One-neutron transfer study of ${}^{137}\mathrm{Xe}$ and systematics of $13/2_1^{+}$ and $13/2_2^{+}$ levels in $N=83$ nuclei

Excited states in ${}^{137}\mathrm{Xe}$ have been studied by using the near-barrier single-neutron transfer reactions ${}^{13}\mathrm{C}({}^{136}\mathrm{Xe},{}^{12}\mathrm{C}\gamma ){}^{137}\mathrm{Xe}$ and ${}^9\mathrm{Be}({}^{136}\mathrm{Xe},{}^8\mathrm{Be}\gamma ){}^{137}\mathrm{Xe}$ in inverse kinematics. Particle-$\gamma$ and particle-$\gamma \gamma$ coincidence measurements have been performed with the Phoswich Wall and Digital Gammasphere detector arrays. Evidence is found for a $13/2_2^{+}$ level $\left(E=3137\mathrm{keV}\right)$ and for additional high-lying $3/2^{-}$ and $5/2^{-}$ states. The results are discussed in the framework of realistic shell-model calculations. These calculations are also extended to the $13/2_1^{+}$ and $13/2_2^{+}$ levels in the $N=83$ isotonic chain. They indicate that there is a need for a value of the neutron $0i_{13/2}$ single-particle energy $\left(E_{\mathrm{SPE}}=2366\mathrm{keV}\right)$ lower than the one proposed in the literature. It is also demonstrated that the population patterns of the $j=\ell \pm 1/2$ single-particle states in ${}^{137}\mathrm{Xe}$ are different for the two targets used in these measurements and the implications of this effect are addressed.

Figure 1

An $(A,C)$ particle map for the data taken with the ${}^9\mathrm{Be}$ target. The two-dimensional gate selects ${}^8\mathrm{Be}\to 2\alpha$ events. The other two particle groups represent beryllium and $\alpha \text{−}\mathrm{particle}/{}^5\mathrm{He}$ events associated with projectile Coulomb excitation and incomplete fusion, respectively. The map is for pixel 152 of the Phoswich Wall. The color scale shown on the right provides the range of $z$-axis values in this example.

Figure 2

Representative $\gamma$-ray spectra for the 560-MeV ${}^{136}\mathrm{Xe}+{}^{13}\mathrm{C}$ reaction. (a) Total projection of a $\gamma \text{−}\gamma$ coincidence matrix gated with carbon ions in the $A\text{−}C$ map (see text). Transitions are labeled by their energies in keV. For ${}^{135}\mathrm{Xe}$, the open and filled symbols indicate firm and tentative assignments, respectively. (b) Coincidence spectrum for ${}^{137}\mathrm{Xe}$ obtained by gating on the 1220-keV transition. Note the change in scale at a $\gamma$-ray energy of 1000 keV. Transitions with labels given in parentheses are associated with an interfering 1218-keV line (see text). (c) Similar to (b) but with gating transitions of 1384 (main panel) and 533 keV (inset). The position of the gate is indicated by the letter G.

Figure 3

Representative $\gamma$-ray spectra for the 560-MeV ${}^{136}\mathrm{Xe}+{}^9\mathrm{Be}$ reaction. (a) Total projection of a $\gamma \text{−}\gamma$ matrix gated on $2a$ events (see text). Note that the 1303-keV peak is composed of a ${}^{137}\mathrm{Xe}$ ground-state transition and ${}^{139}\mathrm{Ba}$ lines with $1306\mathrm{keV}\le E_{\gamma }\le 1319\mathrm{keV}$. (b) Coincidence spectrum for ${}^{137}\mathrm{Xe}$ obtained by gating on the 385-keV transition. The inset provides the extension of the spectrum toward higher energies. The letter G indicates the position of the gate. The $\gamma$ rays labeled by a plus sign are newly observed. (c) Similar to (b) but for the 1963- and 2349-keV gating transitions. The latter gated spectrum is shown in the inset.

Figure 4

The level scheme for ${}^{137}\mathrm{Xe}$ obtained in the 560-MeV ${}^{136}\mathrm{Xe}+{}^{13}\mathrm{C}$ (a) and ${}^{136}\mathrm{Xe}+{}^9\mathrm{Be}$ (b) reactions with the feeding of the $9/2^{-}$ state shown separately (c). The widths of the arrows are proportional to the measured $\gamma$-ray intensities. The energies are in keV. The assignments given in parentheses are tentative. The transitions marked in red are new to this work.

Figure 5

Representative $\gamma$-ray angular distributions, with respect to the spin direction, for transitions in ${}^{137}\mathrm{Xe}({}^{136}\mathrm{Xe}+{}^{13}\mathrm{C}\mathrm{data})$. Panels (a)–(c) are for the 533-, 400-, and 1384-keV transitions, respectively. The former two cases are established stretched dipole $\left(E1\right)$ and quadrupole $\left(E2\right)$ transitions, respectively.

Figure 6

Decay intensity versus energy for levels in ${}^{137}\mathrm{Xe}$ obtained in the (a) carbon and (b) beryllium measurements. The sequences of levels based on the $3/2_1^{-}$ and $1/2^{-}$ states, the $5/2_1^{-}$ level, the $11/2_1^{-}$ yrast, and the $13/2_1^{+}$ unique-parity states are represented by circles, squares, diamonds, and triangles, respectively. The data points are labeled by the corresponding spin-parity assignments [except the levels in panel (b) with $E=2090,2310$, and 2949 keV]. The most strongly populated states in a sequence are connected by straight lines.

Figure 7

The $13/2_1^{+}$ and $13/2_2^{+}$ systematics from Refs. [4, 14] and the present data (red circle), and results from two sets of calculations described in Ref. [6] and in the text (red crosses and asterisks), and presented in the text as (a) calc1 and (b) calc2, respectively. The filled and open circles distinguish between firmly established and candidate $13/2_2^{+}$ levels, respectively. See the text for details.

Figure 8

A combined plot similar to Fig. 7. (a) The $\nu 0i_{13/2}$ effective single-particle energies, obtained from the calc2 calculations, are shown together with the $3^{-}$ energy levels in the corresponding $N=82$ isotopes and a quantity reflecting excitations involving the coupling of an $i_{13/2}$ neutron with the yrast $2^{+}$ and $4^{+}$ states in the same even-mass nuclei (see text). (b) Shown are the yrast $2^{+}$ and $4^{+}$ energy levels as considered in the top panel. The experimental data are reported in Refs. [4, 14].