}$, using the GCN50:82 interaction (filled blue boxes) and the SN100PN interaction (empty red boxes) into their proton and neutron spins $I_{\pi }\otimes I_{\nu }$.