Spectroscopy of states in ${}^{136}\mathrm{Ba}$ using the ${}^{138}\mathrm{Ba}(p,t)$ reaction

Background: The ${}^{136}\mathrm{Ba}$ isotope is the daughter nucleus in ${}^{136}\mathrm{Xe}\beta \beta$ decay. It also lies in a shape transitional region of the nuclear chart, making it a suitable candidate to test a variety of nuclear models.

Purpose: To obtain spectroscopic information on states in ${}^{136}\mathrm{Ba}$, which will allow a better understanding of its low-lying structure. These data may prove useful to constrain future ${}^{136}\mathrm{Xe}\to {}^{136}\mathrm{Ba}$ neutrinoless $\beta \beta$ decay matrix element calculations.

Methods: A ${}^{138}\mathrm{Ba}(p,t)$ reaction was used to populate states in ${}^{136}\mathrm{Ba}$ up to approximately 4.6 MeV in excitation energy. The tritons were detected using a high-resolution Q3D magnetic spectrograph. A distorted wave Born approximation analysis was performed for the measured triton angular distributions.

Results: 102 excited states in ${}^{136}\mathrm{Ba}$ were observed, out of which 52 are reported for the first time. Definite spin-parity assignments are made for 26 newly observed states, while previously ambiguous assignments for ten other states are resolved. Together with other available data, the results are used to determine level densities in ${}^{136}\mathrm{Ba}$. These were compared with theory predictions, obtained using shell model calculations with Hamiltonians previously used for ${}^{136}\mathrm{Xe}$ neutrinoless $\beta \beta$ decay matrix element evaluations.

Conclusions: The shell model predicted level densities agree reasonably well for the two Hamiltonians. However the results for theory and experiment are found to agree only at lower energies, diverging from one another for the higher lying states, with the discrepancy increasing with energy. This is presumably because of lower production cross sections for a majority of the higher-lying predicted states and the experimental limitations in resolving a large number of nearly degenerate states predicted by the theory.

Figure 1

Excitation energy spectrum for ${}^{136}\mathrm{Ba}$, obtained from ${}^{138}\mathrm{Ba}(p,t)$ at ${\theta }_{\mathrm{lab}}={15}^{\circ }$. The red lines indicate new states observed in this work. Since our target was enriched to $99.8\%$, significant contributions from isotopic impurities are not expected. This is observed in the spectra, where the small triton peaks from the dominant ${}^{137}\mathrm{Ba}(p,t)$ contaminant reaction are marked with asterisks. All other peaks correspond to previously known states in ${}^{136}\mathrm{Ba}$.

Figure 2

Experimental ${}^{138}\mathrm{Ba}(p,p)$ angular distribution from this work, compared with various DWBA predictions. For the latter we used global proton optical model parameters recommended by Becchetti and Greenlees (BG) [33], Koning and Delaroche (KD) [34], Varner et al. [35], Menet et al. [36], and Walter and Guss (WG) [37].

Figure 3

Measured ${}^{138}\mathrm{Ba}(p,t)$ angular distribution for the ground state in ${}^{136}\mathrm{Ba}$. The data are compared with normalized DWBA predictions obtained using the proton OMPs by Varner et al. [35] and the triton OMP parameters by Becchetti and Greenlees (BG) [40, 41] and Li et al. [39].

Figure 4

Experimental angular distributions for all observed $0^{+}$ states in ${}^{136}\mathrm{Ba}$. The solid blue lines represent normalized dwuck4 cross sections for $L=0$ transfer. The dashed green line, corresponding to $L=2$ transfer is shown for comparison.

Figure 5

Experimental angular distribution for all the $2^{+}$ states observed in this work compared with normalized $L=2$ DWBA predictions, shown in solid blue lines. States with tentative $2^{+}$ assignments are presented in Sec. 4h.

Figure 6

Experimental angular distribution for all definite $3^{-}$ assignments from this work. The solid blue lines represent normalized DWBA cross sections for $L=3$ transitions.

Figure 7

Angular distributions of states for which we could make a definite $J^{\pi }=4^{+}$ assignment. The blue lines represent the $L=4$ normalized DWBA cross sections. The green and magenta dashed lines are included for comparison.

Figure 8

Experimental angular distributions for all $5^{-}$ states observed in this work. Normalized DWBA cross sections for the $L=5$ transfer is shown in blue.

Figure 9

Experimental angular distribution for the two $6^{+}$ states observed in this work and normalized DWBA curves for $L=6$ transfer.

Figure 10

Experimental angular distribution and normalized $L=7$ DWBA predictions (solid blue line) for the two $7^{-}$ states observed in this work.

Figure 11

Experimental angular distribution for all the $(1,2^{+})$ states observed in this work. The continuous curves are normalized DWBA cross sections.

Figure 12

Experimental angular distributions for states where multiple DWBA predictions agree reasonably well with the experimental data.

Figure 13

Excited states in ${}^{136}\mathrm{Ba}$ for whom the triton angular distributions are nearly isotropic.

Figure 14

Comparison of measured level densities of states in ${}^{136}\mathrm{Ba}$ with shell model predictions.

Figure 15

A similar comparison as Fig. 14, but for higher-lying $1^{-}$ states. Here, we include all the $J=1$ states reported in the literature [59], as they were mostly identified via inelastic photon scattering which has high selectivity in populating $1^{-}$ levels.