Isomers and high-spin structures in the $N=81$ isotones ${}^{135}\mathrm{Xe}$ and ${}^{137}\mathrm{Ba}$

The high-spin structures and isomers of the $N=81$ isotones ${}^{135}\mathrm{Xe}$ and ${}^{137}\mathrm{Ba}$ are investigated after multinucleon-transfer (MNT) and fusion-evaporation reactions. Both nuclei are populated (i) in ${}^{136}\mathrm{Xe}+{}^{238}\mathrm{U}$ and (ii) ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ MNT reactions employing the high-resolution Advanced Gamma Tracking Array (AGATA) coupled to the magnetic spectrometer PRISMA, (iii) in the ${}^{136}\mathrm{Xe}+{}^{198}\mathrm{Pt}$ MNT reaction employing the $\gamma$-ray array GAMMASPHERE in combination with the gas-detector array CHICO, and (iv) via a ${}^{11}\mathrm{B}+{}^{130}\mathrm{Te}$ fusion-evaporation reaction with the HORUS $\gamma$-ray array at the University of Cologne. The high-spin level schemesof ${}^{135}\mathrm{Xe}$ and ${}^{137}\mathrm{Ba}$ are considerably extended to higher energies. The 2058-keV $(19/2^{-})$ state in ${}^{135}\mathrm{Xe}$ is identified as an isomer, closing a gap in the systematics along the $N=81$ isotones. Its half-life is measured to be 9.0(9) ns, corresponding to a reduced transition probability of $B(E2,19/2^{-}\to 15/2^{-})=0.52\left(6\right)$ W.u. The experimentally deduced reduced transition probabilities of the isomeric states are compared to shell-model predictions. Latest shell-model calculations reproduce the experimental findings generally well and provide guidance to the interpretation of the new levels.

Figure 1

Comparison of high-spin states and isomer half-lives along the $N=81$ isotones; data taken from Refs. [18, 26, 27, 28, 29, 30, 31, 32, 33, 34]. A sequence of $J^{\pi }=19/2^{-}$ isomers is found in the isotones ranging from ${}^{133}\mathrm{Te}$ to ${}^{139}\mathrm{Ce}$. Tentative assignments are written in parentheses.

Figure 2

Level scheme of ${}^{135}\mathrm{Xe}$ with the newly observed 214-, 243-, 250-, 493-, and 659-keV $\gamma$-ray transitions marked with an asterisk. Spins and parities of the states below 2.3 MeV are taken from Refs. [13, 15, 18]. Intensities are extracted from the ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ experiment and normalized to the 1132-keV $\gamma$-ray transition. See text for details.

Figure 3

Doppler-corrected ${}^{135}\mathrm{Xe} \gamma$-ray spectra from the ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ experiment: (a) Gate on low TKEL, (b) gate on intermediate TKEL, and (c) gate on large TKEL corresponding to higher excitation energies after the deep-inelastic MNT reaction. The applied gates on the TKEL distributions are shown in the three insets, respectively. The main peaks of the TKEL distributions are shifted to negative values due to large energy losses in the thick Pb targets. A gate on the prompt time peak between AGATA and PRISMA is applied to all spectra.

Figure 4

GAMMASPHERE prompt $\gamma \gamma$-coincidence spectra with gates on (a) 298, (b) 814, (c) 243, (d) 250, (e) 659, and (f) 214 keV. Coincidences are labeled by arrow heads. Vertical lines corresponding to peak energies observed in ${}^{135}\mathrm{Xe}$ are drawn to guide the eye.

Figure 5

(a) GAMMASPHERE delayed out-of-beam $\gamma$-ray spectrum gated by the delayed 1222-keV transition in ${}^{135}\mathrm{Xe}$. (b) Same spectrum as in (a), gated on the 310-keV transition. (c) Linear GAMMASPHERE time spectrum gated by the 310-keV transition (black data points) with an exponential decay-curve fit (red solid line). A background prompt time spectrum is plotted with solid steps. (d) Same as (c), but with a logarithmic scale. The fitted half-life is $T_{1/2}=9.0\left(9\right)$ ns.

Figure 6

Level scheme assigned to ${}^{137}\mathrm{Ba}$ in the present work. Transition and excitation energies are given in keV. The decay of the $11/2^{-}$ isomer is not observed due to its long half-life. $\gamma$-ray intensities of transitions above the 2349.9-keV isomer are deduced from the ${}^{11}\mathrm{B}+{}^{130}\mathrm{Te}$ experiment and normalized to the 274.5-keV transition. Isomeric states are marked with thick lines and labeled with the corresponding half-lives. Spins and parities of the states below 2.35 MeV follow the systematics of the $N=81$ isotonic chain. New $\gamma$-ray transitions are marked with an asterisk. See text for details.

Figure 7

(a) GAMMASPHERE delayed out-of-beam $\gamma$-ray spectrum gated by the delayed 120-keV transition in ${}^{137}\mathrm{Ba}$. Contaminants from ${}^{134}\mathrm{Ba}$ are labeled in the spectrum. Contaminants are marked with $c$; $\text{Ge}(n,n^{\prime }\gamma )$ edges with $n$. (b) Same spectrum as in (a), gated on the 1568-keV transition; no major contaminants are visible. (c) Time spectrum gated by the 1568-keV transition (data points) from which the decay curve (solid line) is obtained with a half-life of $T_{1/2}=589\left(20\right)$ ns. (d) GAMMASPHERE delayed-prompt $\gamma \gamma$-coincidence spectrum with a gate on the delayed 1568-keV transition (partial level scheme shown in the inset). The spectrum contains prompt transitions feeding the 2349.9-keV isomer.

Figure 8

(a) ${}^{137}\mathrm{Ba}$ ejectile Doppler-corrected $\gamma$-ray spectrum, corrected for contamination of the isobar ${}^{137}\mathrm{Cs}$ by subtracting the corresponding normalized mass-gated $\gamma$-ray spectra. Random background is subtracted with a gate on the prompt peak in the spectrum of time differences between AGATA and PRISMA. Only the 275-keV $\gamma$ ray was previously known. (b) Mass spectrum of the Ba isotopes obtained with PRISMA. The applied mass gate on ${}^{137}\mathrm{Ba}$ is marked in black.

Figure 9

Prompt HORUS $\gamma \gamma$ double- and $\gamma \gamma \gamma$ triple-coincidence spectra with gates on (a) 1568, (b) 1195, (c) 1195 & 296, (d) 275, (e) 275 & 289 keV. Coincidences are labeled by filled arrow heads. Thin grey lines corresponding to peak energies observed in Figs. 8 and 7 are drawn to guide the eye.

Figure 10

Comparison of experimental energy spectra with the results of shell-model calculations for (a) ${}^{135}\mathrm{Xe}$ and (b) ${}^{137}\mathrm{Ba}$. Experimental energy spectra are shown in the left panels. The arrangement of experimental levels for ${}^{137}\mathrm{Ba}$ mirrors the layout of the level scheme shown in Fig. 6. The middle panels show the results for both the first and the second excited states obtained with the PQM130 interaction [3]. The right panels show the results of the shell-model calculations within the SN100PN interaction. Note that the states are separated into columns for the negative- and the positive-parity states. The first columns contain yrast states; second columns with yrare states are added for clarity.

Figure 11

Decomposition of the total angular momentum of the $15/2_1^{-}, 19/2_1^{-}$, and $19/2_2^{-}$ states in ${}^{133}\mathrm{Te}, {}^{135}\mathrm{Xe}$, and ${}^{137}\mathrm{Ba}$ into their neutron ($I_{\nu }$) and proton ($I_{\pi }$) spin components in the SN100PN calculation. The area of the boxes corresponds to the percentage of the particular $I_{\nu }\otimes I_{\pi }$ configuration. Percentages above $1\%$ are shown; percentages of the largest component are also given in numbers for scale.