Millisecond $23/2^{+}$ isomers in the $N=79$ isotones ${}^{133}\mathrm{Xe}$ and ${}^{135}\mathrm{Ba}$

Detailed information on isomeric states in $A\approx 135$ nuclei is exploited to benchmark shell-model calculations in the region northwest of doubly magic nucleus ${}^{132}\mathrm{Sn}$. The $N=79$ isotones ${}^{133}\mathrm{Xe}$ and ${}^{135}\mathrm{Ba}$ are studied after multinucleon transfer in the ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ 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 a pulsed-beam experiment at the FN tandem accelerator of the University of Cologne, Germany utilizing a ${}^9\mathrm{Be}+{}^{130}\mathrm{Te}$ fusion-evaporation reaction at a beam energy of 40 MeV. Isomeric states are identified via delayed $\gamma$-ray spectroscopy. Hitherto tentative excitation energy, spin, and parity assignments of the 2107-keV $J^{\pi }=23/2^{+}$ isomer in ${}^{133}\mathrm{Xe}$ are confirmed and a half-life of $T_{1/2}=8.64\left(13\right)$ ms is measured. The 2388-keV state in ${}^{135}\mathrm{Ba}$ is identified as a $J^{\pi }=23/2^{+}$ isomer with a half-life of 1.06(4) ms. The new results show a smooth onset of isomeric $J^{\pi }=23/2^{+}$ states along the $N=79$ isotones and close a gap in the high-spin systematics towards the recently investigated $J^{\pi }=23/2^{+}$ isomer in ${}^{139}\mathrm{Nd}$. The resulting systematics of $M2$ reduced transition probabilities is discussed within the framework of the nuclear shell model. Latest large-scale shell-model calculations employing the SN100PN, GCN50:82, SN100-KTH, and a realistic effective interaction reproduce the experimental findings generally well and give insight into the structure of the isomers.

Figure 1

Evolution of excited states along the $N=79$ chain. Dashed lines connecting levels of same spin and parity are drawn to guide the eye. The $J^{\pi }=23/2_1^{+}$ states in ${}^{129}\mathrm{Sn}, {}^{131}\mathrm{Te}$, and ${}^{139}\mathrm{Nd}$ are isomers. A candidate for a $J^{\pi }=23/2^{+}$ isomer at $E_x=2107+x$ keV was reported in ${}^{133}\mathrm{Xe}$ [5]. It is expected that a corresponding long-lived state is also present in ${}^{135}\mathrm{Ba}$. Data extracted from the ENSDF database [8] and Refs. [1, 5, 6, 7].

Figure 2

Partial level schemes of (a) ${}^{133}\mathrm{Xe}$ and (b) ${}^{135}\mathrm{Ba}$. The reduced transition strengths of the 231-keV transition in ${}^{133}\mathrm{Xe}$ and the 254-keV transition in ${}^{135}\mathrm{Ba}$ are subject of this paper. Dominating transitions in the HORUS fusion-evaporation experiment are presented with thicker arrows.

Figure 3

(a) Doppler-corrected $\gamma$-ray spectrum gated on ${}^{135}\mathrm{Ba}$ identified with PRISMA in the ${}^{136}\mathrm{Xe}$+${}^{208}\mathrm{Pb}$ experiment. Insets show the zoomed spectrum around the expected transitions at (b) 254-keV and (c) 1184-keV. (d) Projection of the $\gamma -t$ matrix gated on a time window between 80 and 90 ms relative to the reference time at the beginning of the beam flash. (f) Similar data for a gate on a time window between 75 and 80 ms. Delayed transitions below the $J^{\pi }=23/2_1^{+}$ isomers in ${}^{133}\mathrm{Xe}, {}^{135}\mathrm{Ba}$, and below the $J^{\pi }={10}_1^{+}$ isomer in ${}^{132}\mathrm{Xe}$ are marked with symbols and dashed lines to guide the eye. Both insets (e) and (g) present the $\gamma -t$ matrix relative to the reference time. The applied time gates are surrounded by black boxes.

Figure 4

Prompt in-beam $\gamma \gamma$ coincidence spectrum with a gate on the 1253-keV transition in ${}^{133}\mathrm{Xe}$ above the $J^{\pi }=23/2^{+}$ isomer. Coincidences at energies of 465 and 468 keV are visible.

Figure 5

Gates on background-subtracted $\gamma$-time matrices and half-life fits for the gating conditions (${\mathrm{a}}_{1-2}$) 819 keV in ${}^{136}\mathrm{Ba}$ measured in the seconds-pulsing experiment, (${\mathrm{b}}_{1-2}$) 538 keV and (${\mathrm{c}}_{1-2}$) 668 keV in ${}^{132}\mathrm{Xe}$, (${\mathrm{d}}_{1-2}$) 231 keV, (${\mathrm{e}}_{1-2}$) 947 keV, and (${\mathrm{f}}_{1-2}$) 695 keV in ${}^{133}\mathrm{Xe}$, (${\mathrm{g}}_{1-2}$) 254 keV, (${\mathrm{h}}_{1-2}$) 1184 keV, and (${\mathrm{i}}_{1-2}$) 682 keV in ${}^{135}\mathrm{Ba}$ obtained in the milliseconds-pulsing experiment. The corresponding residual, defined as difference between absolute value and fit function, is shown in panels (${\mathrm{a}}_3$), (${\mathrm{b}}_3$), (${\mathrm{c}}_3$), (${\mathrm{d}}_3$), (${\mathrm{e}}_3$), (${\mathrm{f}}_3$), (${\mathrm{g}}_3$), (${\mathrm{h}}_3$), and (${\mathrm{i}}_3$), respectively. Half-lives are determined from exponential fits of the delayed component. The fit is drawn with a solid red line. Random background is determined separately (dashed blue line) and incorporated into the fit model.

Figure 6

(a) Total conversion coefficient for the 231-keV transition in ${}^{133}\mathrm{Xe}$ compared with predicted values from the BrIcc v2.3 database [51]. (b) Similar comparison for the 254-keV transition in ${}^{135}\mathrm{Ba}$. The multipolarity of the 231 and 254-keV transition can be restricted to $M2/E3$ character. $\gamma \gamma$ off-beam angular correlations for (c) the known 1120-609-keV cascade in ${}^{214}\mathrm{Po}$, (d) the 231-948-keV cascade in ${}^{133}\mathrm{Xe}$, and (e) the 254-1184-keV cascade in ${}^{135}\mathrm{Ba}$. Experimental values (black points) are compared to calculated angular-correlation functions $W(J_1,{\delta }_1,J_2,{\delta }_2,J_3,\mathrm{\Theta },\sigma )$ (lines) for three correlation groups.

Figure 7

Comparison of experimental energy spectra of ${}^{133}\mathrm{Xe}$ [left panel, (a)] with the results of shell-model calculations employing the (b) Realistic SM, (c) SN100PN, (d) GCN50:82, and (e) SN100-KTH interaction. Note that the states are separated into columns for the negative- and the positive-parity states.

Figure 8

Comparison of experimental energy spectra of ${}^{135}\mathrm{Ba}$ [left panel, (a)] with the results of shell-model calculations employing the (b) Realistic SM, (c) SN100PN, (d) GCN50:82, and (e) SN100-KTH interactions. The arrangement of the states mirrors the layout in Fig. 7.

Figure 9

Decomposition of the total angular momentum $I=I_{\pi }\otimes I_{\nu }$ into its proton and neutron components for the $J^{\pi }=19/2_1^{-}, 19/2_2^{-}, 21/2_1^{-}$, and $23/2_1^{-}$ states in (a)–(d) ${}^{131}\mathrm{Te}$, (e)–(h) ${}^{133}\mathrm{Xe}$, and (i)–(l) ${}^{135}\mathrm{Ba}$ calculated with the GCN50:82 interaction. Strongest components are labeled with corresponding percentages.

Figure 10

Decomposition of the $J^{\pi }=19/2^{-}$ and $23/2^{+}$ states of (a),(b) ${}^{131}\mathrm{Te}$, (c),(d) ${}^{133}\mathrm{Xe}$, and (e),(f) ${}^{135}\mathrm{Ba}$ into their proton and neutron configurations computed by the GCN50:82 interaction. Strongest components are labeled with corresponding percentages.