High-spin structure in the transitional nucleus ${}^{131}\mathrm{Xe}$: Competitive neutron and proton alignment in the vicinity of the $N=82$ shell closure

The transitional nucleus ${}^{131}\mathrm{Xe}$ is investigated after multinucleon transfer in the ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ and ${}^{136}\mathrm{Xe}+{}^{238}\mathrm{U}$ reactions employing the high-resolution Advanced $\gamma$-Tracking Array (AGATA) coupled to the magnetic spectrometer PRISMA at the Laboratori Nazionali di Legnaro, Italy, and as an elusive reaction product in the fusion-evaporation reaction ${}^{124}\mathrm{Sn}({}^{11}\mathrm{B},p3n){}^{131}\mathrm{Xe}$ employing the High-efficiency Observatory for $\gamma$-Ray Unique Spectroscopy (HORUS) $\gamma$-ray array coupled to a double-sided silicon strip detector at the University of Cologne, Germany. The level scheme of ${}^{131}\mathrm{Xe}$ is extended to 5 MeV. A pronounced backbending is observed at $\hslash \omega \approx 0.4\mathrm{MeV}$ along the negative-parity one-quasiparticle $\nu h_{11/2}(\alpha =-1/2)$ band. The results are compared to the high-spin systematics of the $Z=54$ isotopes and the $N=77$ isotones. Large-scale shell-model calculations employing the PQM130, SN100PN, GCN50:82, SN100-KTH, and a realistic effective interaction reproduce the experimental findings and provide guidance to elucidate the structure of the high-spin states. Further calculations in ${}^{129-132}\mathrm{Xe}$ provide insight into the changing nuclear structure along the Xe chain towards the $N=82$ shell closure. Proton occupancy in the $\pi 0h_{11/2}$ orbital is found to be decisive for the description of the observed backbending phenomenon.

Figure 1

Total aligned angular momentum against the rotational frequency $\hslash \omega$ for the yrast bands in the Xe isotopes with masses ranging from $A=117$ to $A=132$. For definitions see text. Going toward the $N=82$ shell closure, backbending occurs between the $J^{\pi }={10}_1^{+}$ and ${12}_1^{+}$ states in ${}^{126}\mathrm{Xe}$ and between the $J^{\pi }=8_1^{+}$ and $J^{\pi }={10}_1^{+}$ states in ${}^{128,130}\mathrm{Xe}$. In ${}^{132}\mathrm{Xe}$ the position of the $J^{\pi }=8_1^{+}$ state is not known to date. Data extracted from Ref. [32].

Figure 2

Level scheme assigned to ${}^{131}\mathrm{Xe}$ in the present study. Transition and excitation energies are given in keV. Intensities of the cascades above the 164-keV isomer are deduced from the HORUS experiment and normalized to the 642-keV transition. New $\gamma$-ray transitions are marked in red with asterisks. See text for details.

Figure 3

(a) Doppler-corrected $\gamma$-ray spectrum gated on ${}^{131}\mathrm{Xe}$ identified with PRISMA in the ${}^{136}\mathrm{Xe}+{}^{208}\mathrm{Pb}$ experiment. Random background is subtracted with a gate on the prompt peak in the spectrum of time differences between AGATA and PRISMA. (c) Similar data from the ${}^{136}\mathrm{Xe}+{}^{238}\mathrm{U}$ experiment. Both insets (b) and (d) represent the mass spectra of the Xe isotopes obtained with PRISMA. The applied mass gates for ${}^{131}\mathrm{Xe}$ are marked black. (e) Projection of the $\gamma \gamma$ matrix gated on evaporated protons [cf. inset (f)] obtained in the HORUS fusion-evaporation reaction ${}^{11}\mathrm{B}+{}^{124}\mathrm{Sn}$. Remaining contaminant transitions are marked with symbols and dominant transitions from ${}^{131}\mathrm{Xe}$ are marked with dashed lines to guide the eye.

Figure 4

Prompt HORUS $\gamma \gamma$-double and $\gamma \gamma \gamma$-triple coincidence-spectra with gates on (a) 642, (b) 810, (c) 901, (d) 662, (e) 634, (f) 1131, and (g) 810 and 1131 keV. Thin gray lines mark peak energies identified in both MNT experiments (see Table 1). Coincidences are labeled by filled arrow heads.

Figure 5

$\gamma \gamma$ angular correlations. The experimental intensities (data points) are compared to calculated angular-correlation functions (lines). (a) Fit of the 417–644-keV cascade in ${}^{130}\mathrm{Cs}$, (b) of the 810–642-keV, (c) of the 901–810-keV, and (d) of the 662–901-keV cascade in ${}^{131}\mathrm{Xe}$. See text for details.

Figure 6

Evolution of excited states in the negative-parity band along (a) the odd-mass $N=77$ isotones from $Z=50$ to $Z=64$ [72, 73, 74, 75, 76, 77] and along (b) the odd-mass $Z=54$ isotopes from $N=69$ to $N=77$ [16, 43, 78]. Newly discovered states in ${}^{131}\mathrm{Xe}$ are marked with thick lines. (c) Net aligned angular momenta $i_x\left(\hslash \right)$ of favored negative-parity bands in odd-mass ${}^{123-131}\mathrm{Xe}$ isotopes as a function of the rotational frequency $\hslash \omega$.

Figure 7

Comparison of experimental energy spectra with the results of shell-model calculations for ${}^{131}\mathrm{Xe}$. (a) Experimental energy spectrum. The results obtained with the different interactions are separated in different columns: (b) PQM130, (c) SN100PN, (d) GCN50:82, (e) realistic SM, and (f) SN100-KTH. For clarity, the states are arranged into two columns for the negative- and the positive-parity states.

Figure 8

Energy differences between experimental and calculated excitation energies with different shell-model interactions plotted against the spin of the state.

Figure 9

Average neutron (top row) and proton (bottom row) occupation numbers in the proton and neutron $h_{11/2}$ orbitals in ${}^{131}\mathrm{Xe}$, calculated with the (a), (b) SN100PN and (c), (d) GCN50:82 interaction. (e), (f) Similar results for ${}^{129}\mathrm{Xe}$ calculated with the SN100PN interaction.

Figure 10

Decomposition of selected states of ${}^{131}\mathrm{Xe}$ into their proton and neutron configurations computed by (${\mathrm{a}}_1$)–(${\mathrm{f}}_1$) the SN100PN and (${\mathrm{a}}_2$)–(${\mathrm{f}}_2$) the GCN50:82 interaction. The three largest percentages are written inside the squares. Percentages below 2% are not visualized.

Figure 11

Decomposition of selected states of ${}^{129}\mathrm{Xe}$ into their proton and neutron configuration computed by the SN100PN interaction.

Figure 12

(a) Comparison between experimental and calculated total aligned angular momenta $I_x$ as a function of the rotational frequency $\hslash \omega$, employing the SN100PN, GCN50:82, SN100-KTH, and realistic SM calculations for ${}^{131}\mathrm{Xe}$. (b) Comparison between experimental and calculated total aligned angular momenta $I_x$ as a function of the rotational frequency $\hslash \omega$, employing the SN100PN and GCN50:82 with a truncation of only one allowed proton in the $\pi h_{11/2}$ orbital. (c) Similar comparison for ${}^{129}\mathrm{Xe}$ employing the SN100PN calculation: (i) untruncated and (ii) truncated with only one proton allowed in the $\pi h_{11/2}$ orbital. Experimental data for ${}^{129}\mathrm{Xe}$ are taken from Ref. [16].

Figure 13

(a) Comparison between experimental and calculated total aligned angular momenta $I_x$ as a function of the rotational frequency $\hslash \omega$, employing the SN100PN calculation for (a) ${}^{130}\mathrm{Xe}$ and (b) ${}^{132}\mathrm{Xe}$. The SN100PN interaction is employed in two different calculations: (i) untruncated and (ii) truncated with only one proton allowed in the $\pi h_{11/2}$ orbital. Experimental data taken from Refs. [39, 95].