High-$j$ neutron excitations outside ${}^{136}\mathrm{Xe}$

The $\nu 0h_{9/2}$ and $\nu 0i_{13/2}$ strength at ${}^{137}\mathrm{Xe}$, a single neutron outside the $N=82$ shell closure, has been determined using the ${}^{136}\mathrm{Xe}(\alpha ,{}^3\mathrm{He}){}^{137}\mathrm{Xe}$ reaction carried out at 100 MeV. We confirm the recent observation of the second $13/2^{+}$ state and reassess previous data on the $9/2^{-}$ states, obtaining spectroscopic factors. These new data provide additional constraints on predictions of the same single-neutron excitations at ${}^{133}\mathrm{Sn}$.

Figure 1

Outgoing ${}^3\mathrm{He}$ spectra following the ($\alpha ,{}^3\mathrm{He}$) reaction on isotopes of ${}^{144}\mathrm{Sm}$ (a) and ${}^{136}\mathrm{Xe}$ (b) from $E_{\alpha }=100$ MeV and ${\theta }_{\mathrm{lab}}=6^{\circ }$. The $9/2^{-}$ ($\ell =5$) states are shaded red and $13/2^{+}$ states ($\ell =6$) in blue. The 3440-keV state (hatched) is tentatively assigned as a third $13/2^{+}$ state.

Figure 2

Angular distributions for states populated in the ${}^{136}\mathrm{Xe}(\alpha ,{}^3\mathrm{He}){}^{137}\mathrm{Xe}$ reaction at 100 MeV. Panel (a) shows the ground-state $\ell =3$ transition (circles) and the 3440-keV state with $\ell =5$ or $\ell =6$ transfer ($\times 10$, diamonds) and (b) the known $9/2^{-}$ (squares) and $13/2^{+}$ ($\times 5$, triangles) states. The curves are DWBA calculations fitted to the data for the respective $\ell$ transfers.

Figure 3

The excitation energies of the $9/2^{-}$ (a) and $13/2^{+}$ (b) states at $N=83$. The solid symbols are states for which spectroscopic factors from the ($\alpha ,{}^3\mathrm{He}$) reaction are available. A third tentatively assigned $13/2^{+}$ state in ${}^{137}\mathrm{Xe}$ is also shown. The $0h_{9/2}$ and $0i_{13/2}$ centroids, ${\epsilon }_{h_{9/2}}$ and ${\epsilon }_{i_{13/2}}$, are also shown as black dots.

Figure 4

Binding energies of the neutron $0h_{9/2}$ and $0i_{13/2}$ excitations, corresponding to the centroids in Fig. 3, as a function of proton number.

Figure 5

(a) The differences in the centroids of the $0i_{13/2}$ and $0h_{9/2}$ single-neutron strengths (where data for Ba, Ce, Nd, and Sm are from Ref. [1]) are shown as the black squares connected by a solid line. The dashed line is the energy difference between the $13/2_1^{+}$ and $9/2_1^{-}$ states for the $N=83$ isotones between Te and Sm [37]. In Panel (b) the black squares connected by the solid line are the experimental differences as in (a). The shaded and hatched areas represent calculations based on the tensor interaction [9], anchored to estimates of the $0i_{13/2}$ single-particle energy in ${}^{133}\mathrm{Sn}$, based on two different predictions. The shaded region is anchored to the gray circle at $Z=50$, which is based on the average value of ${\epsilon }_{i_{13/2}}$ from Urban et al. [38] and Korgul et al. [39], 2.682 MeV. The location of the ${\epsilon }_{h_{9/2}}$ is taken as 1.561 MeV, the location of the observed $9/2_1^{-}$ state [37]. The hatched area represents a similar calculation but anchored to the gray square at $Z=50$ which uses the estimate of ${\epsilon }_{i_{13/2}}=2.366$ MeV of Reviol et al. [15]. The width of the shaded region reflects the uncertainties in the proton occupancies [19, 36].

Figure 6

The mixing matrix elements. The error bars reflect the uncertainties in the derived values.

Figure 7

The excitation energy of the core $2^{+}$ state and the perturbed ($E$) and unperturbed ($E^{\prime }$) $9/2^{-}$ excitations; $E_{9/2}^{\prime }\left(1\right)\equiv {\epsilon }_{h_{9/2}}$.

Figure 8

(a) The measured excitation energy ($E$) of the $13/2^{+}$ states in $N=83$ nuclei from $54<Z<62$, the calculated unperturbed energies ($E^{\prime }$), and the core ($N=82$) $3^{-}$ energy. Panel (b) shows information on the core $2^{+}$ states. Note, $E_{13/2}^{\prime }\left(1\right)\equiv {\epsilon }_{i_{13/2}}$.

Figure 9

A schematic of the two-level mixing model used in the analysis in Sec. 4b. This is shown for $13/2^{+}$ states—the same definitions apply for the $9/2^{-}$ states. The energies, spectroscopic factors, and weak-coupling interaction energy are defined in the accompanying text.